HMH Go Math

Go Math Grade 5 Chapter 6 Answer Key Pdf: Download Go Math Grade 5 Answer Key Chapter 6 Add and Subtract Fractions with Unlike Denominators pdf for free. The HMH Go Math Grade 5 Answer Key includes Addition and Subtraction with unlike denominators, Estimate fraction sums and differences, Least Common Denominators, etc. Start studying the Go Math Grade 5 Chapter 6 Solution Key Add and Subtract Fractions with Unlike Denominators to score the highest marks in the exams.

Add and Subtract Fractions with Unlike Denominators Go Math Grade 5 Chapter 6 Answer Key Pdf

The Go Math Grade 5 Answer Key Add and Subtract Fractions with Unlike Denominators pdf covers the material presented in Chapter 6 Review/Test answers. You can expect the answers for homework and exercise problems in our Go Math Answer Key for Grade 5 Chapter 6 Add and Subtract Fractions with Unlike Denominators. Check out the topics covered in this chapter from the below section.

Lesson 1: Investigate • Addition with Unlike Denominators

• Share and Show – Page No. 244
• Investigate • Addition with Unlike Denominators Page No. 245
• Problem Solving – Page No. 246

Lesson 2: Investigate • Subtraction with Unlike Denominators

• Share and Show – Page No. 248
• Investigate • Subtraction with Unlike Denominators Page No. 249
• UNLOCK the Problem – Page No. 250

Lesson 3: Estimate Fraction Sums and Differences

• Share and Show – Page No. 253
• Problem Solving – Page No. 254

Lesson 4: Common Denominators and Equivalent Fractions

• Share and Show – Page No. 256
• Common Denominators and Equivalent Fractions Page No. 257
• UNLOCK the Problem – Page No. 258

Lesson 5: Add and Subtract Fractions

• Share and Show – Page No. 260
• On Your Own – Page No. 261
• Problem Solving – Page No. 262

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Vocabulary – Page No. 263
• Mid-Chapter Checkpoint – Page No. 264

Lesson 6: Add and Subtract Mixed Numbers

• Share and Show – Page No. 266
• Page No. 267
• Problem Solving – Page No. 268

Lesson 7: Subtraction with Renaming

• Share and Show – Page No. 270
• Subtraction with Renaming Page No. 271
• Subtraction with Renaming Page No. 272

Lesson 8: Algebra • Patterns with Fractions

• Share and Show – Page No. 275
• Problem Solving – Page No. 276

Lesson 9: Problem Solving • Practice Addition and Subtraction

• Share and Show – Page No. 279
• On Your Own – Page No. 280

Lesson 10: Algebra • Use Properties of Addition

• Share and Show – Page No. 283
• Problem Solving – Page No. 284

Chapter 6 Review/Test

• Chapter Review/Test – Vocabulary – Page No. 285
• Chapter Review/Test – Page No. 286
• Chapter Review/Test – Page No. 287
• Chapter Review/Test – Page No. 288

Share and Show – Page No. 244

Use fraction strips to find the sum. Write your answer in simplest form.

Question 1.

\(\frac{1}{2}+\frac{3}{8}=\)
\(\frac{□}{□}\)

Answer: \(\frac{7}{8}\)
Explanation:
Step 1:
Place three \(\frac{1}{8}\) fractions strips under the 1 whole strip on your Mathboard. Then place a \(\frac{1}{2}\) fraction strip beside the three \(\frac{1}{8}\) strips.
Step 2:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{1}{2}\) and \(\frac{3}{8}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{1}{2}\) = \(\frac{1}{2}\) × \(\frac{4}{4}\) = \(\frac{4}{8}\)
\(\frac{3}{8}\)
Step 3:
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{4}{8}\) + \(\frac{3}{8}\) = \(\frac{7}{8}\)

Go Math Chapter 6 Add and Subtract Fractions with Unlike Denominators Question 2.

\(\frac{1}{2}+\frac{2}{5}=\)
\(\frac{□}{□}\)

Answer: \(\frac{9}{10}\)
Explanation:
Step 1:
Place two \(\frac{1}{5}\) fractions strips under the 1 whole strip on your Mathboard. Then place a \(\frac{1}{2}\) fraction strip beside the two \(\frac{1}{5}\) strips.
Step 2:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{1}{2}\) and \(\frac{2}{5}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{1}{2}\) = \(\frac{1}{2}\) × \(\frac{5}{5}\) = \(\frac{5}{10}\)
\(\frac{2}{5}\) = \(\frac{2}{5}\) × \(\frac{2}{2}\) = \(\frac{4}{10}\)
Step 3:
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{5}{10}\) + \(\frac{4}{10}\) = \(\frac{9}{10}\)
Thus, \(\frac{1}{2}\) + \(\frac{2}{5}\) = \(\frac{9}{10}\)

Page No. 245

Use fraction strips to find the sum. Write your answer in the simplest form.

Question 3.

\(\frac{3}{8}+\frac{1}{4}=\)
\(\frac{□}{□}\)

Answer: \(\frac{5}{8}\)
Explanation:
Step 1:
Place three \(\frac{1}{8}\) fractions strips under the 1 whole strip on your Mathboard. Then place a \(\frac{1}{4}\) fraction strip beside the three \(\frac{1}{8}\) strips.
Step 2:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{1}{4}\) and \(\frac{3}{8}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{1}{4}\) × \(\frac{2}{2}\) = \(\frac{2}{8}\)
Step 3:
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{2}{8}\) + \(\frac{3}{8}\) = \(\frac{5}{8}\)

Question 4.

\(\frac{3}{4}+\frac{1}{3}=\)
______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{12}\)
Explanation:
Step 1:
Place three \(\frac{3}{4}\) fractions strips under the 1 whole strip on your Mathboard. Then place a \(\frac{1}{3}\) fraction strip beside the three \(\frac{1}{4}\) strips.
Step 2:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{1}{3}\) and \(\frac{3}{4}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{1}{3}\) × \(\frac{4}{4}\) = \(\frac{4}{12}\)
\(\frac{3}{4}\) × \(\frac{3}{3}\) = \(\frac{9}{12}\)
Step 3:
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{4}{12}\) + \(\frac{9}{12}\) = \(\frac{13}{12}\) = 1 \(\frac{1}{12}\)

Use fraction strips to find the sum. Write your answer in simplest form.

Question 5.
\(\frac{2}{5}+\frac{3}{10}=\)
\(\frac{□}{□}\)

Answer: \(\frac{7}{10}\)
Explanation:
Step 1:
Place three \(\frac{1}{10}\) fractions strips under the 1 whole strip on your Mathboard. Then place a two \(\frac{2}{5}\) fraction strip beside the three \(\frac{1}{10}\) strips.
Step 2:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{2}{5}\) and \(\frac{3}{10}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{2}{5}\) • \(\frac{2}{2}\) = \(\frac{4}{10}\)
Step 3:
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{4}{10}\) + \(\frac{3}{10}\) = \(\frac{7}{10}\)

Question 6.
\(\frac{1}{4}+\frac{1}{12}=\)
\(\frac{□}{□}\)

Answer: \(\frac{4}{12}\)
Explanation:
Step 1:
Place \(\frac{1}{12}\) fractions strips under the 1 whole strip on your Mathboard. Then place a \(\frac{1}{4}\) fraction strip beside the \(\frac{1}{12}\) strips.
Step 2:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{1}{12}\) and \(\frac{1}{4}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{1}{4}\) • \(\frac{3}{3}\) = \(\frac{3}{12}\)
\(\frac{1}{12}\)
Step 3:
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{3}{12}\) + \(\frac{1}{12}\) = \(\frac{4}{12}\)

Go Math Standards Practice Book Grade 5 Question 7.
\(\frac{1}{2}+\frac{3}{10}=\)
\(\frac{□}{□}\)

Answer: \(\frac{8}{10}\)
Explanation:
Step 1:
Place three \(\frac{1}{10}\) fractions strips under the 1 whole strip on your Mathboard. Then place a \(\frac{1}{2}\) fraction strip beside the three \(\frac{1}{10}\) strips.
Step 2:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{1}{2}\) and \(\frac{3}{10}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{1}{2}\) • \(\frac{5}{5}\) = \(\frac{5}{10}\)
Step 3:
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{5}{10}\) + \(\frac{3}{10}\) = \(\frac{8}{10}\)

Question 8.
\(\frac{2}{3}+\frac{1}{6}=\)
\(\frac{□}{□}\)

Answer: \(\frac{5}{6}\)
Explanation:
Step 1:
Place two \(\frac{1}{3}\) fractions strips under the 1 whole strip on your Mathboard. Then place a \(\frac{1}{6}\) fraction strip beside the two \(\frac{1}{3}\) strips.
Step 2:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{1}{6}\) and \(\frac{2}{3}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{2}{3}\) = \(\frac{2}{3}\) • \(\frac{2}{2}\) = \(\frac{4}{6}\)
Step 3:
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{4}{6}\) + \(\frac{1}{6}\) = \(\frac{5}{6}\)

Question 9.
\(\frac{5}{8}+\frac{1}{4}=\)
\(\frac{□}{□}\)

Answer: \(\frac{7}{8}\)
Explanation:
Step 1:
Place five \(\frac{1}{8}\) fractions strips under the 1 whole strip on your Mathboard. Then place a \(\frac{1}{4}\) fraction strip beside the five \(\frac{1}{8}\) strips.
Step 2:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{1}{4}\) and \(\frac{5}{8}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{1}{4}\) • \(\frac{2}{2}\) = \(\frac{2}{8}\)
Step 3:
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{2}{8}\) + \(\frac{5}{8}\) = \(\frac{7}{8}\)

Question 10.
\(\frac{1}{2}+\frac{1}{5}=\)
\(\frac{□}{□}\)

Answer: \(\frac{7}{10}\)
Explanation:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{1}{5}\) and \(\frac{1}{2}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{1}{5}\) • \(\frac{2}{2}\) = \(\frac{2}{10}\)
\(\frac{1}{2}\) • \(\frac{5}{5}\) = \(\frac{5}{10}\)
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{2}{10}\) + \(\frac{5}{10}\) = \(\frac{7}{10}\)

Question 11.
\(\frac{3}{4}+\frac{1}{6}=\)
\(\frac{□}{□}\)

Answer: \(\frac{11}{12}\)
Explanation:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{3}{4}\) and \(\frac{1}{6}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{3}{4}\) • \(\frac{3}{3}\) = \(\frac{9}{12}\)
\(\frac{1}{6}\) • \(\frac{2}{2}\)  = \(\frac{2}{12}\)
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{9}{12}\) + \(\frac{2}{12}\) = \(\frac{11}{12}\)

Question 12.
\(\frac{1}{2}+\frac{2}{3}=\)
______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{6}\)
Explanation:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{2}{3}\) and \(\frac{1}{2}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{2}{3}\) • \(\frac{2}{2}\) = \(\frac{4}{6}\)
\(\frac{1}{2}\) • \(\frac{3}{3}\) = \(\frac{3}{6}\)
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{4}{6}\) + \(\frac{3}{6}\) = \(\frac{7}{6}\)
\(\frac{7}{6}\) is greater than 1.
Convert the fraction into the mixed fraction
\(\frac{7}{6}\) = 1 \(\frac{1}{6}\)

Go Math 5th Grade Chapter 6 Review Test Answer Key Question 13.
\(\frac{7}{8}+\frac{1}{4}=\)
______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{8}\)
Explanation:
Find fraction strips, all with the same denominator, that are equivalent to \(\frac{7}{8}\) and \(\frac{1}{4}\). Place the fraction strips under the sum. At the right, draw a picture of the model and write the equivalent fractions.
\(\frac{1}{4}\) • \(\frac{2}{2}\) = \(\frac{2}{8}\)
Add the fractions with like denominators. Use the 1 whole strip to rename the sum in the simplest form.
\(\frac{7}{8}\) + \(\frac{2}{8}\) = \(\frac{9}{8}\)
Convert \(\frac{9}{8}\) into the mixed fraction.
\(\frac{9}{8}\) = 1 \(\frac{1}{8}\)

Question 14.
Explain how using fraction strips with like denominators makes it possible to add fractions with unlike denominators.
Type below:
_________

Answer: The strips for both fractions need to be the same size. Finding denominators is done by trying smaller strips so they can all be the same size.

Problem Solving – Page No. 246

Question 15.
Maya makes trail mix by combining \(\frac{1}{3}\) cup of mixed nuts and \(\frac{1}{4}\) cup of dried fruit. What is the total amount of ingredients in her trail mix?
\(\frac{1}{3}+\frac{1}{4}=\frac{7}{12}\)
Maya uses \(\frac{1}{12}\) cup of ingredients.
Write a new problem using different amounts for each ingredient. Each amount should be a fraction with a denominator of 2, 3, or 4. Then use fraction strips to solve your problem.
Pose a problem                          Solve your problem. Draw a picture of the
fraction strips you use to solve the problem.
Explain why you chose the amounts you did for your problem.
Type below:
_________

Answer:
\(\frac{1}{3}+\frac{1}{4}=\frac{7}{12}\)
Maya uses \(\frac{1}{12}\) cup of ingredients.
Maya makes trail mix by combining \(\frac{1}{2}\) cup of mixed nuts and \(\frac{1}{3}\) cup of dried fruit and \(\frac{1}{4}\) cup of chocolate morsels. What is the total amount of ingredients in her trail mix?
\(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) = x
2 • \(\frac{1}{2}\) +  2 • \(\frac{1}{3}\) +  2 • \(\frac{1}{4}\) =  2 • x
1 + \(\frac{2}{3}\) + \(\frac{1}{2}\) = 2x
Now multiply with 3 on both sides
3 • 1 + 3 • \(\frac{2}{3}\) + 3 • \(\frac{1}{2}\) = 3 • 2x
3 + 2 + \(\frac{3}{2}\) = 6x
6 + 4 + 1 = 12 x
11 = 12x
x = \(\frac{11}{12}\)
\(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) = \(\frac{11}{12}\)

Share and Show – Page No. 248

Use fraction strips to find the difference. Write your answer in simplest form.

Question 1.

\(\frac{7}{10}-\frac{2}{5}=\)
\(\frac{□}{□}\)

Answer:
\(\frac{7}{10}\) – \(\frac{2}{5}\)
\(\frac{7}{10}\) – \(\frac{2}{5}\) • \(\frac{2}{2}\)
\(\frac{7}{10}\) – \(\frac{4}{10}\) = \(\frac{3}{10}\)

Question 2.

\(\frac{2}{3}-\frac{1}{4}=\)
\(\frac{□}{□}\)

Answer:
\(\frac{2}{3}\) – \(\frac{1}{4}\)
Now we have to make the fractions like denominators
\(\frac{2}{3}\) • \(\frac{4}{4}\) – \(\frac{1}{4}\) • \(\frac{3}{3}\)
\(\frac{8}{12}\) – \(\frac{3}{12}\) = \(\frac{5}{12}\)

Page No. 249

Use fraction strips to find the difference. Write your answer in simplest form.

Question 3.

\(\frac{5}{6}-\frac{1}{4}=\)
\(\frac{□}{□}\)

Answer:
Step 1:
Find fraction strips, all with the same denominator, that fit exactly under the difference \(\frac{5}{6}-\frac{1}{4}\)
Step 2:
Find another set of fraction strips, all with the same denominator, that fit exactly under the difference \(\frac{5}{6}-\frac{1}{4}\)
Step 3:
Find other fraction strips, all with the same denominator, that fit exactly under the difference \(\frac{5}{6}-\frac{1}{4}\)
\(\frac{5}{6}\) • \(\frac{4}{4}\) – \(\frac{1}{4}\) • \(\frac{6}{6}\)
\(\frac{20}{24}\) – \(\frac{6}{24}\) = \(\frac{14}{24}\) = \(\frac{7}{12}\)
Thus, \(\frac{5}{6}-\frac{1}{4}\) = \(\frac{7}{12}\)

Go Math Lesson 6.2 5th Grade Question 4.

\(\frac{1}{2}-\frac{3}{10}=\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{2}-\frac{3}{10}\)
\(\frac{1}{2}\) • \(\frac{5}{5}\) – \(\frac{3}{10}\)
\(\frac{5}{10}\) – \(\frac{3}{10}\) = \(\frac{2}{10}\)

Question 5.

\(\frac{3}{8}-\frac{1}{4}=\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{8}-\frac{1}{4}\)
\(\frac{3}{8}\) – \(\frac{1}{4}\) • \(\frac{2}{2}\)
= \(\frac{3}{8}\) – \(\frac{2}{8}\) = \(\frac{1}{8}\)

Question 6.

\(\frac{2}{3}-\frac{1}{2}=\)
\(\frac{□}{□}\)

Answer:
\(\frac{2}{3}-\frac{1}{2}\)
\(\frac{2}{3}\) • \(\frac{2}{2}\) – \(\frac{1}{2}\) • \(\frac{3}{3}\)
\(\frac{4}{6}-\frac{3}{6}\) = \(\frac{1}{6}\)

Use fraction strips to find the difference. Write your answer in simplest form.

Question 7.
\(\frac{3}{5}-\frac{3}{10}=\) \(\frac{□}{□}\)

Answer:
\(\frac{3}{5}-\frac{3}{10}\)
\(\frac{3}{5}\) • \(\frac{2}{2}\) – \(\frac{3}{10}\)
= \(\frac{6}{10}\) – \(\frac{3}{10}\) = \(\frac{3}{10}\)

Question 8.
\(\frac{5}{12}-\frac{1}{3}=\) \(\frac{□}{□}\)

Answer:
\(\frac{5}{12}-\frac{1}{3}\)
Make the denominators equal and then subtract the subtract the fraction with lide denominators.
\(\frac{5}{12}\) – \(\frac{1}{3}\) • \(\frac{4}{4}\)
\(\frac{5}{12}\) – \(\frac{4}{12}\) = \(\frac{1}{12}\)

Question 9.
\(\frac{1}{2}-\frac{1}{10}=\) \(\frac{□}{□}\)

Answer:
\(\frac{1}{2}-\frac{1}{10}\)
Make the denominators equal and then subtract the subtract the fraction with lide denominators.
\(\frac{1}{2}\) • \(\frac{5}{5}\) – \(\frac{1}{10}\)
\(\frac{5}{10}\) – \(\frac{1}{10}\) = \(\frac{4}{10}\)

Question 10.
\(\frac{3}{5}-\frac{1}{2}=\) \(\frac{□}{□}\)

Answer:
\(\frac{3}{5}-\frac{1}{2}\)
Make the denominators equal and then subtract the fraction with like denominators.
\(\frac{3}{5}\) • \(\frac{2}{2}\) – \(\frac{1}{2}\) • \(\frac{5}{5}\)
\(\frac{6}{10}-\frac{5}{10}\) = \(\frac{1}{10}\)

Question 11.
\(\frac{7}{8}-\frac{1}{4}=\) \(\frac{□}{□}\)

Answer:
\(\frac{7}{8}-\frac{1}{4}\)
Make the denominators equal and then subtract the fraction with like denominators.
\(\frac{7}{8}\) – \(\frac{1}{4}\) • \(\frac{2}{2}\)
\(\frac{7}{8}\) – \(\frac{2}{8}\) = \(\frac{5}{8}\)

Question 12.
\(\frac{5}{6}-\frac{2}{3}=\) \(\frac{□}{□}\)

Answer:
\(\frac{5}{6}-\frac{2}{3}\)
Make the denominators equal and then subtract the fraction with like denominators.
\(\frac{5}{6}\) – \(\frac{2}{3}\) • \(\frac{2}{2}\)
\(\frac{5}{6}\) – \(\frac{4}{6}\)
\(\frac{1}{6}\)

Question 13.
\(\frac{3}{4}-\frac{1}{3}=\) \(\frac{□}{□}\)

Answer:
\(\frac{3}{4}-\frac{1}{3}\)
\(\frac{3}{4}\) • \(\frac{3}{3}\) – \(\frac{1}{3}\) • \(\frac{4}{4}\)
\(\frac{9}{12}\) – \(\frac{4}{12}\) = \(\frac{5}{12}\)

Go Math Grade 5 Chapter 6 Review/Test Pdf Question 14.
\(\frac{5}{6}-\frac{1}{2}=\) \(\frac{□}{□}\)

Answer:
\(\frac{5}{6}-\frac{1}{2}\)
\(\frac{5}{6}\) – \(\frac{1}{2}\) • \(\frac{3}{3}\)
\(\frac{5}{6}\) – \(\frac{3}{6}\) = \(\frac{2}{6}\)
\(\frac{5}{6}-\frac{1}{2}=\) \(\frac{2}{6}\)

Question 15.
\(\frac{3}{4}-\frac{7}{12}=\) \(\frac{□}{□}\)

Answer:
\(\frac{3}{4}-\frac{7}{12}\)
\(\frac{3}{4}\) • \(\frac{3}{3}\) – \(\frac{7}{12}\)
\(\frac{9}{12}\) – \(\frac{7}{12}\) = \(\frac{2}{12}\)
\(\frac{3}{4}-\frac{7}{12}=\) \(\frac{2}{12}\)

Question 16.
Explain how your model for \(\frac{3}{5}-\frac{1}{2}\) is different from your model for \(\frac{3}{5}-\frac{3}{10}\).
Type below:
_________

Answer:
\(\frac{3}{5}-\frac{3}{10}\)
\(\frac{3}{5}\) • \(\frac{2}{2}\) – \(\frac{3}{10}\)
\(\frac{6}{10}\) – \(\frac{3}{10}\) = \(\frac{3}{10}\)

UNLOCK the Problem – Page No. 250

Question 17.
The picture at the right shows how much pizza was left over from lunch. Jason eats \(\frac{1}{4}\) of the whole pizza for dinner. Which subtraction sentence represents the amount of pizza that is remaining after dinner?

a. What problem are you being asked to solve?
Type below:
_________

Answer: I am asked to solve which subtraction sentence represents the amount of pizza that is remaining after dinner.

Question 17.
b. How will you use the diagram to solve the problem?
Type below:
_________

Answer: I will use number of slices left in the pizza to solve the problem.

Question 17.
c. Jason eats \(\frac{1}{4}\) of the whole pizza. How many slices does he eat?
______ slices

Answer: 2 slices

Explanation:
Given that, Jason eats \(\frac{1}{4}\) of the whole pizza.
The pizza is cut into 8 slices.
So, 8 × \(\frac{1}{4}\) = 2 slices.
Thus Jason ate 2 slices.

Question 17.
d. Redraw the diagram of the pizza. Shade the sections of pizza that are remaining after Jason eats his dinner.
Type below:
_________

Question 17.
e. Write a fraction to represent the amount of pizza that is remaining.
\(\frac{□}{□}\) of a pizza

Answer: \(\frac{3}{8}\) of a pizza

Explanation:
The fraction of pizzz Jason ate = \(\frac{1}{4}\)
Number of slices left = \(\frac{5}{8}\)
Now subtract \(\frac{5}{8}\) – \(\frac{1}{4}\)
= \(\frac{3}{8}\)
Thus the fraction to represent the amount of pizza that is remaining is \(\frac{3}{8}\)

Question 17.
f. Fill in the bubble for the correct answer choice above.
Options:
a. 1 – \(\frac{1}{4}\) = \(\frac{3}{4}\)
b. \(\frac{5}{8}\) – \(\frac{1}{4}\) = \(\frac{3}{8}\)
c. \(\frac{3}{8}\) – \(\frac{1}{4}\) = \(\frac{2}{8}\)
d. 1 – \(\frac{3}{8}\) = \(\frac{5}{8}\)

Answer: B
The fraction of pizzz Jason ate = \(\frac{1}{4}\)
Number of slices left = \(\frac{5}{8}\)
Now subtract \(\frac{5}{8}\) – \(\frac{1}{4}\) = \(\frac{3}{8}\)
Thus the correct answer is option B.

Go Math Grade 5 Chapter 6 Review/Test Answer Key Question 18.
The diagram shows what Tina had left from a yard of fabric. She now uses \(\frac{2}{3}\) yard of fabric for a project. How much of the original yard of fabric does Tina have left after the project?

Options:
a. \(\frac{2}{3}\) yard
b. \(\frac{1}{2}\) yard
c. \(\frac{1}{3}\) yard
d. \(\frac{1}{6}\) yard

Answer: \(\frac{1}{3}\) yard

Explanation:
The original yard of fabric is 6
Tina uses \(\frac{2}{3}\) yard of fabric for a project.
\(\frac{1}{1}\) – \(\frac{2}{3}\)
\(\frac{3}{3}\) – \(\frac{2}{3}\) = \(\frac{1}{3}\) yard

Share and Show – Page No. 253

Estimate the sum or difference.

Question 1.
\(\frac{5}{6}+\frac{3}{8}\)
a. Round \(\frac{5}{6}\) to its closest benchmark. ____
b. Round \(\frac{3}{8}\) to its closest benchmark. ____
c. Add to find the estimate. ____ + ____ = ____
_____ \(\frac{□}{□}\)

Answer:
a. Round \(\frac{5}{6}\) to its closest benchmark. \(\frac{6}{6}\) or 1.
b. Round \(\frac{3}{8}\) to its closest benchmark. \(\frac{4}{8}\) or \(\frac{1}{2}\)
c. Add to find the estimate. ____ + ____ = ____
1 + \(\frac{1}{2}\) = \(\frac{3}{2}\) = 1 \(\frac{1}{2}\)

Question 2.
\(\frac{5}{9}-\frac{3}{8}\)
_____

Answer: 0

Explanation:
Step 1: Place a point at \(\frac{5}{9}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\).
The fraction rounded to \(\frac{5}{9}\) is \(\frac{1}{2}\)
Step 2: Place a point at \(\frac{3}{8}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\).
The fraction rounded to \(\frac{3}{8}\) is \(\frac{1}{2}\).
\(\frac{1}{2}\) – \(\frac{1}{2}\) = 0

Question 3.
\(\frac{6}{7}+2 \frac{4}{5}\)
_____

Answer: 4

Explanation:
Step 1: Place a point at \(\frac{6}{7}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 2: Place a point at \(\frac{4}{5}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
1 + 3 = 4

Go Math Grade 5 Lesson 6.3 Answer Key Question 4.
\(\frac{5}{6}+\frac{2}{5}\)
_____ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{2}\)

Explanation:
Step 1: Place a point at \(\frac{5}{6}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 2: Place a point at \(\frac{2}{5}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\).
1 + \(\frac{1}{2}\) = \(\frac{3}{2}\) = 1 \(\frac{1}{2}\)

Question 5.
\(3 \frac{9}{10}-1 \frac{2}{9}\)
_____

Answer: 3

Explanation:

Step 1: Place a point at \(\frac{9}{10}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 2: Place a point at \(\frac{2}{9}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\).
3 × 1 – 1 × 0 = 3 – 0 = 3
\(3 \frac{9}{10}-1 \frac{2}{9}\) = 3

Question 6.
\(\frac{4}{6}+\frac{1}{9}\)
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:

Step 1: Place a point at \(\frac{4}{6}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 2: Place a point at \(\frac{1}{9}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\).
So, \(\frac{1}{2}\) + 0 = \(\frac{1}{2}\)
\(\frac{4}{6}+\frac{1}{9}\) = \(\frac{1}{2}\)

Question 7.
\(\frac{9}{10}-\frac{1}{9}\)
_____

Answer: 1

Explanation:
Step 1: Place a point at \(\frac{9}{10}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 2: Place a point at \(\frac{1}{9}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\).
1 – 0 = 1
\(\frac{9}{10}-\frac{1}{9}\) = 1

On Your Own

Estimate the sum or difference.

Question 8.
\(\frac{5}{8}-\frac{1}{5}\)
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
Step 1: Place a point at \(\frac{5}{8}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 2: Place a point at \(\frac{1}{5}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\).
1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)

Question 9.
\(\frac{1}{6}+\frac{3}{8}\)
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
Step 1: Place a point at \(\frac{1}{6}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\)
Step 2: Place a point at \(\frac{3}{8}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\)
0 + \(\frac{1}{2}\) = \(\frac{1}{2}\)

Question 10.
\(\frac{6}{7}-\frac{1}{5}\)
_____

Answer: 1

Explanation:
Step 1: Place a point at \(\frac{6}{7}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 2: Place a point at \(\frac{1}{5}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\)
1 – 0 = 1
\(\frac{6}{7}-\frac{1}{5}\) = 1

Question 11.
\(\frac{11}{12}+\frac{6}{10}\)
_____ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{2}\)

Explanation:
Step 1: Place a point at \(\frac{11}{12}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1
Step 2: Place a point at \(\frac{6}{10}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1
1 + \(\frac{1}{2}\) = \(\frac{3}{2}\) = 1 \(\frac{1}{2}\)
\(\frac{11}{12}+\frac{6}{10}\) = 1 \(\frac{1}{2}\)

Question 12.
\(\frac{9}{10}-\frac{1}{2}\)
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
Step 1: Place a point at \(\frac{9}{10}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 2: Place a point at \(\frac{1}{2}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\)
1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)
\(\frac{9}{10}-\frac{1}{2}\) = \(\frac{1}{2}\)

Question 13.
\(\frac{3}{6}+\frac{4}{5}\)
_____ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{2}\)

Explanation:
Step 1: Place a point at \(\frac{3}{6}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\)
Step 2: Place a point at \(\frac{4}{5}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1
\(\frac{1}{2}\) + 1 = \(\frac{3}{2}\) = 1 \(\frac{1}{2}\)
\(\frac{3}{6}+\frac{4}{5}\) = 1 \(\frac{1}{2}\)

Go Math Chapter 6 5th Grade Question 14.
\(\frac{5}{6}-\frac{3}{8}\)
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
Step 1: Place a point at \(\frac{5}{6}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 2: Place a point at \(\frac{3}{8}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\)
1 – \(\frac{1}{2}\) = \(\frac{1}{2}\)
\(\frac{5}{6}-\frac{3}{8}\) = \(\frac{1}{2}\)

Question 15.
\(\frac{1}{7}+\frac{8}{9}\)
_____

Answer: 1

Explanation:
Step 1: Place a point at \(\frac{1}{7}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\)
Step 2: Place a point at \(\frac{8}{9}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
0 + 1 = 1
\(\frac{1}{7}+\frac{8}{9}\) = 1

Question 16.
\(3 \frac{5}{12}-3 \frac{1}{10}\)
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
Step 1: Place a point at \(\frac{5}{12}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\)
Step 2: Place a point at \(\frac{1}{10}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\)
\(\frac{1}{2}\) – 0 = \(\frac{1}{2}\)
\(3 \frac{5}{12}-3 \frac{1}{10}\) = \(\frac{1}{2}\)

Problem Solving – Page No. 254

Question 17.
Lisa and Valerie are picnicking in Trough Creek State Park in Pennsylvania. Lisa has brought a salad that she made with \(\frac{3}{4}\) cup of strawberries, \(\frac{7}{8}\) cup of peaches, and \(\frac{1}{6}\) cup of blueberries. About how many total cups of fruit are in the salad?
_____ cups

Answer: 2 cups

Explanation:
Lisa and Valerie are picnicking in Trough Creek State Park in Pennsylvania.
Lisa has brought a salad that she made with \(\frac{3}{4}\) cup of strawberries, \(\frac{7}{8}\) cup of peaches, and \(\frac{1}{6}\) cup of blueberries.
Step 1: Place \(\frac{3}{4}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 2: Place \(\frac{7}{8}\) on the number line.
The fraction is between \(\frac{1}{2}\) and 1.
Step 3: Place \(\frac{1}{6}\) on the number line.
The fraction is between 0 and \(\frac{1}{2}\).
1 + 1 + 0 = 2
Thus 2 cups of fruit are in the salad.

Question 18.
At Trace State Park in Mississippi, there is a 25-mile mountain bike trail. If Tommy rode \(\frac{1}{2}\) of the trail on Saturday and \(\frac{1}{5}\) of the trail on Sunday, about what fraction of the trail did he ride?
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
At Trace State Park in Mississippi, there is a 25-mile mountain bike trail.
If Tommy rode \(\frac{1}{2}\) of the trail on Saturday and \(\frac{1}{5}\) of the trail on Sunday
Step 1: Place \(\frac{1}{2}\) on the number line.
\(\frac{1}{2}\) lies between 0 and \(\frac{1}{2}\)
Step 2: Place \(\frac{1}{5}\) on the number line.
\(\frac{1}{5}\) 0 and \(\frac{1}{2}\)
The number closer to \(\frac{1}{5}\) is 0
\(\frac{1}{2}\) – 0 = \(\frac{1}{2}\)
The estimated fraction of the trail he rides is \(\frac{1}{2}\)

Question 19.
Explain how you know that \(\frac{5}{8}+\frac{6}{10}\) is greater than 1.
Type below:
__________

Answer:
Step 1: Place \(\frac{5}{8}\) on the number line.
\(\frac{5}{8}\) is closer to \(\frac{1}{2}\)
Step 2: Place \(\frac{6}{10}\) on the number line.
\(\frac{6}{10}\) lies between \(\frac{1}{2}\) and 1.
\(\frac{6}{10}\) is closer to \(\frac{1}{2}\)
\(\frac{1}{2}\) + \(\frac{1}{2}\) = 1

Question 20.
Nick estimated that \(\frac{5}{8}+\frac{4}{7}\) is about 2.
Explain how you know his estimate is not reasonable.
Type below:
__________

Answer:
Step 1: Place \(\frac{5}{8}\) on the number line.
\(\frac{5}{8}\) is closer to \(\frac{1}{2}\)
Step 2: Place \(\frac{4}{7}\) on the number line.
\(\frac{4}{7}\) lies between \(\frac{1}{2}\) and 1.
\(\frac{1}{2}\) + \(\frac{1}{2}\) = 1
By this, we can say that Nick’s estimation was wrong.

Question 21.
Test Prep Jake added \(\frac{1}{8}\) cup of sunflower seeds and \(\frac{4}{5}\) cup of banana chips to his sundae. Which is the best estimate of the total amount of toppings Jake added to his sundae?
Options:
a. about \(\frac{1}{2}\) cup
b. about 1 cup
c. about 1 \(\frac{1}{2}\) cups
d. about 2 cups

Answer: about 1 cup

Explanation:
Given, Test Prep Jake added \(\frac{1}{8}\) cup of sunflower seeds and \(\frac{4}{5}\) cup of banana chips to his sundae
Step 1: Place \(\frac{1}{8}\) on the number line.
\(\frac{1}{8}\) lies between 0 and \(\frac{1}{2}\)
Step 2: Place \(\frac{4}{5}\) on the number line.
\(\frac{4}{5}\) lies between \(\frac{1}{2}\) and 1.
0 + 1 = 1
The best estimate of the total amount of toppings Jake added to his sundae is about 1 cup.

Share and Show – Page No. 256

Question 1.
Find a common denominator of \(\frac{1}{6}\) and \(\frac{1}{9}\) . Rewrite the pair of fractions using the common denominator.
• Multiply the denominators.
A common denominator of \(\frac{1}{6}\) and \(\frac{1}{9}\) is ____.
• Rewrite the pair of fractions using the common denominator.
Type below:
_________

Answer:
Common denominator is 18.
\(\frac{1}{6}\) × \(\frac{3}{3}\) = \(\frac{3}{18}\)
\(\frac{1}{9}\) × \(\frac{2}{2}\) = \(\frac{2}{18}\)
The pair of fractions using the common denominator is \(\frac{3}{18}\), \(\frac{2}{18}\)

Use a common denominator to write an equivalent fraction for each fraction.

Question 2.
\(\frac{1}{3}, \frac{1}{5}\)
common denominator: _________
Type below:
_________

Answer: 15

Explanation:
Multiply the denominators of the fraction.
\(\frac{1}{3}\) × \(\frac{1}{5}\) = \(\frac{1}{15}\)
Thus the common denominator is 15.

Go Math Grade 5 Lesson 6.4 Factors Question 3.
\(\frac{2}{3}, \frac{5}{9}\)
common denominator: _________
Type below:
_________

Answer: 27

Explanation:
Multiply the denominators
\(\frac{2}{3}\) × \(\frac{5}{9}\)
= 3 × 9 = 27
Thus the common denominator of \(\frac{2}{3}, \frac{5}{9}\) is 27.

Question 4.
\(\frac{2}{9}, \frac{1}{15}\)
common denominator: _________
Type below:
_________

Answer: 45

Explanation:
Multiply the denominators
\(\frac{2}{9}\) × \(\frac{1}{15}\)
The least common denominator of 15 and 9 is 45.
So, the common denominator of \(\frac{2}{9}, \frac{1}{15}\) is 45.

Page No. 257

Use the least common denominator to write an equivalent fraction for each fraction.

Question 5.
\(\frac{1}{4}, \frac{3}{8}\)
least common denominator: ______
Type below:
_________

Answer: 8

Explanation:

First multiply the denominators of the fractions \(\frac{1}{4}, \frac{3}{8}\)
4 × 8 = 32
The least common denominator is 8
The equivalent fractions with LCD
\(\frac{1}{4}\) = \(\frac{2}{8}\)
\(\frac{3}{8}\) = \(\frac{3}{8}\)

Question 6.
\(\frac{11}{12}, \frac{5}{8}\)
least common denominator: ______
Type below:
_________

Answer: 24

Explanation:
First, multiply the denominators of the fractions.
12 × 8 = 96
The least common denominator of 12 and 8 is 24.
The equivalent fractions with LCD
\(\frac{11}{12}\) × \(\frac{2}{2}\)= \(\frac{22}{24}\)
\(\frac{5}{8}\) × \(\frac{3}{3}\) = \(\frac{15}{24}\)

Question 7.
\(\frac{4}{5}, \frac{1}{6}\)
least common denominator: ______
Type below:
_________

Answer: 30

Explanation:
First, multiply the denominators of the fractions.
5 × 6 = 30
The least common denominator (LCD) = 30
\(\frac{4}{5}\) × \(\frac{6}{6}\)= \(\frac{24}{30}\)
\(\frac{1}{6}\) × \(\frac{5}{5}\) = \(\frac{5}{30}\)

On Your Own

Use a common denominator to write an equivalent fraction for each fraction.

Question 8.
\(\frac{3}{5}, \frac{1}{4}\)
common denominator: ______
Type below:
_________

Answer: 20

Explanation:
Multiply the denominators of the fractions to find the common denominator.
5 × 4 = 20
So, the common denominator of \(\frac{3}{5}, \frac{1}{4}\) is 20.

Question 9.
\(\frac{5}{8}, \frac{1}{5}\)
common denominator: ______
Type below:
_________

Answer: 40

Explanation:
Multiply the denominators of the fractions to find the common denominator.
8 × 5 = 40
So, the common denominator of \(\frac{5}{8}, \frac{1}{5}\) is 40.

Go Math Grade 5 Chapter 6 Review Test Question 10.
\(\frac{1}{12}, \frac{1}{2}\)
common denominator: ______
Type below:
_________

Answer: 24

Explanation:
Multiply the denominators of the fractions to find the common denominator.
12 × 2 = 24
The common denominator of \(\frac{1}{12}, \frac{1}{2}\) is 24.

Practice: Copy and Solve Use the least common denominator to write an equivalent fraction for each fraction.

Question 11.
\(\frac{1}{6}, \frac{4}{9}\)
Type below:
_________

Answer: \(\frac{3}{18}, \frac{8}{18}\)

Explanation:
Multiply the denominators of the fractions.
The Least Common Denominator = 18
Now rewrite the fractions
\(\frac{1}{6}\) × \(\frac{3}{3}\) = \(\frac{3}{18}\)
\(\frac{4}{9}\) × \(\frac{2}{2}\) = \(\frac{8}{18}\)

Question 12.
\(\frac{7}{9}, \frac{8}{27}\)
Type below:
_________

Answer: \(\frac{21}{27}, \frac{8}{27}\)

Explanation:
Multiply the denominators of the fractions.
The Least Common Denominator = 27
Now rewrite the fractions
\(\frac{7}{9}\) × \(\frac{3}{3}\) = \(\frac{21}{27}\)
\(\frac{8}{27}\) × \(\frac{1}{1}\) = \(\frac{8}{27}\)

Question 13.
\(\frac{7}{10}, \frac{3}{8}\)
Type below:
_________

Answer: \(\frac{28}{40}, \frac{15}{40}\)

Explanation:
Multiply the denominators of the fractions.
The Least Common Denominator = 40
Now rewrite the fractions
\(\frac{7}{10}\) × \(\frac{4}{4}\) = \(\frac{28}{40}\)
\(\frac{3}{8}\) × \(\frac{5}{5}\) = \(\frac{15}{40}\)

Question 14.
\(\frac{1}{3}, \frac{5}{11}\)
Type below:
_________

Answer: \(\frac{11}{33}, \frac{15}{33}\)

Explanation:
Multiply the denominators of the fractions.
The Least Common Denominator = 33
Now rewrite the fractions
\(\frac{1}{3}\) × \(\frac{11}{11}\) = \(\frac{11}{33}\)
\(\frac{5}{11}\) × \(\frac{3}{3}\) = \(\frac{15}{33}\)

Question 15.
\(\frac{5}{9}, \frac{4}{15}\)
Type below:
_________

Answer: \(\frac{25}{45}, \frac{12}{45}\)

Explanation:
Multiply the denominators of the fractions.
The Least Common Denominator of \(\frac{5}{9}, \frac{4}{15}\)= 45
Now rewrite the input fractions
\(\frac{5}{9}\) × \(\frac{5}{5}\) = \(\frac{25}{45}\)
\(\frac{4}{15}\) × \(\frac{3}{3}\) = \(\frac{12}{45}\)

Question 16.
\(\frac{1}{6}, \frac{4}{21}\)
Type below:
_________

Answer: \(\frac{7}{42}, \frac{8}{42}\)

Explanation:
Multiply the denominators of the fractions.
The Least Common Denominator = 42
Now rewrite the fractions
\(\frac{1}{6}\) × \(\frac{7}{7}\) = \(\frac{7}{42}\)
\(\frac{4}{21}\) × \(\frac{2}{2}\) = \(\frac{8}{42}\)

Question 17.
\(\frac{5}{14}, \frac{8}{42}\)
Type below:
_________

Answer: \(\frac{15}{42}, \frac{8}{42}\)

Explanation:
Multiply the denominators of the fractions.
The Least Common Denominator = 42
Now rewrite the fractions
\(\frac{5}{14}\) × \(\frac{3}{3}\) = \(\frac{15}{42}\)
\(\frac{8}{42}\) × \(\frac{1}{1}\) = \(\frac{8}{42}\)

Question 18.
\(\frac{7}{12}, \frac{5}{18}\)
Type below:
_________

Answer: \(\frac{21}{36}, \frac{10}{36}\)

Explanation:
Multiply the denominators of the fractions.
The Least Common Denominator = 36
Now rewrite the fractions
\(\frac{7}{12}\) × \(\frac{3}{3}\) = \(\frac{21}{36}\)
\(\frac{5}{18}\) × \(\frac{2}{2}\) = \(\frac{10}{36}\)

Algebra Write the unknown number for each ■.

Question 19.
\(\frac{1}{5}, \frac{1}{8}\)
least common denominator: ■
■ = ______

Answer: 40

Explanation:
Multiply the denominators of the fractions.
5 × 8 = 40
Therefore, ■ = 40

Question 20.
\(\frac{2}{5}, \frac{1}{■}\)
least common denominator: 15
■ = ______

Answer: 3

Explanation:
Multiply the denominators of the fractions.
5 × ■ = 15
■ = 15/5 = 3
Thus ■ = 3

Question 21.
\(\frac{3}{■}, \frac{5}{6}\)
least common denominator: 42
■ = ______

Answer: 7

Explanation:
\(\frac{3}{■}, \frac{5}{6}\)
■ × 6 = 42
■ = 42/6
■ = 7

UNLOCK the Problem – Page No. 258

Question 22.
Katie made two pies for the bake sale. One was cut into three equal slices and the other into 5 equal slices. She will continue to cut the pies so each one has the same number of equal-sized slices. What is the least number of equal-sized slices each pie could have?
a. What information are you given?
Type below:
_________

Answer: I have the information about the two pies for the bake sale. One was cut into three equal slices and the other into 5 equal slices. She will continue to cut the pies so each one has the same number of equal-sized slices.

Question 22.
b. What problem are you being asked to solve?
Type below:
_________

Answer: I am asked to solve the least number of equal-sized slices each pie could have.

Question 22.
c. When Katie cuts the pies more, can she cut each pie the same number of times and have all the slices the same size? Explain.
Type below:
_________

Answer: Yes she can cut into more equal pieces. Katie can cut the pie into 6 equal pieces and 10 equal pieces. But the least number of equal-sized slices each pie could have is 3 and 5.

Question 22.
d. Use the diagram to show the steps you use to solve the problem.

Type below:
_________

Answer:
There are 2 pies. One pie is cut into 3 equal pieces and the second pie is cut into 5 equal pieces.
So, there are 15 pieces of pies.

Question 22.
e. Complete the sentences.
The least common denominator of \(\frac{1}{3}\) and \(\frac{1}{5}\) is ____.
Katie can cut each piece of the first pie into ____ and each piece of the second pie into ____ .
That means that Katie can cut each pie into pieces that are ____ of the whole pie.
Type below:
_________

Answer:
The least common denominator of \(\frac{1}{3}\) and \(\frac{1}{5}\) is 15
5 × 3 = 15
Katie can cut each piece of the first pie into three and each piece of the second pie into five.
That means that Katie can cut each pie into pieces that are 15 of the whole pie.

Question 23.
A cookie recipe calls for \(\frac{1}{3}\) cup of brown sugar and \(\frac{1}{8}\) cup of walnuts. Find the least common denominator of the fractions used in the recipe.
____

Answer: 24

Explanation:

A cookie recipe calls for \(\frac{1}{3}\) cup of brown sugar and \(\frac{1}{8}\) cup of walnuts.
We can calculate the LCD by multiplying the denominators of the fraction.
3 × 8 = 24.

Question 24.
Test Prep Which fractions use the least common denominator and are equivalent to \(\frac{5}{8}\) and \(\frac{7}{10}\) ?
Options:
a. \(\frac{10}{40} \text { and } \frac{14}{40}\)
b. \(\frac{25}{40} \text { and } \frac{28}{40}\)
c. \(\frac{25}{80} \text { and } \frac{21}{80}\)
d. \(\frac{50}{80} \text { and } \frac{56}{80}\)

Answer: \(\frac{50}{80} \text { and } \frac{56}{80}\)

Explanation:
The least common denominator of \(\frac{5}{8}\) and \(\frac{7}{10}\) is 80.
\(\frac{5}{8}\) × \(\frac{10}{10}\) and \(\frac{7}{10}\) × \(\frac{8}{8}\)
= \(\frac{50}{80} \text { and } \frac{56}{80}\)
Thus the correct answer is option D.

Share and Show – Page No. 260

Find the sum or difference. Write your answer in simplest form.

Question 1.
\(\frac{5}{12}+\frac{1}{3}\)
\(\frac{□}{□}\)

Answer:
Find a common denominator by multiplying the denominators.
\(\frac{5}{12}+\frac{1}{3}\)
\(\frac{5}{12}\) + \(\frac{1}{3}\) × \(\frac{4}{4}\)
\(\frac{5}{12}\) + \(\frac{4}{12}\)
\(\frac{9}{12}\)

Question 2.
\(\frac{2}{5}+\frac{3}{7}\)
\(\frac{□}{□}\)

Answer:
Find a common denominator by multiplying the denominators.
Use the common denominator to write equivalent fractions with like denominators. Then add, and write your answer in simplest form.
\(\frac{2}{5}+\frac{3}{7}\)
\(\frac{2}{5}\) × \(\frac{7}{7}\) + \(\frac{3}{7}\) × \(\frac{5}{5}\)
\(\frac{14}{35}+\frac{15}{35}\)
= \(\frac{29}{35}\)
\(\frac{2}{5}+\frac{3}{7}\) = \(\frac{29}{35}\)

Question 3.
\(\frac{1}{6}+\frac{3}{4}\)
\(\frac{□}{□}\)

Answer:
Find a common denominator by multiplying the denominators.
Use the common denominator to write equivalent fractions with like denominators. Then add, and write your answer in simplest form.
\(\frac{1}{6}\) × \(\frac{2}{2}\) + \(\frac{3}{4}\) × \(\frac{3}{3}\)
\(\frac{2}{12}+\frac{9}{12}\) = \(\frac{11}{12}\)
So, \(\frac{1}{6}+\frac{3}{4}\) = \(\frac{11}{12}\)

Question 4.
\(\frac{3}{4}-\frac{1}{8}\)
\(\frac{□}{□}\)

Answer:
First, find a common denominator by multiplying the denominators.
Use the common denominator to write equivalent fractions with like denominators. Then add, and write your answer in simplest form.
\(\frac{3}{4}-\frac{1}{8}\)
\(\frac{3}{4}\) × \(\frac{2}{2}\) – \(\frac{1}{8}\)
\(\frac{6}{8}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)
Thus \(\frac{3}{4}-\frac{1}{8}\) = \(\frac{5}{8}\)

Go Math Lesson 6.5 Answers Grade 5 Question 5.
\(\frac{1}{4}-\frac{1}{7}\)
\(\frac{□}{□}\)

Answer:
First, find a common denominator by multiplying the denominators.
Use the common denominator to write equivalent fractions with like denominators. Then add, and write your answer in simplest form.
\(\frac{1}{4}-\frac{1}{7}\)
\(\frac{1}{4}\) × \(\frac{7}{7}\) – \(\frac{1}{7}\) × \(\frac{4}{4}\)
\(\frac{7}{28}\) – \(\frac{4}{28}\) = \(\frac{3}{28}\)
\(\frac{1}{4}-\frac{1}{7}\) = \(\frac{3}{28}\)

Question 6.
\(\frac{9}{10}-\frac{1}{4}\)
\(\frac{□}{□}\)

Answer:
First, find a common denominator by multiplying the denominators.
Use the common denominator to write equivalent fractions with like denominators. Then add, and write your answer in simplest form.
\(\frac{9}{10}-\frac{1}{4}\)
\(\frac{9}{10}\) × \(\frac{4}{4}\) – \(\frac{1}{4}\) × \(\frac{10}{10}\)
\(\frac{36}{40}\) – \(\frac{10}{40}\) = \(\frac{26}{40}\)
\(\frac{9}{10}-\frac{1}{4}\) = \(\frac{26}{40}\)

On Your Own – Page No. 261

Find the sum or difference. Write your answer in simplest form.

Question 7.
\(\frac{3}{8}+\frac{1}{4}\)
\(\frac{□}{□}\)

Answer: \(\frac{5}{8}\)

Explanation:
\(\frac{3}{8}+\frac{1}{4}\) = \(\frac{3}{8}\) + \(\frac{1}{4}\)
LCD = 8
\(\frac{3}{8}\) + \(\frac{1}{4}\) × \(\frac{2}{2}\)
\(\frac{3}{8}\) + \(\frac{2}{8}\) = \(\frac{5}{8}\)
Thus \(\frac{3}{8}+\frac{1}{4}\) = \(\frac{5}{8}\)

Question 8.
\(\frac{7}{8}+\frac{1}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{7}{8}+\frac{1}{10}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 40
\(\frac{7}{8}\) × \(\frac{5}{5}\) + \(\frac{1}{10}\) × \(\frac{4}{4}\)
\(\frac{35}{40}\) + \(\frac{4}{40}\) = \(\frac{39}{40}\)
\(\frac{7}{8}+\frac{1}{10}\) = \(\frac{39}{40}\)

Question 9.
\(\frac{2}{7}+\frac{3}{10}\)
\(\frac{□}{□}\)

Answer:
\(\frac{2}{7}+\frac{3}{10}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 70
\(\frac{2}{7}\) × \(\frac{10}{10}\) + \(\frac{3}{10}\) × \(\frac{7}{7}\)
\(\frac{20}{70}\) + \(\frac{21}{70}\) = \(\frac{41}{70}\)
\(\frac{2}{7}+\frac{3}{10}\) = \(\frac{41}{70}\)

Question 10.
\(\frac{5}{6}+\frac{1}{8}\)
\(\frac{□}{□}\)

Answer:
\(\frac{5}{6}+\frac{1}{8}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
\(\frac{5}{6}\) + \(\frac{1}{8}\)
LCD = 24
\(\frac{5}{6}\) × \(\frac{4}{4}\) + \(\frac{1}{8}\) × \(\frac{3}{3}\)
\(\frac{20}{24}\) + \(\frac{3}{24}\) = \(\frac{23}{24}\)
\(\frac{5}{6}+\frac{1}{8}\) = \(\frac{23}{24}\)

Question 11.
\(\frac{5}{12}+\frac{5}{18}\)
\(\frac{□}{□}\)

Answer:
\(\frac{5}{12}+\frac{5}{18}\) = \(\frac{5}{12}\) + \(\frac{5}{18}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 36
\(\frac{5}{12}\) × \(\frac{3}{3}\) + \(\frac{5}{18}\) × \(\frac{2}{2}\)
\(\frac{15}{36}\) + \(\frac{10}{36}\) = \(\frac{25}{36}\)
\(\frac{5}{12}+\frac{5}{18}\) = \(\frac{25}{36}\)

Lesson 6.5 Answer Key 5th Grade Question 12.
\(\frac{7}{16}+\frac{1}{4}\)
\(\frac{□}{□}\)

Answer:
\(\frac{7}{16}+\frac{1}{4}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 16
\(\frac{7}{16}\) + \(\frac{1}{4}\) = \(\frac{7}{16}\) + \(\frac{1}{4}\) × \(\frac{4}{4}\)
\(\frac{7}{16}\) + \(\frac{4}{16}\) = \(\frac{11}{16}\)

Question 13.
\(\frac{5}{6}+\frac{3}{8}\)
\(\frac{□}{□}\)

Answer:
\(\frac{5}{6}+\frac{3}{8}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
\(\frac{5}{6}\) + \(\frac{3}{8}\)
LCD = 24
\(\frac{5}{6}\) × \(\frac{4}{4}\) + \(\frac{3}{8}\) × \(\frac{3}{3}\)
= \(\frac{20}{24}\) + \(\frac{9}{24}\) = \(\frac{29}{24}\)
\(\frac{5}{6}+\frac{3}{8}\) = \(\frac{29}{24}\)

Question 14.
\(\frac{3}{4}+\frac{1}{2}\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{4}+\frac{1}{2}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
\(\frac{3}{4}\) + \(\frac{1}{2}\)
LCD = 4
\(\frac{3}{4}\) + \(\frac{1}{2}\) × \(\frac{2}{2}\)
= \(\frac{3}{4}\) + \(\frac{2}{4}\) = \(\frac{5}{4}\)
The miced fractiion of \(\frac{5}{4}\) is 1 \(\frac{1}{4}\)

Question 15.
\(\frac{5}{12}+\frac{1}{4}\)
\(\frac{□}{□}\)

Answer:
\(\frac{5}{12}+\frac{1}{4}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
\(\frac{5}{12}\) + \(\frac{1}{4}\)
LCD = 12
\(\frac{5}{12}\) + \(\frac{1}{4}\) × \(\frac{3}{3}\)
\(\frac{5}{12}\) + \(\frac{3}{12}\) = \(\frac{8}{12}\) = \(\frac{2}{3}\)

Practice: Copy and Solve Find the sum or difference. Write your answer in simplest form.

Question 16.
\(\frac{1}{3}+\frac{4}{18}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{3}+\frac{4}{18}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 18
\(\frac{1}{3}\) + \(\frac{4}{18}\)
\(\frac{1}{3}\) × \(\frac{6}{6}\) + \(\frac{4}{18}\)
\(\frac{6}{18}\) + \(\frac{4}{18}\) = \(\frac{10}{18}\) = \(\frac{5}{9}\)
\(\frac{1}{3}+\frac{4}{18}\) = \(\frac{5}{9}\)

Question 17.
\(\frac{3}{5}+\frac{1}{3}\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{5}+\frac{1}{3}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 15
\(\frac{3}{5}\) + \(\frac{1}{3}\)
\(\frac{3}{5}\) × \(\frac{3}{3}\) + \(\frac{1}{3}\) × \(\frac{5}{5}\)
\(\frac{9}{15}\) + \(\frac{5}{15}\) = \(\frac{14}{15}\)
\(\frac{3}{5}+\frac{1}{3}\) = \(\frac{14}{15}\)

Question 18.
\(\frac{3}{10}+\frac{1}{6}\)
\(\frac{□}{□}\)

Answer:
\(\frac{3}{10}+\frac{1}{6}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 30
\(\frac{3}{10}\) + \(\frac{1}{6}\)
\(\frac{3}{10}\) × \(\frac{3}{3}\) + \(\frac{1}{6}\) × \(\frac{5}{5}\)
\(\frac{9}{30}\) + \(\frac{5}{30}\) = \(\frac{14}{30}\)
\(\frac{3}{10}+\frac{1}{6}\) = \(\frac{14}{30}\)

Question 19.
\(\frac{1}{2}+\frac{4}{9}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{2}+\frac{4}{9}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 18
\(\frac{1}{2}\) + \(\frac{4}{9}\)
\(\frac{1}{2}\) × \(\frac{9}{9}\) + \(\frac{4}{9}\) × \(\frac{2}{2}\)
= \(\frac{9}{18}\) + \(\frac{8}{18}\) = \(\frac{17}{18}\)
\(\frac{1}{2}+\frac{4}{9}\) = \(\frac{17}{18}\)

Question 20.
\(\frac{1}{2}-\frac{3}{8}\)
\(\frac{□}{□}\)

Answer:
\(\frac{1}{2}-\frac{3}{8}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 8
\(\frac{1}{2}\) – \(\frac{3}{8}\)
\(\frac{1}{2}\) × \(\frac{4}{4}\) – \(\frac{3}{8}\)
\(\frac{4}{8}\) – \(\frac{3}{8}\) = \(\frac{1}{8}\)
\(\frac{1}{2}-\frac{3}{8}\) = \(\frac{1}{8}\)

Question 21.
\(\frac{5}{7}-\frac{2}{3}\)
\(\frac{□}{□}\)

Answer:
\(\frac{5}{7}-\frac{2}{3}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 21
\(\frac{5}{7}\) – \(\frac{2}{3}\)
\(\frac{5}{7}\) × \(\frac{3}{3}\) – \(\frac{2}{3}\) × \(\frac{7}{7}\)
\(\frac{15}{21}\) – \(\frac{14}{21}\) = \(\frac{1}{21}\)
\(\frac{5}{7}-\frac{2}{3}\) = \(\frac{1}{21}\)

Question 22.
\(\frac{4}{9}-\frac{1}{6}\)
\(\frac{□}{□}\)

Answer:
\(\frac{4}{9}-\frac{1}{6}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 18
\(\frac{4}{9}\) – \(\frac{1}{6}\)
\(\frac{4}{9}\) × \(\frac{2}{2}\) – \(\frac{1}{6}\) × \(\frac{3}{3}\)
\(\frac{8}{18}\) – \(\frac{3}{18}\) = \(\frac{5}{18}\)
\(\frac{4}{9}-\frac{1}{6}\) = \(\frac{5}{18}\)

Question 23.
\(\frac{11}{12}-\frac{7}{15}\)
\(\frac{□}{□}\)

Answer:
\(\frac{11}{12}-\frac{7}{15}\)
First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD = 60
\(\frac{11}{12}\) – \(\frac{7}{15}\)
\(\frac{11}{12}\) × \(\frac{5}{5}\) – \(\frac{7}{15}\) × \(\frac{4}{4}\)
\(\frac{55}{60}\) – \(\frac{28}{60}\) = \(\frac{27}{60}\)
\(\frac{11}{12}-\frac{7}{15}\) = \(\frac{27}{60}\) = \(\frac{9}{20}\)

Algebra Find the unknown number.

Question 24.
\(\frac{9}{10}\) − ■ = \(\frac{1}{5}\)
■ = \(\frac{□}{□}\)

Answer:
\(\frac{9}{10}\) – \(\frac{1}{5}\) = ■
■ = \(\frac{9}{10}\) – \(\frac{1}{5}\)
■ = \(\frac{9}{10}\) – \(\frac{2}{10}\) = \(\frac{7}{10}\)
■ = \(\frac{7}{10}\)

Question 25.
\(\frac{5}{12}\) + ■ = \(\frac{1}{2}\)
■ = \(\frac{□}{□}\)

Answer:
\(\frac{5}{12}\) + ■ = \(\frac{1}{2}\)
\(\frac{5}{12}\) − \(\frac{1}{2}\) = – ■
– ■ = \(\frac{5}{12}\) − \(\frac{1}{2}\)
– ■ = \(\frac{5}{12}\) − \(\frac{1}{2}\) × \(\frac{6}{6}\)
– ■ = \(\frac{5}{12}\) − \(\frac{6}{12}\) = – \(\frac{1}{12}\)
■ = \(\frac{1}{12}\)

Problem Solving – Page No. 262

Use the picture for 26–27.

Question 26.
Sara is making a key chain using the bead design shown. What fraction of the beads in her design are either blue or red?
\(\frac{□}{□}\)

Answer: \(\frac{11}{15}\)

Explanation:
Total number of red beads = 6
Total number of blue beads = 5
Total number of beads = 6 + 5 = 11
The fraction of beads = \(\frac{11}{15}\)

Question 27.
In making the key chain, Sara uses the pattern of beads 3 times. After the key chain is complete, what fraction of the beads in the key chain are either white or blue?
______ \(\frac{□}{□}\)

Answer: 1 \(\frac{4}{5}\)

Explanation:
In making the key chain, Sara uses the pattern of beads 3 times.
Given that Sara uses the pattern of beads 3 times.
Total number of blue beads = 5
5 × 3 = 15
Number of white beads = 4
4 × 3 = 12
15 + 12 = 27
Actual number of beads = 15
So, the fraction is \(\frac{27}{15}\) = \(\frac{9}{5}\)
The mixed fraction of \(\frac{9}{5}\) is 1 \(\frac{4}{5}\)

Question 28.
Jamie had \(\frac{4}{5}\) of a spool of twine. He then used \(\frac{1}{2}\) of a spool of twine to make friendship knots. He claims to have \(\frac{3}{10}\) of the original spool of twine left over. Explain how you know whether Jamie’s claim is reasonable.
Type below:
_________

Answer: Jamie’s claim is reasonable

Explanation:
Jamie had \(\frac{4}{5}\) of a spool of twine. He then used \(\frac{1}{2}\) of a spool of twine to make friendship knots. He claims to have \(\frac{3}{10}\) of the original spool of twine left over.
To know whether his estimation is reasonable or not we have to subtract the total spool of twine from used spool of twine.
\(\frac{4}{5}\) – \(\frac{1}{2}\)
LCD = 10
\(\frac{4}{5}\) × \(\frac{2}{2}\)  – \(\frac{1}{2}\) × \(\frac{5}{5}\)
\(\frac{8}{10}\) – \(\frac{5}{10}\) = \(\frac{3}{10}\)
By this is can that Jamie’s claim is reasonable.

Question 29.
Test Prep Which equation represents the fraction of beads that are green or yellow?

Options:
a. \(\frac{1}{4}+\frac{1}{8}=\frac{3}{8}\)
b. [atex]\frac{1}{2}+\frac{1}{4}=\frac{3}{4}[/latex]
c. \(\frac{1}{2}+\frac{1}{8}=\frac{5}{8}\)
d. \(\frac{3}{4}+\frac{2}{8}=1\)

Answer: [atex]\frac{1}{2}+\frac{1}{4}=\frac{3}{4}[/latex]

Explanation:
Number of green beads = 4 = [atex]\frac{1}{2}[/latex]
Number of blue beads = 3 = [atex]\frac{3}{4}[/latex]
Number of yellow beads = 1 [atex]\frac{1}{4}[/latex]
The fraction of beads that are green or yellow is [atex]\frac{1}{2}+\frac{1}{4}=\frac{3}{4}[/latex]
The correct answer is option B.

Mid-Chapter Checkpoint – Vocabulary – Page No. 263

Choose the best term from the box.

Question 1.
A ________ is a number that is a multiple of two or more numbers.
________

Answer: Common Multiple
A Common Multiple is a number that is a multiple of two or more numbers.

Question 2.
A ________ is a common multiple of two or more denominators.
________

Answer: Common denominator
A Common denominator is a common multiple of two or more denominators.

Concepts and Skills

Estimate the sum or difference.

Question 3.
\(\frac{8}{9}+\frac{4}{7}\)
about ______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{2}\)

Place \(\frac{8}{9}\) on the number line.
\(\frac{8}{9}\) lies between \(\frac{1}{2}\) and 1.
\(\frac{8}{9}\) is closer to 1.
Place \(\frac{4}{7}\) on the number line.
\(\frac{4}{7}\) lies between \(\frac{1}{2}\) and 1.
\(\frac{4}{7}\) is closer to \(\frac{1}{2}\).
1 + \(\frac{1}{2}\) = 1 \(\frac{1}{2}\)

Question 4.
\(3 \frac{2}{5}-\frac{5}{8}\)
about ______

Answer: 3

Explanation:
Place \(\frac{2}{5}\) on the number line.
\(\frac{2}{5}\) lies between 0 and \(\frac{1}{2}\)
\(\frac{2}{5}\) is closer to \(\frac{1}{2}\)
Place \(\frac{5}{8}\) on the number line.
\(\frac{5}{8}\) lies between \(\frac{1}{2}\) and 1.
\(\frac{5}{8}\) is closer to \(\frac{1}{2}\)
3 + \(\frac{1}{2}\) – \(\frac{1}{2}\) = 3
\(3 \frac{2}{5}-\frac{5}{8}\) = 3

Question 5.
\(1 \frac{5}{6}+2 \frac{2}{11}\)
about ______

Answer: 4

Explanation:
Place \(\frac{5}{6}\) on the number line.
\(\frac{5}{6}\) lies between \(\frac{1}{2}\) and 1.
\(\frac{5}{6}\) is closer to 1.
Place \(\frac{2}{11}\) on the number line.
\(\frac{2}{11}\) lies between \(\frac{1}{2}\) and 0.
\(\frac{2}{11}\) is closer to 0
1 + 1 + 2 + 0 = 4
\(1 \frac{5}{6}+2 \frac{2}{11}\) = 4

Use a common denominator to write an equivalent fraction for each fraction.

Question 6.
\(\frac{1}{6}, \frac{1}{9}\)
common denominator:
Type below:
__________

Answer: 54
Multiply the denominators
6 × 9 = 54
Thus the common denominator of \(\frac{1}{6}, \frac{1}{9}\) is 54

Question 7.
\(\frac{3}{8}, \frac{3}{10}\)
common denominator:
Type below:
__________

Answer: 80
Multiply the denominators
8 × 10 = 80
The common denominator of \(\frac{3}{8}, \frac{3}{10}\) is 80

Question 8.
\(\frac{1}{9}, \frac{5}{12}\)
common denominator:
Type below:
__________

Answer: 36
Multiply the denominators
9 × 12 = 108
The common denominator of \(\frac{1}{9}, \frac{5}{12}\) is 108

Use the least common denominator to write an equivalent fraction for each fraction.

Question 9.
\(\frac{2}{5}, \frac{1}{10}\)
least common denominator: ______
Explain:
__________

Answer: 10

Explanation:
Multiply the denominators
5 × 10 = 50
The least common denominators of \(\frac{2}{5}, \frac{1}{10}\) is 10.

Question 10.
\(\frac{5}{6}, \frac{3}{8}\)
least common denominator: ______
Explain:
__________

Answer: 24

Explanation:
Multiply the denominators
The least common denominator of 6 and 8 is 24
Thus the LCD of \(\frac{5}{6}, \frac{3}{8}\) is 24

Question 11.
\(\frac{1}{3}, \frac{2}{7}\)
least common denominator: ______
Explain:
__________

Answer: 21

Explanation:
Multiply the denominators
The least common denominator of 3 and 7 is 21.
Thus the LCD of \(\frac{1}{3}, \frac{2}{7}\) is 21.

Find the sum or difference. Write your answer in simplest form.

Question 12.
\(\frac{11}{18}-\frac{1}{6}\)
\(\frac{□}{□}\)

Answer: \(\frac{8}{18}\)

Explanation:
Make the fractions like denominators.
\(\frac{11}{18}\) – \(\frac{1}{6}\)
\(\frac{1}{6}\) × \(\frac{3}{3}\) = \(\frac{3}{18}\)
\(\frac{11}{18}\) – \(\frac{3}{18}\) = \(\frac{8}{18}\)

Question 13.
\(\frac{2}{7}+\frac{2}{5}\)
\(\frac{□}{□}\)

Answer: \(\frac{24}{35}\)

Explanation:
Make the fractions like denominators.
\(\frac{2}{7}\) × \(\frac{5}{5}\) = \(\frac{10}{35}\)
\(\frac{2}{5}\) × \(\frac{7}{7}\) = \(\frac{14}{35}\)
\(\frac{10}{35}\) + \(\frac{14}{35}\) = \(\frac{24}{35}\)
Thus \(\frac{2}{7}+\frac{2}{5}\) = \(\frac{24}{35}\)

Question 14.
\(\frac{3}{4}-\frac{3}{10}\)
\(\frac{□}{□}\)

Answer: \(\frac{18}{40}\)

Explanation:
Make the fractions like denominators.
\(\frac{3}{4}\) × \(\frac{10}{10}\) = \(\frac{30}{40}\)
\(\frac{3}{10}\) × \(\frac{4}{4}\) = \(\frac{12}{40}\)
\(\frac{30}{40}\) – \(\frac{12}{40}\) = \(\frac{18}{40}\)

Mid-Chapter Checkpoint – Page No. 264

Question 15.
Mrs. Vargas bakes a pie for her book club meeting. The shaded part of the diagram below shows the amount of pie left after the meeting. That evening, Mr. Vargas eats \(\frac{1}{4}\) of the whole pie. What fraction represents the amount of pie remaining?

\(\frac{□}{□}\)

Answer: \(\frac{1}{4}\)

Explanation:
Mrs. Vargas bakes a pie for her book club meeting. The shaded part of the diagram below shows the amount of pie left after the meeting.
So, the fraction of the pie is \(\frac{1}{2}\)
That evening, Mr. Vargas eats \(\frac{1}{4}\) of the whole pie.
\(\frac{1}{2}\) – \(\frac{1}{4}\) = \(\frac{1}{4}\)
Thus the fraction represents the amount of pie remaining is \(\frac{1}{4}\)

Question 16.
Keisha makes a large sandwich for a family picnic. She takes \(\frac{1}{2}\) of the sandwich to the picnic. At the picnic, her family eats \(\frac{3}{8}\) of the whole sandwich. What fraction of the whole sandwich does Keisha bring back from the picnic?
\(\frac{□}{□}\)

Answer: \(\frac{1}{8}\)

Explanation:
Keisha makes a large sandwich for a family picnic. She takes \(\frac{1}{2}\) of the sandwich to the picnic.
At the picnic, her family eats \(\frac{3}{8}\) of the whole sandwich.
\(\frac{1}{2}\) – \(\frac{3}{8}\)
\(\frac{1}{2}\) × \(\frac{4}{4}\) – \(\frac{3}{8}\)
\(\frac{4}{8}\) – \(\frac{3}{8}\) = \(\frac{1}{8}\)
Thus Keisha brought \(\frac{1}{8}\) of the sandwich from the picnic.

Question 17.
Mike is mixing paint for his walls. He mixes \(\frac{1}{6}\) gallon blue paint and \(\frac{5}{8}\) gallon green paint in a large container. What fraction represents the total amount of paint Mike mixes?
\(\frac{□}{□}\)

Answer: \(\frac{19}{24}\)

Explanation:
Mike is mixing paint for his walls. He mixes \(\frac{1}{6}\) gallon blue paint and \(\frac{5}{8}\) gallon green paint in a large container.
\(\frac{1}{6}\) + \(\frac{5}{8}\)
\(\frac{1}{6}\) × \(\frac{8}{8}\)  + \(\frac{5}{8}\) × \(\frac{6}{6}\)
\(\frac{8}{48}\)  + \(\frac{30}{48}\)
\(\frac{38}{48}\) = \(\frac{19}{24}\)
Therefore the total amount of paint Mike mixes is \(\frac{19}{24}\)

Share and Show – Page No. 266

Question 1.
Use a common denominator to write equivalent fractions with like denominators and then find the sum. Write your answer in the simplest form.
7 \(\frac{2}{5}\) = ■
+ 4 \(\frac{3}{4}\) = + ■
—————————
■
_____ \(\frac{□}{□}\)

Answer: 12 \(\frac{3}{20}\)

Explanation:
First convert the mixed fraction to proper fraction.
7 \(\frac{2}{5}\) = \(\frac{37}{5}\)
4 \(\frac{3}{4}\) = \(\frac{19}{4}\)
\(\frac{37}{5}\) + \(\frac{19}{4}\)
= \(\frac{37}{5}\) × \(\frac{4}{4}\) = \(\frac{148}{20}\)
\(\frac{19}{4}\) × \(\frac{5}{5}\) = \(\frac{95}{20}\)
\(\frac{148}{20}\) + \(\frac{95}{20}\) = \(\frac{243}{20}\)
Now convert it into mixed fraction = 12 \(\frac{3}{20}\)

Find the sum. Write your answer in simplest form.

Question 2.
\(2 \frac{3}{4}+3 \frac{3}{10}\)
_____ \(\frac{□}{□}\)

Answer: 6 \(\frac{1}{20}\)

Explanation:
First convert the mixed fraction to proper fraction.
\(2 \frac{3}{4}\) = \(\frac{11}{4}\)
3 \(\frac{3}{10}\) = \(\frac{33}{10}\)
Now make the common denominators of the above fractions.
\(\frac{11}{4}\) × \(\frac{10}{10}\) = \(\frac{110}{40}\)
\(\frac{33}{10}\) × \(\frac{4}{4}\) = \(\frac{132}{40}\) = \(\frac{121}{20}\)
Now convert the fraction into a mixed fraction.
\(\frac{121}{20}\) = 6 \(\frac{1}{20}\)

Lesson 6.6 Go Math 5th Grade Question 3.
\(5 \frac{3}{4}+1 \frac{1}{3}\)
_____ \(\frac{□}{□}\)

Answer: 7 \(\frac{1}{12}\)

Explanation:
First convert the mixed fraction to proper fraction.
5 \(\frac{3}{4}\) = \(\frac{23}{4}\)
1 \(\frac{1}{3}\) = \(\frac{4}{3}\)
\(\frac{23}{4}\) + \(\frac{4}{3}\)
\(\frac{23}{4}\) × \(\frac{3}{3}\) = \(\frac{69}{12}\)
\(\frac{4}{3}\) × \(\frac{4}{4}\) = \(\frac{16}{12}\)
\(\frac{69}{12}\) + \(\frac{16}{12}\) = \(\frac{85}{12}\)
The mixed fraction of \(\frac{85}{12}\) = 7 \(\frac{1}{12}\)

Question 4.
\(3 \frac{4}{5}+2 \frac{3}{10}\)
_____ \(\frac{□}{□}\)

Answer: 6 \(\frac{1}{10}\)

Explanation:
First convert the mixed fraction to proper fraction.
3 \(\frac{4}{5}\) = \(\frac{19}{5}\)
2 \(\frac{3}{10}\) = \(\frac{23}{10}\)
\(\frac{19}{5}\) + \(\frac{23}{10}\)
Now make the common denominators of the above fractions.
\(\frac{19}{5}\) × \(\frac{2}{2}\) = \(\frac{38}{10}\)
\(\frac{38}{10}\) + \(\frac{23}{10}\) = \(\frac{61}{10}\)
The mixed fraction of \(\frac{61}{10}\) = 6 \(\frac{1}{10}\)

Page No. 267

Find the difference. Write your answer in simplest form.

Question 5.
\(9 \frac{5}{6}-2 \frac{1}{3}\)
_____ \(\frac{□}{□}\)

Answer: 7 \(\frac{1}{2}\)

Explanation:
\(9 \frac{5}{6}-2 \frac{1}{3}\) = \(\frac{59}{6}\) – \(\frac{14}{6}\)
= \(\frac{45}{6}\) = \(\frac{15}{2}\) = 7 \(\frac{1}{2}\)

Question 6.
\(10 \frac{5}{9}-9 \frac{1}{6}\)
_____ \(\frac{□}{□}\)

Answer: 1 \(\frac{7}{18}\)

Explanation:
\(10 \frac{5}{9}-9 \frac{1}{6}\) = \(\frac{95}{9}\) – \(\frac{55}{6}\)
= \(\frac{190}{18}\) – \(\frac{165}{18}\) = \(\frac{25}{18}\)
= 1 \(\frac{7}{18}\)
\(10 \frac{5}{9}-9 \frac{1}{6}\) = 1 \(\frac{7}{18}\)

Question 7.
\(7 \frac{2}{3}-3 \frac{1}{6}\)
_____ \(\frac{□}{□}\)

Answer: 4 \(\frac{1}{2}\)

Explanation:
\(7 \frac{2}{3}-3 \frac{1}{6}\)
\(\frac{23}{3}\) – \(\frac{19}{6}\) = \(\frac{46}{6}\) – \(\frac{19}{6}\)
= \(\frac{27}{6}\) = 4 \(\frac{1}{2}\)
\(7 \frac{2}{3}-3 \frac{1}{6}\) = 4 \(\frac{1}{2}\)

On Your Own

Find the sum or difference. Write your answer in simplest form.

Question 8.
\(1 \frac{3}{10}+2 \frac{2}{5}\)
_____ \(\frac{□}{□}\)

Answer: 3 \(\frac{7}{10}\)

Explanation:
\(1 \frac{3}{10}+2 \frac{2}{5}\)
\(\frac{13}{10}\) + \(\frac{12}{5}\) = \(\frac{13}{10}\) + \(\frac{24}{10}\)
= \(\frac{37}{10}\) = 3 \(\frac{7}{10}\)
Thus \(1 \frac{3}{10}+2 \frac{2}{5}\) = 3 \(\frac{7}{10}\)

Question 9.
\(3 \frac{4}{9}+3 \frac{1}{2}\)
_____ \(\frac{□}{□}\)

Answer: 6 \(\frac{17}{18}\)

Explanation:
\(3 \frac{4}{9}+3 \frac{1}{2}\)
\(\frac{31}{9}\) + \(\frac{7}{2}\) = \(\frac{62}{18}\) + \(\frac{63}{18}\)
\(\frac{125}{18}\) = 6 \(\frac{17}{18}\)
\(3 \frac{4}{9}+3 \frac{1}{2}\) = 6 \(\frac{17}{18}\)

Question 10.
\(2 \frac{1}{2}+2 \frac{1}{3}\)
_____ \(\frac{□}{□}\)

Answer: 4 \(\frac{5}{6}\)

Explanation:
\(2 \frac{1}{2}+2 \frac{1}{3}\) = \(\frac{5}{2}\) + \(\frac{7}{3}\)
\(\frac{15}{6}\) + \(\frac{14}{6}\)= \(\frac{29}{6}\)
The mixed fraction of \(\frac{29}{6}\) is 4 \(\frac{5}{6}\)

Go Math Grade 5 Chapter 6 Lesson 6.6 Answer Key Question 11.
\(5 \frac{1}{4}+9 \frac{1}{3}\)
_____ \(\frac{□}{□}\)

Answer: 14 \(\frac{7}{12}\)

Explanation:
\(5 \frac{1}{4}+9 \frac{1}{3}\) = \(\frac{21}{4}\) + \(\frac{28}{3}\)
\(\frac{63}{12}\) + \(\frac{112}{12}\) = \(\frac{175}{12}\)
The mixed fraction of \(\frac{175}{12}\) is 14 \(\frac{7}{12}\)

Question 12.
\(8 \frac{1}{6}+7 \frac{3}{8}\)
_____ \(\frac{□}{□}\)

Answer: 15 \(\frac{13}{24}\)

Explanation:
\(8 \frac{1}{6}+7 \frac{3}{8}\) = \(\frac{49}{6}\) + \(\frac{59}{8}\)
\(\frac{196}{24}\) + \(\frac{177}{24}\) = \(\frac{373}{24}\)
The mixed fraction of \(\frac{373}{24}\) is 15 \(\frac{13}{24}\)

Question 13.
\(14 \frac{7}{12}-5 \frac{1}{4}\)
_____ \(\frac{□}{□}\)

Answer: 9 \(\frac{1}{3}\)

Explanation:
\(14 \frac{7}{12}-5 \frac{1}{4}\) = \(\frac{175}{12}\) – \(\frac{21}{4}\)
\(\frac{175}{12}\) – \(\frac{63}{12}\) = \(\frac{112}{12}\)
The mixed fraction of \(\frac{112}{12}\) is 9 \(\frac{1}{3}\)

Question 14.
\(12 \frac{3}{4}-6 \frac{1}{6}\)
_____ \(\frac{□}{□}\)

Answer: 6 \(\frac{7}{12}\)

Explanation:
\(12 \frac{3}{4}-6 \frac{1}{6}\) = \(\frac{51}{4}\) – \(\frac{37}{6}\)
\(\frac{153}{12}\) – \(\frac{74}{12}\) = \(\frac{79}{12}\)
The mixed fraction of \(\frac{79}{12}\) is 6 \(\frac{7}{12}\)

Question 15.
\(2 \frac{5}{8}-1 \frac{1}{4}\)
_____ \(\frac{□}{□}\)

Answer: 1 \(\frac{3}{8}\)

Explanation:
\(2 \frac{5}{8}-1 \frac{1}{4}\)
\(\frac{21}{8}\) – \(\frac{5}{4}\) = \(\frac{21}{8}\) – \(\frac{10}{8}\)
= \(\frac{11}{8}\)
The mixed fraction of \(\frac{11}{8}\) is 1 \(\frac{3}{8}\)

Question 16.
\(10 \frac{1}{2}-2 \frac{1}{5}\)
_____ \(\frac{□}{□}\)

Answer: 8 \(\frac{3}{10}\)

Explanation:
\(10 \frac{1}{2}-2 \frac{1}{5}\) = \(\frac{21}{2}\) – \(\frac{11}{5}\)
\(\frac{105}{10}\) – \(\frac{22}{10}\) = \(\frac{83}{10}\)
The mixed fraction of \(\frac{83}{10}\) is 8 \(\frac{3}{10}\)

Practice: Copy and Solve Find the sum or difference. Write your answer in simplest form.

Question 17.
\(1 \frac{5}{12}+4 \frac{1}{6}\)
_____ \(\frac{□}{□}\)

Answer: 5 \(\frac{7}{12}\)

Explanation:
\(1 \frac{5}{12}+4 \frac{1}{6}\) = \(\frac{17}{12}\) + \(\frac{25}{6}\)
\(\frac{17}{12}\) + \(\frac{50}{12}\) = \(\frac{67}{12}\)
The mixed fraction of \(\frac{67}{12}\) is 5 \(\frac{7}{12}\)

Question 18.
\(8 \frac{1}{2}+6 \frac{3}{5}\)
_____ \(\frac{□}{□}\)

Answer: 15 \(\frac{1}{10}\)

Explanation:
\(8 \frac{1}{2}+6 \frac{3}{5}\) = \(\frac{17}{2}\) + \(\frac{33}{5}\)
\(\frac{85}{10}\) + \(\frac{66}{10}\) = \(\frac{151}{10}\)
The mixed fraction of \(\frac{151}{10}\) is 15 \(\frac{1}{10}\)
\(8 \frac{1}{2}+6 \frac{3}{5}\) = 15 \(\frac{1}{10}\)

Question 19.
\(2 \frac{1}{6}+4 \frac{5}{9}\)
_____ \(\frac{□}{□}\)

Answer: 6 \(\frac{13}{18}\)

Explanation:
\(2 \frac{1}{6}+4 \frac{5}{9}\) = \(\frac{13}{6}\) + \(\frac{41}{9}\)
\(\frac{39}{18}\) + \(\frac{82}{18}\) = \(\frac{121}{18}\)
The mixed fraction of \(\frac{121}{18}\) is 6 \(\frac{13}{18}\)
\(2 \frac{1}{6}+4 \frac{5}{9}\) = 6 \(\frac{13}{18}\)

Question 20.
\(20 \frac{5}{8}+\frac{5}{12}\)
_____ \(\frac{□}{□}\)

Answer: 21 \(\frac{1}{24}\)

Explanation:
\(20 \frac{5}{8}+\frac{5}{12}\) = \(\frac{165}{8}\) + \(\frac{5}{12}\)
\(\frac{495}{24}\) + \(\frac{10}{24}\) = \(\frac{505}{24}\)
The mixed fraction of \(\frac{505}{24}\) is 21 \(\frac{1}{24}\)
\(20 \frac{5}{8}+\frac{5}{12}\) = 21 \(\frac{1}{24}\)

Question 21.
\(3 \frac{2}{3}-1 \frac{1}{6}\)
_____ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{2}\)

Explanation:
\(3 \frac{2}{3}-1 \frac{1}{6}\) = \(\frac{11}{3}\) – \(\frac{7}{6}\)
\(\frac{22}{6}\) – \(\frac{7}{6}\) = \(\frac{15}{6}\) = \(\frac{5}{2}\)
The mixed fraction of \(\frac{5}{2}\) is 2 \(\frac{1}{2}\)
\(3 \frac{2}{3}-1 \frac{1}{6}\) = 2 \(\frac{1}{2}\)

Question 22.
\(5 \frac{6}{7}-1 \frac{2}{3}\)
_____ \(\frac{□}{□}\)

Answer: 4 \(\frac{4}{21}\)

Explanation:
\(5 \frac{6}{7}-1 \frac{2}{3}\) = \(\frac{41}{7}\) – \(\frac{5}{3}\)
\(\frac{123}{21}\) – \(\frac{35}{21}\) = \(\frac{88}{21}\)
The mixed fraction of \(\frac{88}{21}\) is 4 \(\frac{4}{21}\)

Question 23.
\(2 \frac{7}{8}-\frac{1}{2}\)
_____ \(\frac{□}{□}\)

Answer: 2 \(\frac{3}{8}\)

Explanation:
\(2 \frac{7}{8}-\frac{1}{2}\) = \(\frac{23}{8}\) – \(\frac{1}{2}\)
= \(\frac{23}{8}\) – \(\frac{4}{8}\) = \(\frac{19}{8}\)
The mixed fraction of \(\frac{19}{8}\) is 2 \(\frac{3}{8}\)
So, \(2 \frac{7}{8}-\frac{1}{2}\) = 2 \(\frac{3}{8}\)

Question 24.
\(4 \frac{7}{12}-1 \frac{2}{9}\)
_____ \(\frac{□}{□}\)

Answer: 3 \(\frac{13}{36}\)

Explanation:
\(4 \frac{7}{12}-1 \frac{2}{9}\) = \(\frac{55}{12}\) – \(\frac{11}{9}\)
\(\frac{165}{36}\) – \(\frac{44}{36}\) = \(\frac{121}{36}\)
The mixed fraction of \(\frac{121}{36}\) is 3 \(\frac{13}{36}\)

Problem Solving – Page No. 268

Use the table to solve 25–28.

Question 25.
Gavin is mixing a batch of Sunrise Orange paint for an art project. How much paint does Gavin mix?
_____ \(\frac{□}{□}\) ounces

Answer: 5 \(\frac{7}{8}\) ounces

Explanation:
Gavin is mixing a batch of Sunrise Orange paint for an art project.
2 \(\frac{5}{8}\) + 3 \(\frac{1}{4}\)
Solving the whole numbers
2 + 3 = 5
Add the fraction parts
\(\frac{5}{8}\) + \(\frac{1}{4}\)
LCD = 8
\(\frac{5}{8}\) + \(\frac{2}{8}\) = \(\frac{7}{8}\)
5 + \(\frac{7}{8}\) = 5 \(\frac{7}{8}\) ounces

Question 26.
Gavin plans to mix a batch of Tangerine paint. He expects to have a total of 5 \(\frac{3}{10}\) ounces of paint after he mixes the amounts of red and yellow. Explain how you can tell if Gavin’s expectation is reasonable.
Type below:
_________

Answer:
Gavin plans to mix a batch of Tangerine paint. He expects to have a total of 5 \(\frac{3}{10}\) ounces of paint after he mixes the amounts of red and yellow.
To mix a batch of Tangerine paint he need 3 \(\frac{9}{10}\) red and 2 \(\frac{3}{8}\) yellow paint.
Add the fractions
3 + \(\frac{9}{10}\) + 2 + \(\frac{3}{8}\)
Solving the whole numbers
3 + 2 = 5
\(\frac{9}{10}\) + \(\frac{3}{8}\)
LCD = 40
\(\frac{9}{10}\) + \(\frac{3}{8}\) = \(\frac{36}{40}\) + \(\frac{15}{40}\) = \(\frac{51}{40}\) = 1 \(\frac{11}{40}\)
5 + 1 \(\frac{11}{40}\) = 6 \(\frac{11}{40}\)

Question 27.
For a special project, Gavin mixes the amount of red from one shade of paint with the amount of yellow from a different shade. He mixes the batch so he will have the greatest possible amount of paint. What amounts of red and yellow from which shades are used in the mixture for the special project? Explain your answer.
Type below:
_________

Answer:
Gavin used red paint from mango and yellow paint from Sunrise Orange.
5 \(\frac{5}{6}\) + 3 \(\frac{1}{4}\)
Solving the parts of the whole number
5 + 3 = 8
Solving the fraction part
\(\frac{5}{6}\) + \(\frac{1}{4}\)
LCD = 12
\(\frac{10}{12}\) + \(\frac{3}{12}\) = \(\frac{13}{12}\)
\(\frac{13}{12}\) = 1 \(\frac{1}{12}\)

Question 28.
Gavin needs to make 2 batches of Mango paint. Explain how you could find the total amount of paint Gavin mixed.
Type below:
_________

Answer:
Gavin used Red paint and Yellow Paint to make Mango shade.
For one batch he need to add 5 \(\frac{5}{6}\) + 5 \(\frac{5}{6}\)
Foe 2 batches
5 \(\frac{5}{6}\)+ 5 \(\frac{5}{6}\) + 5 \(\frac{5}{6}\) + 5 \(\frac{5}{6}\)
Solving the whole numbers
5 + 5 + 5 + 5 = 20
Solving the fractions part
\(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\) + \(\frac{5}{6}\) = \(\frac{20}{6}\)
= \(\frac{10}{3}\)
Gavin mixed \(\frac{10}{3}\) of paint to make 2 batches of Mango Paint.

Question 29.
Test Prep Yolanda walked 3 \(\frac{6}{10}\) miles. Then she walked 4 \(\frac{1}{2}\) more miles. How many miles did Yolanda walk?
Options:
a. 7 \(\frac{1}{10}\) miles
b. 7 \(\frac{7}{10}\) miles
c. 8 \(\frac{1}{10}\) miles
d. 8 \(\frac{7}{10}\) miles

Answer: 8 \(\frac{1}{10}\) miles

Explanation:
Test Prep Yolanda walked 3 \(\frac{6}{10}\) miles.
Then she walked 4 \(\frac{1}{2}\) more miles.
3 \(\frac{6}{10}\) + 4 \(\frac{1}{2}\) = 3 + \(\frac{6}{10}\) + 4 + \(\frac{1}{2}\)
Add whole numbers
3 + 4 = 7
Add the fractions
\(\frac{6}{10}\) + \(\frac{1}{2}\)
LCD = 10
\(\frac{6}{10}\) + \(\frac{5}{10}\) = \(\frac{11}{10}\)
\(\frac{11}{10}\) = 8 \(\frac{1}{10}\) miles
Thus the correct answer is option C.

Share and Show – Page No. 270

Estimate. Then find the difference and write it in simplest form.

Question 1.
Estimate: ______
1 \(\frac{3}{4}-\frac{7}{8}\)
Estimate: _____ \(\frac{□}{□}\)
Difference: _____ \(\frac{□}{□}\)

Answer:
Estimate: 1
Difference: \(\frac{7}{8}\)

Explanation:
Estimation: 1 + \(\frac{3}{4}\) – \(\frac{7}{8}\)
\(\frac{7}{8}\) is close to 1.
\(\frac{3}{4}\) is close to 1.
1 + 1 – 1 = 1
Difference: 1 \(\frac{3}{4}-\frac{7}{8}\)
1 + \(\frac{3}{4}\) – \(\frac{7}{8}\)
\(\frac{3}{4}\) – \(\frac{7}{8}\)
\(\frac{3}{4}\) × \(\frac{8}{8}\) – \(\frac{7}{8}\) × \(\frac{4}{4}\)
\(\frac{24}{32}\) – \(\frac{28}{32}\) = – \(\frac{1}{8}\)
1 – \(\frac{1}{8}\) = \(\frac{7}{8}\)

Go Math Grade 5 Chapter 6 Lesson 6.7 Answer Key Question 2.
Estimate: ______
\(12 \frac{1}{9}-7 \frac{1}{3}\)
Estimate: _____ \(\frac{□}{□}\)
Difference: _____ \(\frac{□}{□}\)

Answer:
Estimate: 5
Difference: 4 \(\frac{7}{9}\)

Explanation:
Estimate: 12 + 0 – 7 – 0 = 5
Difference:
12 + \(\frac{1}{9}\) – 7 – \(\frac{1}{3}\)
12 – 7 = 5
\(\frac{1}{9}\) – \(\frac{1}{3}\) = \(\frac{1}{9}\) – \(\frac{3}{9}\) = – \(\frac{2}{9}\)
5 – \(\frac{2}{9}\) = 4 \(\frac{7}{9}\)

Page No. 271

Estimate. Then find the difference and write it in simplest form.

Question 3.
Estimate: ________
\(4 \frac{1}{2}-3 \frac{4}{5}\)
Estimate: _____ \(\frac{□}{□}\)
Difference: _____ \(\frac{□}{□}\)

Answer:
Estimate: \(\frac{1}{2}\)
Difference: \(\frac{7}{10}\)

Explanation:
\(4 \frac{1}{2}-3 \frac{4}{5}\)
4 – \(\frac{1}{2}\) – 3 – 1
= \(\frac{1}{2}\)
Difference:
\(4 \frac{1}{2}-3 \frac{4}{5}\)
4 \(\frac{1}{2}\) – 3 \(\frac{4}{5}\)
Solving the whole number parts
4 – 3 = 1
Solving the fraction parts
\(\frac{1}{2}\) – \(\frac{4}{5}\)
LCD = 10
\(\frac{5}{10}\) – \(\frac{8}{10}\) = – \(\frac{3}{10}\)
1 – \(\frac{3}{10}\) = \(\frac{7}{10}\)

Question 4.
Estimate: ________
\(9 \frac{1}{6}-2 \frac{3}{4}\)
Estimate: _____ \(\frac{□}{□}\)
Difference: _____ \(\frac{□}{□}\)

Answer:
Estimate: 6
Difference: 6 \(\frac{5}{12}\)

Explanation:
\(9 \frac{1}{6}-2 \frac{3}{4}\)
9 + 0 – 2 – 1 = 6
Difference:
\(9 \frac{1}{6}-2 \frac{3}{4}\)
9 + \(\frac{1}{6}\) – 2 – \(\frac{3}{4}\)
9 – 2 = 7
\(\frac{1}{6}\) – \(\frac{3}{4}\)
LCD = 12
\(\frac{2}{12}\) – \(\frac{9}{12}\) = – \(\frac{7}{12}\)
7 – \(\frac{7}{12}\) = 6 \(\frac{5}{12}\)
\(9 \frac{1}{6}-2 \frac{3}{4}\) = 6 \(\frac{5}{12}\)

On Your Own

Estimate. Then find the difference and write it in simplest form.

Question 5.
Estimate: ________
\(3 \frac{2}{3}-1 \frac{11}{12}\)
Estimate: _____ \(\frac{□}{□}\)
Difference: _____ \(\frac{□}{□}\)

Answer:
Estimate: 2
Difference: 1 \(\frac{3}{4}\)

Explanation:
Estimate:
\(3 \frac{2}{3}-1 \frac{11}{12}\)
\(\frac{2}{3}\) is close to 1.
\(\frac{11}{12}\) is close to 1.
3 + 1 – 1 – 1 = 2
Difference:
\(3 \frac{2}{3}-1 \frac{11}{12}\)
3 + \(\frac{2}{3}\) – 1 – \(\frac{11}{12}\)
3 – 1 = 2
Solving the fractions part
\(\frac{2}{3}\) – \(\frac{11}{12}\)
LCD = 12
\(\frac{8}{12}\) – \(\frac{11}{12}\) = – \(\frac{3}{12}\) = – \(\frac{1}{4}\)
3 – \(\frac{1}{4}\) = 1 \(\frac{3}{4}\)
\(3 \frac{2}{3}-1 \frac{11}{12}\) = 1 \(\frac{3}{4}\)

Lesson 6.7 Answer Key 5th Grade Question 6.
Estimate: ________
\(4 \frac{1}{4}-2 \frac{1}{3}\)
Estimate: _____ \(\frac{□}{□}\)
Difference: _____ \(\frac{□}{□}\)

Answer:
Estimate: 2
Difference: 1 \(\frac{11}{12}\)

Explanation:
\(4 \frac{1}{4}-2 \frac{1}{3}\)
\(\frac{1}{4}\) is close to 0.
\(\frac{1}{3}\) is close to 0.
4 – 2 = 2
Solving the fractions part
\(\frac{1}{4}\) – \(\frac{1}{3}\)
LCD = 12
\(\frac{1}{4}\) × \(\frac{3}{3}\) – \(\frac{1}{3}\) × \(\frac{4}{4}\)
\(\frac{3}{12}\) – \(\frac{4}{12}\) = – \(\frac{1}{12}\)
2 – \(\frac{1}{12}\) = 1 \(\frac{11}{12}\)

Question 7.
Estimate: ________
\(5 \frac{2}{5}-1 \frac{1}{2}\)
Estimate: _____ \(\frac{□}{□}\)
Difference: _____ \(\frac{□}{□}\)

Answer:
Estimate: 4
Difference: 3 \(\frac{9}{10}\)

Explanation:
Estimate:
\(5 \frac{2}{5}-1 \frac{1}{2}\)
5 + \(\frac{1}{2}\) – 1 – \(\frac{1}{2}\)
5 – 1 = 4
Solving the fractions part
\(5 \frac{2}{5}-1 \frac{1}{2}\)
LCD = 10
\(\frac{4}{10}\) – \(\frac{5}{10}\) = – \(\frac{1}{10}\)
4 – \(\frac{1}{10}\) = 3 \(\frac{9}{10}\)

Question 8.
\(7 \frac{5}{9}-2 \frac{5}{6}\)
Estimate: _____ \(\frac{□}{□}\)
Difference: _____ \(\frac{□}{□}\)

Answer:
Estimate: 4 \(\frac{1}{2}\)
Difference: 4 \(\frac{13}{18}\)

Explanation:
Estimate:
\(7 \frac{5}{9}-2 \frac{5}{6}\)
\(\frac{5}{9}\) is close to \(\frac{1}{2}\)
\(\frac{5}{6}\) is close to 1.
7 + \(\frac{1}{2}\) – 2 – 1
4 \(\frac{1}{2}\)
Difference:
\(7 \frac{5}{9}-2 \frac{5}{6}\)
7 + \(\frac{5}{9}\) – 2 – \(\frac{5}{6}\)
Solving the whole numbers
7 – 2 = 5
Solving the fraction part
\(\frac{5}{9}\) – \(\frac{5}{6}\)
LCD = 18
\(\frac{10}{18}\) – \(\frac{15}{18}\) = – \(\frac{5}{18}\)
5 – \(\frac{5}{18}\) = 4 \(\frac{13}{18}\)

Question 9.
Estimate: ________
\(7-5 \frac{2}{3}\)
Estimate: _____ \(\frac{□}{□}\)
Difference: _____ \(\frac{□}{□}\)

Answer:
Estimate: 1
Difference: 1 \(\frac{1}{3}\)

Explanation:
Estimate:
\(7-5 \frac{2}{3}\)
7 – 5 – \(\frac{2}{3}\)
7 – 5 – 1 = 1
Difference:
\(7-5 \frac{2}{3}\)
7 – 5 = 2
2 – \(\frac{2}{3}\) = 1 \(\frac{1}{3}\)
Thus \(7-5 \frac{2}{3}\) = 1 \(\frac{1}{3}\)

Question 10.
Estimate: ________
\(2 \frac{1}{5}-1 \frac{9}{10}\)
Estimate: _____ \(\frac{□}{□}\)
Difference: _____ \(\frac{□}{□}\)

Answer:
Estimate: 0
Difference: \(\frac{3}{10}\)

Explanation:
Estimate:
\(2 \frac{1}{5}-1 \frac{9}{10}\)
2 + 0 – 1 – 1 = 0
Difference:
\(2 \frac{1}{5}-1 \frac{9}{10}\)
2 \(\frac{1}{5}\) – 1 \(\frac{9}{10}\)
2 + \(\frac{1}{5}\) – 1 – \(\frac{9}{10}\)
Solving the whole number parts
2 – 1 = 1
\(\frac{1}{5}\) – \(\frac{9}{10}\)
LCD = 10
\(\frac{2}{10}\) – \(\frac{9}{10}\) = – \(\frac{7}{10}\)
1 – \(\frac{7}{10}\) = \(\frac{3}{10}\)

Practice: Copy and Solve Find the difference and write it in simplest form.

Question 11.
\(11 \frac{1}{9}-3 \frac{2}{3}\)
_____ \(\frac{□}{□}\)

Answer: 7 \(\frac{4}{9}\)

Explanation:
Rewriting our equation with parts separated
11 + \(\frac{1}{9}\) – 3 – \(\frac{2}{3}\)
Solving the whole number of parts
11 – 3 = 8
Solving the fraction parts
LCD = 9
\(\frac{1}{9}\) – \(\frac{2}{3}\)
\(\frac{1}{9}\) – \(\frac{6}{9}\) = – \(\frac{5}{9}\)
8 – \(\frac{5}{9}\) = 7 \(\frac{4}{9}\)

Question 12.
\(6-3 \frac{1}{2}\)
_____ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{2}\)

Explanation:
Rewriting our equation with parts separated
6 – 3 – \(\frac{1}{2}\)
3 – \(\frac{1}{2}\) = 2 \(\frac{1}{2}\)

Question 13.
\(4 \frac{3}{8}-3 \frac{1}{2}\)
\(\frac{□}{□}\)

Answer: \(\frac{7}{8}\)

Explanation:
Rewriting our equation with parts separated
4 + \(\frac{3}{8}\) – 3 – \(\frac{1}{2}\)
Solving the whole number parts
4 – 3 = 1
Solving the fraction parts
\(\frac{3}{8}\) – \(\frac{1}{2}\) = \(\frac{3}{8}\) – \(\frac{4}{8}\)
= – \(\frac{1}{8}\)
1 – \(\frac{1}{8}\) = \(\frac{7}{8}\)

Question 14.
\(9 \frac{1}{6}-3 \frac{5}{8}\)
_____ \(\frac{□}{□}\)

Answer: 5 \(\frac{13}{24}\)

Explanation:
Rewriting our equation with parts separated
9 + \(\frac{1}{6}\) – 3 – \(\frac{5}{8}\)
Solving the whole number parts
9 – 3 = 6
Solving the fraction parts
\(\frac{1}{6}\) – \(\frac{5}{8}\)
\(\frac{4}{24}\) – \(\frac{15}{24}\) = – \(\frac{11}{24}\)
6 – \(\frac{11}{24}\) = 5 \(\frac{13}{24}\)

Question 15.
\(1 \frac{1}{5}-\frac{1}{2}\)
\(\frac{□}{□}\)

Answer: \(\frac{7}{10}\)

Explanation:
Rewriting our equation with parts separated
1 + \(\frac{1}{5}\) – \(\frac{1}{2}\)
Solving the whole number parts
1 + 0 = 1
Solving the fraction parts
\(\frac{1}{5}\) – \(\frac{1}{2}\)
LCD = 10
\(\frac{2}{10}\) – \(\frac{5}{10}\) = – \(\frac{3}{10}\)
1 – \(\frac{3}{10}\) = \(\frac{7}{10}\)

Question 16.
\(13 \frac{1}{6}-3 \frac{4}{5}\)
_____ \(\frac{□}{□}\)

Answer: 9 \(\frac{11}{30}\)

Explanation:
Rewriting our equation with parts separated
13 + \(\frac{1}{6}\) – 3 – \(\frac{4}{5}\)
Solving the whole number parts
13 – 3 = 10
Solving the fraction parts
\(\frac{1}{6}\) – \(\frac{4}{5}\)
LCD = 30
\(\frac{5}{30}\) – \(\frac{24}{30}\) = – \(\frac{19}{30}\)
10 – \(\frac{19}{30}\) = 9 \(\frac{11}{30}\)

Question 17.
\(12 \frac{2}{5}-5 \frac{3}{4}\)
_____ \(\frac{□}{□}\)

Answer: 6 \(\frac{13}{20}\)

Explanation:
Rewriting our equation with parts separated
12 + \(\frac{2}{5}\) – 5 – \(\frac{3}{4}\)
Solving the whole number parts
12 – 5 = 7
Solving the fraction parts
\(\frac{2}{5}\) – \(\frac{3}{4}\)
LCD = 20
\(\frac{8}{20}\) – \(\frac{15}{20}\) = – \(\frac{7}{20}\)
7 – \(\frac{7}{20}\) = 6 \(\frac{13}{20}\)

Question 18.
\(7 \frac{3}{8}-2 \frac{7}{9}\)
_____ \(\frac{□}{□}\)

Answer: 4 \(\frac{43}{72}\)

Explanation:
7 + \(\frac{3}{8}\) – 2 – \(\frac{7}{9}\)
7 – 2 = 5
\(\frac{3}{8}\) – \(\frac{7}{9}\) = \(\frac{27}{72}\) – \(\frac{56}{72}\)
– \(\frac{29}{72}\)
5 – \(\frac{29}{72}\) = 4 \(\frac{43}{72}\)

Page No. 272

Connect to Reading

Summarize
An amusement park in Sandusky, Ohio, offers 17 amazing roller coasters for visitors to ride. One of the roller coasters runs at 60 miles per hour and has 3,900 feet of twisting track. This coaster also has 3 trains with 8 rows per train. Riders stand in rows of 4, for a total of 32 riders per train.

The operators of the coaster recorded the number of riders on each train during a run. On the first train, the operators reported that 7 \(\frac{1}{4}\) rows were filled. On the second train, all 8 rows were filled, and on the third train, 5 \(\frac{1}{2}\) rows were filled. How many more rows were filled on the first train than on the third train?

When you summarize, you restate the most important information in a shortened form to more easily understand what you have read.
Summarize the information given.
______________________
Use the summary to solve.

Question 19.
Solve the problem above.
Type below:
_________

Answer:
On the first train, the operators reported that 7 \(\frac{1}{4}\) rows were filled.
On the third train, 5 \(\frac{1}{2}\) rows were filled.
7 \(\frac{1}{4}\) – 5 \(\frac{1}{2}\)
Solving the whole numbers
7 – 5 = 2
Solving the fractions
\(\frac{1}{4}\) – \(\frac{1}{2}\) = – \(\frac{1}{4}\)
2 – \(\frac{1}{4}\) = 1 \(\frac{3}{4}\)
1 \(\frac{3}{4}\) more rows were filled on the first train than on the third train.

Question 20.
How many rows were empty on the third train? How many additional riders would it take to fill the empty rows? Explain your answer.
Type below:
_________

Answer:
The coaster also has 3 trains with 8 rows per train.
The third train has 8 rows.
On the third train, 5 \(\frac{1}{2}\) rows were filled.
8 – 5 \(\frac{1}{2}\)
8 – 5 – \(\frac{1}{2}\) = 2 \(\frac{1}{2}\)
2 \(\frac{1}{2}\) rows are empty.
So, it takes 10 additional riders to fill the empty rows on the third train.

Share and Show – Page No. 275

Write a rule for the sequence.

Question 1.
\(\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \cdots\)
Think: Is the sequence increasing or decreasing?
Rule: _________
Type below:
_________

Answer: The sequence is increasing order with difference \(\frac{1}{4}\)

Question 2.
\(\frac{1}{9}, \frac{1}{3}, \frac{5}{9}, \ldots\)
Type below:
_________

Answer: The sequence is increasing order with difference 2 in numerataor.

Write a rule for the sequence. Then, find the unknown term.

Question 3.
\(\frac{3}{10}, \frac{2}{5}\), \(\frac{□}{□}\) , \(\frac{3}{5}, \frac{7}{10}\)

Answer: The sequence is increasing order with difference \(\frac{1}{2}\)
LCD = 10
Add \(\frac{1}{2}\) to each term
Let the unknown fraction be x
\(\frac{3}{10}\), \(\frac{4}{10}\), x, \(\frac{6}{10}\), \(\frac{7}{10}\)
x = \(\frac{5}{10}\) = \(\frac{1}{2}\)

Question 4.
\(10 \frac{2}{3}, 9 \frac{11}{18}, 8 \frac{5}{9}\), ______ \(\frac{□}{□}\) , \(6 \frac{4}{9}\)

Answer: 7 \(\frac{1}{2}\)

Explanation:
\(\frac{32}{3}\), \(\frac{173}{18}\), \(\frac{77}{9}\), x, \(\frac{58}{9}\)
LCD = 54
\(\frac{576}{54}\), \(\frac{519}{54}\), \(\frac{462}{54}\), x, \(\frac{348}{54}\)
According to the series x = \(\frac{405}{54}\) = \(\frac{15}{2}\)
The mixed fraction of \(\frac{15}{2}\) is 7 \(\frac{1}{2}\)

Go Math Lesson 6 Extra Practice Answer Key Grade 5 Question 5.
\(1 \frac{1}{6}\), ______ \(\frac{□}{□}\) , \(1, \frac{11}{12}, \frac{5}{6}\)

Answer: 1 \(\frac{1}{12}\)

Explanation:
\(1 \frac{1}{6}\), ______ \(\frac{□}{□}\) , \(1, \frac{11}{12}, \frac{5}{6}\)
The LCD of the above fractons is 12
Convert them into improper fractions
\(\frac{14}{12}\), x, \(\frac{12}{12}\), \(\frac{11}{12}\), \(\frac{10}{12}\)
According to the series x = \(\frac{13}{12}\)
The mixed fraction of \(\frac{13}{12}\) is 1 \(\frac{1}{12}\)

Question 6.
\(2 \frac{3}{4}, 4,5 \frac{1}{4}, 6 \frac{1}{2}\), ______ \(\frac{□}{□}\)

Answer: 7 \(\frac{3}{4}\)

Explanation:
\(2 \frac{3}{4}, 4,5 \frac{1}{4}, 6 \frac{1}{2}\), ______ \(\frac{□}{□}\)
Convert the mixed fractions into improper fractions
\(\frac{11}{4}\), \(\frac{4}{1}\), \(\frac{21}{4}\), \(\frac{13}{2}\), x
\(\frac{11}{4}\), \(\frac{16}{4}\), \(\frac{21}{4}\), \(\frac{26}{4}\), x
According to the series x = \(\frac{31}{4}\)
The mixed fraction of \(\frac{31}{4}\) is 7 \(\frac{3}{4}\)

On Your Own

Write a rule for the sequence. Then, find the unknown term.

Question 7.
\(\frac{1}{8}, \frac{1}{2}\), \(\frac{□}{□}\) , \(1 \frac{1}{4}, 1 \frac{5}{8}\)

Answer: \(\frac{7}{8}\)

Explanation:
\(\frac{1}{8}, \frac{1}{2}\), \(1 \frac{1}{4}, 1 \frac{5}{8}\), x
LCD = 8
\(\frac{1}{8}, \frac{4}{8}\), \(\frac{10}{8}, \frac{26}{8}\), x
\(\frac{1}{8}\), \(\frac{4}{8}\), x, \(\frac{10}{8}\), \(\frac{26}{8}\)
The difference between the series is 3 in the numerator.
x = \(\frac{7}{8}\)

Question 8.
\(1 \frac{2}{3}, 1 \frac{3}{4}, 1 \frac{5}{6}, 1 \frac{11}{12}\), ______

Answer: 2

Explanation:
1 \(\frac{2}{3}\), 1 \(\frac{3}{4}\), 1 \(\frac{5}{6}\), 1 \(\frac{11}{12}\)
Convert the mixed fractions into improper fractions
\(\frac{5}{3}\), \(\frac{7}{4}\), \(\frac{11}{6}\), \(\frac{23}{12}\), x
The LCD is 12
\(\frac{20}{12}\), \(\frac{21}{12}\), \(\frac{22}{12}\), \(\frac{23}{12}\), x
x = \(\frac{24}{12}\) = 2

Question 9.
\(12 \frac{7}{8}, 10 \frac{3}{4}\), ______ \(\frac{□}{□}\) , \(6 \frac{1}{2}, 4 \frac{3}{8}\)

Answer: 8 \(\frac{5}{8}\)

Explanation:
\(12 \frac{7}{8}, 10 \frac{3}{4}\), x , \(6 \frac{1}{2}, 4 \frac{3}{8}\)
Convert the mixed fractions into improper fractions
\(\frac{103}{8}\), \(\frac{43}{4}\), x, \(\frac{13}{2}\), \(\frac{35}{8}\)
The LCD is 8
\(\frac{103}{8}\), \(\frac{86}{8}\), x, \(\frac{52}{8}\), \(\frac{35}{8}\)
x = \(\frac{69}{8}\)
The mixed fraction of \(\frac{69}{8}\) is 8 \(\frac{5}{8}\)

Question 10.
\(9 \frac{1}{3}\), ______ \(\frac{□}{□}\) , \(6 \frac{8}{9}, 5 \frac{2}{3}, 4 \frac{4}{9}\)

Answer: 8 \(\frac{1}{9}\)

Explanation:
\(9 \frac{1}{3}\), x , \(6 \frac{8}{9}, 5 \frac{2}{3}, 4 \frac{4}{9}\)
Convert the mixed fractions into improper fractions
\(\frac{28}{3}\), x, \(\frac{62}{9}\), \(\frac{17}{3}\), \(\frac{40}{9}\)
LCD = 9
\(\frac{84}{9}\), x, \(\frac{62}{9}\), \(\frac{51}{9}\), \(\frac{40}{9}\)
According to the series x =  \(\frac{73}{9}\) = 8 \(\frac{1}{9}\)

Write the first four terms of the sequence.

Question 11.
Rule: start at 5 \(\frac{3}{4}\), subtract \(\frac{5}{8}\)
First term: ______ \(\frac{□}{□}\)
Second term: ______ \(\frac{□}{□}\)
Third term: ______ \(\frac{□}{□}\)
Fourth term: ______ \(\frac{□}{□}\)

Answer:
Let the first term be 5 \(\frac{3}{4}\)
Second term = 5 \(\frac{3}{4}\) – \(\frac{5}{8}\) = \(\frac{41}{8}\) = 5 \(\frac{1}{8}\)
Third term = 5 \(\frac{1}{8}\) – \(\frac{5}{8}\) = \(\frac{36}{8}\) = 4 \(\frac{1}{2}\)
Fourth term = \(\frac{36}{8}\) – \(\frac{5}{8}\) = \(\frac{31}{8}\) = 3 \(\frac{7}{8}\)

Question 12.
Rule: start at \(\frac{3}{8}\), add \(\frac{3}{16}\)
Type below:
_________

Answer:
Let the first term be \(\frac{3}{8}\)
Second term = \(\frac{3}{8}\) + \(\frac{3}{16}\) = \(\frac{9}{16}\)
Third term = \(\frac{9}{16}\) + \(\frac{3}{16}\) = \(\frac{12}{16}\)
Fourth term = \(\frac{12}{16}\) + \(\frac{3}{16}\) = \(\frac{15}{16}\)

Question 13.
Rule: start at 2 \(\frac{1}{3}\), add 2 \(\frac{1}{4}\)
First term: ______ \(\frac{□}{□}\)
Second term: ______ \(\frac{□}{□}\)
Third term: ______ \(\frac{□}{□}\)
Fourth term: ______ \(\frac{□}{□}\)

Answer:
Let the first term be 2 \(\frac{1}{3}\)
Second term = 2 \(\frac{1}{3}\) + 2 \(\frac{1}{4}\) = \(\frac{7}{3}\) + \(\frac{9}{4}\)
= \(\frac{55}{12}\) = 4 \(\frac{7}{12}\)
Third term = 4 \(\frac{7}{12}\) + 2 \(\frac{1}{4}\) = 6 \(\frac{5}{6}\)
Fourth term = 6 \(\frac{5}{6}\) + 2 \(\frac{1}{4}\) = 9 \(\frac{1}{12}\)

Question 14.
Rule: start at \(\frac{8}{9}\), subtract \(\frac{1}{18}\)
Type below:
_________

Answer:
Let the first term be \(\frac{8}{9}\)
Second term = \(\frac{8}{9}\) – \(\frac{1}{18}\) = \(\frac{15}{18}\) = \(\frac{5}{6}\)
Third term = \(\frac{15}{18}\) – \(\frac{1}{18}\) = \(\frac{14}{18}\) = \(\frac{7}{9}\)
Fourth term = \(\frac{14}{18}\) – \(\frac{1}{18}\) = \(\frac{13}{18}\)

Problem Solving – Page No. 276

Question 15.
When Bill bought a marigold plant, it was \(\frac{1}{4}\) inch tall. After the first week, it measured 1 \(\frac{1}{12}\) inches tall. After the second week, it was 1 \(\frac{11}{12}\) inches. After week 3, it was 2 \(\frac{3}{4}\) inches tall. Assuming the growth of the plant was constant, what was the height of the plant at the end of week 4?
______ \(\frac{□}{□}\) inches

Answer: 3 \(\frac{7}{12}\) inches

The sequence is the increasing where the first term is \(\frac{1}{4}\)
LCD = 12
First week is \(\frac{3}{12}\)
Second week = \(\frac{13}{12}\) = 1 \(\frac{1}{12}\)
Third week = 1 \(\frac{11}{12}\) = \(\frac{23}{12}\)
Fourth week = \(\frac{33}{12}\) = 2 \(\frac{3}{4}\)
At the end of fourth week = \(\frac{43}{12}\) = 3 \(\frac{7}{12}\) inches
The height of the plant at the end of the week is 3 \(\frac{7}{12}\) inches.

Question 16.
What if Bill’s plant grew at the same rate but was 1 \(\frac{1}{2}\) inches when he bought it? How tall would the plant be after 3 weeks?
______ inches

Answer: 4 inches

Explanation:
The sequence is increasing.
First week 1 \(\frac{1}{2}\)
Let the first term is \(\frac{6}{12}\)
Second term is 1 \(\frac{16}{12}\)
Third term is 1 \(\frac{26}{12}\)
Fourth week is 1 \(\frac{36}{12}\)
1 \(\frac{36}{12}\) = 1 \(\frac{3}{1}\) = 1 + 3 = 4
After 4 weeks the plant grew 4 inches.

Question 17.
Vicki wanted to start jogging. The first time she ran, she ran \(\frac{3}{16}\) mile. The second time, she ran \(\frac{3}{8}\) mile, and the third time, she ran \(\frac{9}{16}\) mile. If she continued this pattern, when was the first time she ran more than 1 mile? Explain.
Type below:
_________

Answer: Sixth time

Explanation:
Vicki wanted to start jogging. The first time she ran, she ran \(\frac{3}{16}\) mile. The second time, she ran \(\frac{3}{8}\) mile, and the third time, she ran \(\frac{9}{16}\) mile.
The difference is \(\frac{3}{16}\)
First time = \(\frac{3}{16}\) mile
Second time = \(\frac{3}{16}\) + \(\frac{3}{16}\) = \(\frac{3}{8}\) mile
Third time = \(\frac{3}{8}\) + \(\frac{3}{16}\) = \(\frac{9}{16}\) mile
Fourth time = \(\frac{9}{16}\) + \(\frac{3}{16}\) = \(\frac{12}{16}\) mile
Fifth time = \(\frac{12}{16}\) + \(\frac{3}{16}\) = \(\frac{15}{16}\) mile
Sixth time = \(\frac{15}{16}\) + \(\frac{3}{16}\) = \(\frac{18}{16}\) mile
\(\frac{18}{16}\) = 1 \(\frac{2}{16}\) = 1 \(\frac{1}{8}\)

Question 18.
Mr. Conners drove 78 \(\frac{1}{3}\) miles on Monday, 77 \(\frac{1}{12}\) miles on Tuesday, and 75 \(\frac{5}{6}\) miles on Wednesday. If he continues this pattern on Thursday and Friday, how many miles will he drive on Friday?
______ \(\frac{□}{□}\) miles

Answer:
Given that,
Mr. Conners drove 78 \(\frac{1}{3}\) miles on Monday, 77 \(\frac{1}{12}\) miles on Tuesday, and 75 \(\frac{5}{6}\) miles on Wednesday.
The sequence is the decreasing where the first term is 78 \(\frac{4}{12}\)
78 \(\frac{4}{12}\) – 77 \(\frac{1}{12}\) = 1 \(\frac{3}{12}\)
The difference between the term is 1 \(\frac{3}{12}\)
On thursday, 75 \(\frac{5}{6}\) – 1 \(\frac{3}{12}\) = 74 \(\frac{7}{12}\)
On friday, 74 \(\frac{7}{12}\) – 1 \(\frac{3}{12}\) = 73 \(\frac{4}{12}\) = 73 \(\frac{1}{3}\)

Question 19.
Test Prep Zack watered his garden with 1 \(\frac{3}{8}\) gallons of water the first week he planted it. He watered it with 1 \(\frac{3}{4}\) gallons the second week, and 2 \(\frac{1}{8}\) gallons the third week. If he continued watering in this pattern, how much water did he use on the fifth week?
Options:
a. 2 \(\frac{1}{2}\) gallons
b. 2 \(\frac{7}{8}\) gallons
c. 3 \(\frac{1}{4}\) gallons
d. 6 \(\frac{7}{8}\) gallons

Answer: 2 \(\frac{7}{8}\) gallons

Explanation:
First term = 1 \(\frac{3}{8}\)
The difference is \(\frac{3}{4}\) – \(\frac{3}{8}\) = \(\frac{3}{8}\)
Second term is 1 \(\frac{3}{8}\) + \(\frac{3}{8}\) = 1 \(\frac{3}{4}\)
Third term = 1 \(\frac{3}{4}\) + \(\frac{3}{8}\) = 1 + 1 \(\frac{1}{8}\) = 2 \(\frac{1}{8}\)
Fourth term = 2 \(\frac{1}{8}\) + \(\frac{3}{8}\) = 2 \(\frac{1}{2}\)
Fifth term = 2 \(\frac{1}{2}\) + \(\frac{3}{8}\) = 2 \(\frac{7}{8}\) gallons
Thus the correct answer is option B.

Share and Show – Page No. 279

Question 1.
Caitlin has 4 \(\frac{3}{4}\) pounds of clay. She uses 1 \(\frac{1}{10}\) pounds to make a cup, and another 2 pounds to make a jar. How many pounds are left?
First, write an equation to model the problem.
Type below:
_________

Answer: 4 \(\frac{3}{4}\) – 1 \(\frac{1}{10}\) – 2

Explanation:
Subtract the total pound of clay from used clay.
So, the equation of the clay leftover is 4 \(\frac{3}{4}\) – 1 \(\frac{1}{10}\) – 2

Question 1.
Next, work backwards and rewrite the equation to find x.
Type below:
_________

Answer: 4 \(\frac{3}{4}\) – 1 \(\frac{1}{10}\) – 2 = x

Explanation:
Let the leftover clay be x
4 \(\frac{3}{4}\) – 1 \(\frac{1}{10}\) – 2 = x
x = 4 \(\frac{3}{4}\) – 1 \(\frac{1}{10}\) – 2

Question 1.
Solve.
_____________________
So, ________ pounds of clay remains.
Type below:
_________

Answer: 1 \(\frac{13}{20}\) pounds

Explanation:
4 \(\frac{3}{4}\) – 1 \(\frac{1}{10}\) – 2
4 + \(\frac{3}{4}\) – 1 – \(\frac{1}{10}\) – 2
4 – 3 = 1
\(\frac{3}{4}\) – \(\frac{1}{10}\) = \(\frac{13}{20}\)
1 + \(\frac{13}{20}\) = 1 \(\frac{13}{20}\) pounds

Question 2.
What if Caitlin had used more than 2 pounds of clay to make a jar? Would the amount remaining have been more or less than your answer to Exercise 1?
Type below:
_________

Answer:
Let us assume that Catlin used 2 \(\frac{1}{4}\) pounds of clay to make a jar and 1 \(\frac{1}{10}\) pounds to make a cup.
4 \(\frac{3}{4}\) – 1 \(\frac{1}{10}\) – 2 \(\frac{1}{4}\) = 2 \(\frac{1}{20}\)

Go Math Lesson 6.9 Grade 5 Answers Question 3.
A pet store donated 50 pounds of food for adult dogs, puppies, and cats to an animal shelter. 19 \(\frac{3}{4}\) pounds was adult dog food and 18 \(\frac{7}{8}\) pounds was puppy food. How many pounds of cat food did the pet store donate?
______ \(\frac{□}{□}\) pounds of cat food

Answer: 11 \(\frac{3}{8}\) pounds of cat food

Explanation:
A pet store donated 50 pounds of food for adult dogs, puppies, and cats to an animal shelter.
19 \(\frac{3}{4}\) pounds was adult dog food and 18 \(\frac{7}{8}\) pounds was puppy food.
19 \(\frac{3}{4}\) + 18 \(\frac{7}{8}\) = 38 \(\frac{5}{8}\)
50 – 38 \(\frac{5}{8}\) = 11 \(\frac{3}{8}\) pounds of cat food
Thus the pet store donate 11 \(\frac{3}{8}\) pounds of cat food

Question 4.
Thelma spent \(\frac{1}{6}\) of her weekly allowance on dog toys, \(\frac{1}{4}\) on a dog collar, and \(\frac{1}{3}\) on dog food. What fraction of her weekly allowance is left?
\(\frac{□}{□}\) of her weekly allowance

Answer: \(\frac{1}{4}\)

Explanation:
Given that, Thelma spent \(\frac{1}{6}\) of her weekly allowance on dog toys, \(\frac{1}{4}\) on a dog collar, and \(\frac{1}{3}\) on dog food.
\(\frac{1}{6}\) + \(\frac{1}{4}\) + \(\frac{1}{3}\)  = \(\frac{3}{4}\)
1 – \(\frac{3}{4}\) = \(\frac{1}{4}\)
\(\frac{1}{4}\) of her weekly allowance.

On Your Own – Page No. 280

Question 5.
Martin is making a model of a Native American canoe. He has 5 \(\frac{1}{2}\) feet of wood. He uses 2 \(\frac{3}{4}\) feet for the hull and 1 \(\frac{1}{4}\) feet for the paddles and struts. How much wood does he have left?
______ \(\frac{□}{□}\) feet

Answer: 1 \(\frac{1}{2}\) feet

Explanation:
Martin is making a model of a Native American canoe.
He has 5 \(\frac{1}{2}\) feet of wood.
He uses 2 \(\frac{3}{4}\) feet for the hull and 1 \(\frac{1}{4}\) feet for the paddles and struts.
2 \(\frac{3}{4}\) + 1 \(\frac{1}{4}\)
2 + \(\frac{3}{4}\) + 1 + \(\frac{1}{4}\)
2 + 1 = 3
\(\frac{3}{4}\) + \(\frac{1}{4}\) = 1
3 + 1 = 4
5 \(\frac{1}{2}\) – 4 = 1 \(\frac{1}{2}\)

Question 6.
What if Martin makes a hull and two sets of paddles and struts? How much wood does he have left?

Answer: 1 \(\frac{1}{4}\)

Explanation:
He has 5 \(\frac{1}{2}\) feet of wood.
If Martin makes a hull and two sets of paddles and struts
1 \(\frac{1}{4}\) + 1 \(\frac{1}{4}\) = 2 \(\frac{1}{2}\)
2 \(\frac{1}{2}\) + 2 \(\frac{3}{4}\) = 4 \(\frac{1}{4}\)
5 \(\frac{1}{2}\) – 4 \(\frac{1}{4}\)
5 + \(\frac{1}{2}\) – 4 – \(\frac{1}{4}\)
1 + \(\frac{1}{4}\) = 1 \(\frac{1}{4}\)

Question 7.
Beth’s summer vacation lasted 87 days. At the beginning of her vacation, she spent 3 weeks at soccer camp, 5 days at her grandmother’s house, and 13 days visiting Glacier National Park with her parents. How many vacation days remained?
______ days

Answer: 48 days

Explanation:
Given,
Beth’s summer vacation lasted 87 days.
At the beginning of her vacation, she spent 3 weeks at soccer camp, 5 days at her grandmother’s house, and 13 days visiting Glacier National Park with her parents.
87 – 21 – 5 – 13 = 48 days
The remaining vacation days are 48.

Question 8.
You can buy 2 DVDs for the same price you would pay for 3 CDs selling for $13.20 apiece. Explain how you could find the price of 1 DVD.
$ ______

Answer: $19.8

Explanation:
To find what is the price of 1 DVD we will find what is the price of 3 DVDs and then because 2 DVDs price is the same than 3 CDs we can easily find the price of 1 DVD.
$13.20 × 3 = $39.6
We will divide $39.6 by 2.
$39.6 ÷ 2 = $19.8
The price of 1 DVD is $19.8

Question 9.
Test Prep During the 9 hours between 8 A.M. and 5 P.M., Bret spent 5 \(\frac{3}{4}\) hours in class and 1 \(\frac{1}{2}\) hours at band practice. How much time did he spend on other activities?
Options:
a. \(\frac{3}{4}\) hour
b. 1 \(\frac{1}{4}\) hour
c. 1 \(\frac{1}{2}\) hour
d. 1 \(\frac{3}{4}\) hour

Answer: 1 \(\frac{3}{4}\) hour

Explanation:
Test Prep During the 9 hours between 8 A.M. and 5 P.M., Bret spent 5 \(\frac{3}{4}\) hours in class and 1 \(\frac{1}{2}\) hours at band practice.
5 \(\frac{3}{4}\) + 1 \(\frac{1}{2}\) = 7 \(\frac{1}{4}\) hour
9 – 7 \(\frac{1}{4}\) hour
8 + 1 – 7 – \(\frac{1}{4}\)
1 \(\frac{3}{4}\) hour
The correct answer is option D.

Share and Show – Page No. 283

Use the properties and mental math to solve. Write your answer in simplest form.

Question 1.
\(\left(2 \frac{5}{8}+\frac{5}{6}\right)+1 \frac{1}{8}\)
______ \(\frac{□}{□}\)

Answer:
\(\left(2 \frac{5}{8}+\frac{5}{6}\right)+1 \frac{1}{8}\)
2 \(\frac{5}{8}\) + \(\frac{5}{6}\)
2 + \(\frac{5}{8}\) + \(\frac{5}{6}\)
LCD = 24
\(\frac{15}{24}\) + \(\frac{20}{24}\) = \(\frac{35}{24}\)
\(\frac{35}{24}\) = 1 \(\frac{11}{24}\)
2 + 1 \(\frac{11}{24}\) = 3 \(\frac{11}{24}\)
3 \(\frac{11}{24}\) + 1 \(\frac{1}{8}\) = 4 \(\frac{7}{12}\)

Go Math 5th Grade 6.9 Answer Key Question 2.
\(\frac{5}{12}+\left(\frac{5}{12}+\frac{3}{4}\right)\)
______ \(\frac{□}{□}\)

Answer:
\(\frac{5}{12}+\left(\frac{5}{12}+\frac{3}{4}\right)\)
\(\frac{5}{12}\) + \(\frac{3}{4}\)
LCD = 12
\(\frac{5}{12}\) + \(\frac{3}{4}\) × \(\frac{3}{3}\)
\(\frac{5}{12}\) + \(\frac{9}{12}\) = \(\frac{14}{12}\)
\(\frac{5}{12}\) + \(\frac{14}{12}\) = \(\frac{19}{12}\)
\(\frac{19}{12}\) = 1 \(\frac{7}{12}\)

Question 3.
\(\left(3 \frac{1}{4}+2 \frac{5}{6}\right)+1 \frac{3}{4}\)
______ \(\frac{□}{□}\)

Answer:

\(\left(3 \frac{1}{4}+2 \frac{5}{6}\right)\)
2 + \(\frac{5}{6}\) + 3 + \(\frac{1}{4}\)
2 + 3 = 5
\(\frac{5}{6}\) + \(\frac{1}{4}\)
LCD = 12
\(\frac{5}{6}\) × \(\frac{2}{2}\) + \(\frac{1}{4}\) × \(\frac{3}{3}\)
\(\frac{10}{12}\) + \(\frac{3}{12}\) = \(\frac{13}{12}\) = 1 \(\frac{1}{12}\)
5 + 1 \(\frac{1}{12}\) = 6 \(\frac{1}{12}\)
6 \(\frac{1}{12}\) + 1 \(\frac{3}{4}\)
6 + \(\frac{1}{12}\) + 1 + \(\frac{3}{4}\)
6 + 1 = 7
\(\frac{1}{12}\) + \(\frac{3}{4}\)
\(\frac{1}{12}\) + \(\frac{9}{12}\) = \(\frac{10}{12}\) = \(\frac{5}{6}\)
7 + \(\frac{5}{6}\) = 7 \(\frac{5}{6}\)

On Your Own

Use the properties and mental math to solve. Write your answer in the simplest form.

Question 4.
\(\left(\frac{2}{7}+\frac{1}{3}\right)+\frac{2}{3}\)
______ \(\frac{□}{□}\)

Answer:
\(\left(\frac{2}{7}+\frac{1}{3}\right)+\frac{2}{3}\)
\(\left(\frac{2}{7}+\frac{1}{3}\right)\)
LCD = 21
\(\left(\frac{6}{21}+\frac{7}{21}\right)\) = \(\frac{13}{21}\)
\(\frac{13}{21}\) + \(\frac{2}{3}\)
LCD = 21
\(\frac{13}{21}\) + \(\frac{14}{21}\)
\(\frac{27}{21}\) = \(\frac{9}{7}\)
= 1 \(\frac{2}{7}\)

Question 5.
\(\left(\frac{1}{5}+\frac{1}{2}\right)+\frac{2}{5}\)
______ \(\frac{□}{□}\)

Answer:
\(\left(\frac{1}{5}+\frac{1}{2}\right)\)
\(\frac{1}{5}\) + \(\frac{1}{2}\)
LCD = 10
\(\frac{2}{10}\) + \(\frac{5}{10}\) = \(\frac{7}{10}\)
\(\frac{7}{10}\) + \(\frac{2}{5}\)
\(\frac{7}{10}\) + \(\frac{4}{10}\) = \(\frac{11}{10}\)
\(\frac{11}{10}\) = 1 \(\frac{1}{10}\)

Question 6.
\(\left(\frac{1}{6}+\frac{3}{7}\right)+\frac{2}{7}\)
\(\frac{□}{□}\)

Answer:
\(\left(\frac{1}{6}+\frac{3}{7}\right)\)
LCD = 42
\(\left(\frac{7}{42}+\frac{18}{42}\right)\) = \(\frac{25}{42}\)
\(\frac{25}{42}\) + \(\frac{2}{7}\)
LCD = 42
\(\frac{25}{42}\) + \(\frac{12}{42}\) = \(\frac{37}{42}\)
\(\left(\frac{1}{6}+\frac{3}{7}\right)+\frac{2}{7}\) = \(\frac{37}{42}\)

Question 7.
\(\left(2 \frac{5}{12}+4 \frac{1}{4}\right)+\frac{1}{4}\)
______ \(\frac{□}{□}\)

Answer:
\(\left(2 \frac{5}{12}+4 \frac{1}{4}\right)\)
2 \(\frac{5}{12}\) + 4 \(\frac{1}{4}\)
2 + \(\frac{5}{12}\) + 4 + \(\frac{1}{4}\)
2 + 4 = 6
\(\frac{5}{12}\) + \(\frac{1}{4}\) = \(\frac{8}{12}\)
6 \(\frac{8}{12}\) = 6 \(\frac{2}{3}\)
6 \(\frac{2}{3}\) + \(\frac{1}{4}\) = 6 \(\frac{11}{12}\)

Question 8.
\(1 \frac{1}{8}+\left(5 \frac{1}{2}+2 \frac{3}{8}\right)\)
______

Answer:
5 \(\frac{1}{2}\) + 2 \(\frac{3}{8}\)
5 + 2 = 7
\(\frac{1}{2}\) + \(\frac{3}{8}\)
LCD = 8
\(\frac{4}{8}\) + \(\frac{3}{8}\) = \(\frac{7}{8}\)
= 7 \(\frac{7}{8}\)
1 \(\frac{1}{8}\) + 7 \(\frac{7}{8}\) = 9

Question 9.
\(\frac{5}{9}+\left(\frac{1}{9}+\frac{4}{5}\right)\)
______ \(\frac{□}{□}\)

Answer:
\(\frac{1}{9}\) + \(\frac{4}{5}\)
LCD = 45
\(\frac{5}{45}\) + \(\frac{36}{45}\) = \(\frac{41}{45}\)
\(\frac{41}{45}\) + \(\frac{5}{9}\)
LCD = 45
\(\frac{41}{45}\) + \(\frac{25}{45}\) = \(\frac{66}{45}\)
\(\frac{66}{45}\) = 1 \(\frac{7}{15}\)

Problem Solving – Page No. 284

Use the map to solve 10–12.

Question 10.
In the morning, Julie rides her bike from the sports complex to the school. In the afternoon, she rides from the school to the mall, and then to Kyle’s house. How far does Julie ride her bike?
______ \(\frac{□}{□}\) miles

Answer: 1 \(\frac{13}{15}\) miles

Explanation:
Julie rides her bike from the sports complex to the school = \(\frac{2}{3}\) mile
In the afternoon, she rides from the school to the mall, and then to Kyle’s house. = \(\frac{2}{5}\) + \(\frac{4}{5}\) = \(\frac{6}{5}\) = 1 \(\frac{1}{5}\)
1 \(\frac{1}{5}\) + \(\frac{2}{3}\) mile = 1 \(\frac{13}{15}\) miles

Question 11.
On one afternoon, Mario walks from his house to the library. That evening, Mario walks from the library to the mall, and then to Kyle’s house. Describe how you can use the properties to find how far Mario walks.
______ \(\frac{□}{□}\) miles

Answer:
Mario walks from his house to the library = 1 \(\frac{3}{5}\) miles
Mario walks from the library to the mall, and then to Kyle’s house = 1 \(\frac{1}{3}\) and \(\frac{4}{5}\)
1 \(\frac{3}{5}\) + (1 \(\frac{1}{3}\) + \(\frac{4}{5}\))
1 \(\frac{3}{5}\) + 2 \(\frac{2}{15}\) = 3 \(\frac{11}{15}\) miles

Question 12.
Pose a Problem Write and solve a new problem that uses the distances between four locations.
Type below:
_________

Answer:
In the evening Kyle rides his bike from the sports complex to school. Then he rides from School to the mall and then to his house. How far does Kyle ride his bike?
The distance from Sports complex to School is \(\frac{2}{3}\) mile
The distance from School to the mall is \(\frac{2}{5}\)
The distance from the mall to Kyle house is \(\frac{4}{5}\)
\(\frac{2}{3}\) + (\(\frac{2}{5}\) + \(\frac{4}{5}\))
\(\frac{2}{3}\) + \(\frac{6}{5}\) = 1 \(\frac{13}{15}\) miles

Question 13.
Test Prep Which property or properties does the problem below use?
\(\frac{1}{9}+\left(\frac{4}{9}+\frac{1}{6}\right)=\left(\frac{1}{9}+\frac{4}{9}\right)+\frac{1}{6}\)
Options:
a. Commutative Property
b. Associative Property
c. Commutative Property and Associative Property
d. Distributive Property

Answer: Associative Property
The associative property states that you can add or multiply regardless of how the numbers are grouped. By ‘grouped’ we mean ‘how you use parenthesis’. In other words, if you are adding or multiplying it does not matter where you put the parenthesis.

Chapter Review/Test – Vocabulary – Page No. 285

Choose the best term from the box.

Question 1.
A _________ is a number that is a common multiple of two or more denominators.
_________

Answer: Common Denominator

Concepts and Skills

Use a common denominator to write an equivalent fraction for each fraction.

Question 2.
\(\frac{2}{5}, \frac{1}{8}\)
common denominator: ______
Explain:
_________

Answer: 40
Multiply the denominators of the fractions
5 × 8 = 40

Question 3.
\(\frac{3}{4}, \frac{1}{2}\)
common denominator: ______
Explain:
_________

Answer: 8
Multiply the denominators of the fractions
4 × 2 = 8

Question 4.
\(\frac{2}{3}, \frac{1}{6}\)
common denominator: ______
Explain:
_________

Answer: 18
Multiply the denominators of the fractions
3 × 6 = 18

Find the sum or difference. Write your answer in simplest form

Question 5.
\(\frac{5}{6}+\frac{7}{8}\)
______ \(\frac{□}{□}\)

Answer: 1 \(\frac{17}{24}\)

Explanation:
\(\frac{5}{6}+\frac{7}{8}\) = \(\frac{20}{24}\) + \(\frac{21}{24}\)
= \(\frac{41}{24}\) = 1 \(\frac{17}{24}\)

Question 6.
\(2 \frac{2}{3}-1 \frac{2}{5}\)
______ \(\frac{□}{□}\)

Answer: 1 \(\frac{4}{15}\)

Question 7.
\(7 \frac{3}{4}+3 \frac{7}{20}\)
______ \(\frac{□}{□}\)

Answer: 11 \(\frac{1}{10 }\)

Estimate. Then find the difference and write it in simplest form.

Question 8.
\(1 \frac{2}{5}-\frac{2}{3}\)
Type below:
________

Answer:
Estimate: \(\frac{1}{2}\)
Difference:
Rewriting our equation with parts separated
1 + \(\frac{2}{5}\) – \(\frac{2}{3}\)
\(\frac{7}{5}\) – \(\frac{2}{3}\)
\(\frac{7}{5}\) × \(\frac{3}{3}\) – \(\frac{2}{3}\) × \(\frac{5}{5}\)
= \(\frac{21}{15}\) – \(\frac{10}{15}\)
= \(\frac{11}{15}\)

Question 9.
\(7-\frac{3}{7}\)
Type below:
________

Answer: 6 \(\frac{4}{7}\)

Explanation:
\(7-\frac{3}{7}\) = \(\frac{49}{7}\) – \(\frac{3}{7}\)
\(\frac{46}{7}\) = 6 \(\frac{4}{7}\)
\(7-\frac{3}{7}\) = 6 \(\frac{4}{7}\)

Go Math Grade 5 Chapter 6 Lesson 6.10 Answer Key Question 10.
\(5 \frac{1}{9}-3 \frac{5}{6}\)
Type below:
________

Answer: 1 \(\frac{5}{18}\)

Explanation:
\(5 \frac{1}{9}-3 \frac{5}{6}\) = 5 + \(\frac{1}{9}\) – 3 – \(\frac{5}{6}\)
5 – 3 = 2
\(\frac{1}{9}\) – \(\frac{5}{6}\) = \(\frac{2}{18}\) – \(\frac{15}{18}\) = – \(\frac{13}{18}\)
2 – \(\frac{13}{18}\) = 1 \(\frac{5}{18}\)

Use the properties and mental math to solve. Write your answer in simplest form.

Question 11.
\(\left(\frac{3}{8}+\frac{2}{3}\right)+\frac{1}{3}\)
______ \(\frac{□}{□}\)

Answer: 1 \(\frac{3}{8}\)

Explanation:
\(\frac{3}{8}\) + \(\frac{2}{3}\) = \(\frac{9}{24}\) + \(\frac{16}{24}\) = \(\frac{25}{24}\)
\(\frac{25}{24}\) + \(\frac{1}{3}\)
= \(\frac{25}{24}\) + \(\frac{8}{24}\) = \(\frac{33}{24}\) = \(\frac{11}{8}\)
The mixed fraction of \(\frac{11}{8}\) is 1 \(\frac{3}{8}\).

Question 12.
\(1 \frac{4}{5}+\left(2 \frac{3}{20}+\frac{3}{5}\right)\)
______ \(\frac{□}{□}\)

Answer: 4 \(\frac{11}{20}\)

Explanation:
Rewriting our equation with parts separated
2 \(\frac{3}{20}\) + \(\frac{3}{5}\) = \(\frac{43}{20}\) + \(\frac{3}{5}\)
\(\frac{43}{20}\) + \(\frac{3}{5}\) = \(\frac{215}{100}\) + \(\frac{60}{100}\)
= \(\frac{275}{100}\) = 2 \(\frac{3}{4}\)
2 \(\frac{3}{4}\) + 1 \(\frac{4}{5}\) = 2 + \(\frac{3}{4}\) + 1 + \(\frac{4}{5}\)
2 + 1 = 3
\(\frac{3}{4}\) + \(\frac{4}{5}\) = \(\frac{15}{20}\) + \(\frac{16}{20}\) = \(\frac{31}{20}\)
\(\frac{31}{20}\) = 4 \(\frac{11}{20}\)

Question 13.
\(3 \frac{5}{9}+\left(1 \frac{7}{9}+2 \frac{5}{12}\right)\)
______ \(\frac{□}{□}\)

Answer: 7 \(\frac{3}{4}\)

Explanation:
1 \(\frac{7}{9}\) + 2 \(\frac{5}{12}\)
1 + 2 = 3
\(\frac{7}{9}\) + \(\frac{5}{12}\)
LCD is 36
\(\frac{28}{36}\) + \(\frac{15}{36}\) = \(\frac{43}{36}\)
\(\frac{43}{36}\) = 1 \(\frac{7}{36}\)
3 + 1 + \(\frac{7}{36}\) = 4 \(\frac{7}{36}\)
4 \(\frac{7}{36}\) + 3 \(\frac{5}{9}\)
4 + \(\frac{7}{36}\) + 3 + \(\frac{5}{9}\)
4 + 3 = 7
\(\frac{7}{36}\) + \(\frac{5}{9}\)
= \(\frac{7}{36}\) + \(\frac{20}{36}\) = \(\frac{27}{36}\) = \(\frac{3}{4}\)
7 + \(\frac{3}{4}\) = 7 \(\frac{3}{4}\)

Chapter Review/Test – Page No. 286

Question 14.
Ursula mixed 3 \(\frac{1}{8}\) cups of dry ingredients with 1 \(\frac{2}{5}\) cups of liquid ingredients. Which answer represents the best estimate of the total amount of ingredients Ursula mixed?
Options:
a. about 4 cups
b. about 4 \(\frac{1}{2}\) cups
c. about 5 cups
d. about 5 \(\frac{1}{2}\) cups

Answer: about 4 \(\frac{1}{2}\) cups

Explanation:
Ursula mixed 3 \(\frac{1}{8}\) cups of dry ingredients with 1 \(\frac{2}{5}\) cups of liquid ingredients.
3 + 1 = 4
\(\frac{1}{8}\) is closer to 0.
\(\frac{2}{5}\) is closer to \(\frac{1}{2}\)
4 + \(\frac{1}{2}\) = 4 \(\frac{1}{2}\)
Thus the correct answer is option B.

Question 15.
Samuel walks in the Labor Day parade. He walks 3 \(\frac{1}{4}\) miles along the parade route and 2 \(\frac{5}{6}\) miles home. How many miles does Samuel walk?
Options:
a. \(\frac{5}{10}\) mile
b. 5 \(\frac{1}{12}\) miles
c. 5 \(\frac{11}{12}\) miles
d. 6 \(\frac{1}{12}\) miles

Answer: 6 \(\frac{1}{12}\) miles

Explanation:
Samuel walks in the Labor Day parade.
He walks 3 \(\frac{1}{4}\) miles along the parade route and 2 \(\frac{5}{6}\) miles home.
3 + \(\frac{1}{4}\) + 2 + \(\frac{5}{6}\)
3 + 2 =5
\(\frac{5}{6}\) + \(\frac{1}{4}\) = \(\frac{10}{12}\) + \(\frac{3}{12}\) = \(\frac{13}{12}\)
\(\frac{13}{12}\) = 6 \(\frac{1}{12}\) miles
Thus the correct answer is option D.

Question 16.
A gardener has a container with 6 \(\frac{1}{5}\) ounces of liquid plant fertilizer. On Sunday, the gardener uses 2 \(\frac{1}{2}\) ounces on a flower garden. How many ounces of liquid plant fertilizer are left?
Options:
a. 3 \(\frac{7}{10}\) ounces
b. 5 \(\frac{7}{10}\) ounces
c. 6 \(\frac{7}{10}\) ounces
d. 9 \(\frac{7}{10}\) ounces

Answer: 9 \(\frac{7}{10}\) ounces

Explanation:
A gardener has a container with 6 \(\frac{1}{5}\) ounces of liquid plant fertilizer.
On Sunday, the gardener uses 2 \(\frac{1}{2}\) ounces on a flower garden.
6 + \(\frac{1}{5}\) + 2 + \(\frac{1}{2}\)
6 + 2 = 8
\(\frac{1}{5}\) + \(\frac{1}{2}\)
LCD = 10
\(\frac{2}{10}\) + \(\frac{5}{10}\) = \(\frac{7}{10}\)
8 \(\frac{7}{10}\)

Question 17.
Aaron is practicing for a triathlon. On Sunday, he bikes 12 \(\frac{5}{8}\) miles and swims 5 \(\frac{2}{3}\) miles. On Monday, he runs 6 \(\frac{3}{8}\) miles. How many total miles does Aaron cover on the two days?
Options:
a. 23 \(\frac{1}{6}\) miles
b. 24 \(\frac{7}{12}\) miles
c. 24 \(\frac{2}{3}\) miles
d. 25 \(\frac{7}{12}\) miles

Answer: 24 \(\frac{2}{3}\) miles

Explanation:
Aaron is practicing for a triathlon.
On Sunday, he bikes 12 \(\frac{5}{8}\) miles and swims 5 \(\frac{2}{3}\) miles.
On Monday, he runs 6 \(\frac{3}{8}\) miles.
5 \(\frac{2}{3}\) + 6 \(\frac{3}{8}\) = 12 \(\frac{1}{24}\)
12 \(\frac{1}{24}\) + 12 \(\frac{5}{8}\) miles
12 + \(\frac{1}{24}\) + 12 + \(\frac{5}{8}\)
12 + 12 = 24
\(\frac{1}{24}\) + \(\frac{5}{8}\) = \(\frac{1}{24}\) + \(\frac{15}{24}\) = \(\frac{16}{24}\) = \(\frac{2}{3}\)
24 + \(\frac{2}{3}\) = 24 \(\frac{2}{3}\) mile
The correct answer is option D.

Chapter Review/Test – Page No. 287

Fill in the bubble completely to show your answer.

Question 18.
Mrs. Friedmon baked a walnut cake for her class. The pictures below show how much cake she brought to school and how much she had left at the end of the day.

Which fraction represents the difference between the amounts of cake Mrs. Friedmon had before school and after school?
Options:
a. \(\frac{5}{8}\)
b. 1 \(\frac{1}{2}\)
c. 1 \(\frac{5}{8}\)
d. 2 \(\frac{1}{2}\)

Answer: 1 \(\frac{5}{8}\)

Explanation:
The fraction for the above figure is 1 \(\frac{7}{8}\)
The fraction for the second figure is \(\frac{1}{4}\)
1 + \(\frac{7}{8}\) – \(\frac{1}{4}\)
\(\frac{7}{8}\) – \(\frac{1}{4}\) = \(\frac{7}{8}\) – \(\frac{2}{8}\)
\(\frac{7}{8}\) – \(\frac{2}{8}\) = \(\frac{5}{8}\)
1 + \(\frac{5}{8}\) = 1 \(\frac{5}{8}\)
The correct answer is option C.

Question 19.
Cody is designing a pattern for a wood floor. The length of the pieces of wood are 1 \(\frac{1}{2}\) inches, 1 \(\frac{13}{16}\) inches, and 2 \(\frac{1}{8}\) inches. What is the length of the 5th piece of wood if the pattern continues?
Options:
a. 2 \(\frac{7}{6}\) inches
b. 2 \(\frac{3}{4}\) inches
c. 3 \(\frac{1}{2}\) inches
d. 4 inches

Answer: 2 \(\frac{3}{4}\) inches

Explanation:
The length of the pieces of wood are 1 \(\frac{1}{2}\) inches, 1 \(\frac{13}{16}\) inches, and 2 \(\frac{1}{8}\) inches
1 \(\frac{1}{2}\) = \(\frac{3}{2}\)
1 \(\frac{13}{16}\) inches = \(\frac{29}{16}\)
\(\frac{29}{16}\) – \(\frac{3}{2}\) = latex]\frac{5}{16}[/latex]
5th piece = \(\frac{3}{2}\) + latex]\frac{5}{16}[/latex] (5 – 1)
= \(\frac{3}{2}\) + latex]\frac{5}{16}[/latex] 4
= \(\frac{3}{2}\) + latex]\frac{20}{16}[/latex]
= \(\frac{3}{2}\) × latex]\frac{8}{8}[/latex] + latex]\frac{20}{16}[/latex]
= latex]\frac{44}{16}[/latex] = 2 latex]\frac{3}{4}[/latex]
Thus the correct answer is option B.

Question 20.
Julie spends \(\frac{3}{4}\) hour studying on Monday and \(\frac{1}{6}\) hour studying on Tuesday. How many hours does Julie study on those two days?
Options:
a. \(\frac{1}{3}\) hour
b. \(\frac{2}{5}\) hour
c. \(\frac{5}{6}\) hour
d. \(\frac{11}{12}\) hour

Answer: \(\frac{11}{12}\) hour

Explanation:
Julie spends \(\frac{3}{4}\) hour studying on Monday and \(\frac{1}{6}\) hour studying on Tuesday.
\(\frac{3}{4}\) + \(\frac{1}{6}\)
LCD = 12
\(\frac{9}{12}\) + \(\frac{2}{12}\) = \(\frac{11}{12}\) hour
So, the correct answer is option D.

Chapter Review/Test – Page No. 288

Constructed Response

Question 21.
A class uses 8 \(\frac{5}{6}\) sheets of white paper and 3 \(\frac{1}{12}\) sheets of red paper for a project. How much more white paper is used than red paper? Show your work using words, pictures, or numbers. Explain how you know your answer is reasonable.
______ \(\frac{□}{□}\) sheet of white paper

Answer: 5 \(\frac{3}{4}\) sheet of white paper

Explanation:
A class uses 8 \(\frac{5}{6}\) sheets of white paper and 3 \(\frac{1}{12}\) sheets of red paper for a project.
8 \(\frac{5}{6}\) – 3 \(\frac{1}{12}\)
8 + \(\frac{5}{6}\) – 3 – \(\frac{1}{12}\)
8 – 3 = 5
\(\frac{5}{6}\) – \(\frac{1}{12}\)
\(\frac{10}{12}\) – \(\frac{1}{12}\) = \(\frac{9}{12}\)
\(\frac{9}{12}\) = \(\frac{3}{4}\)
5 + \(\frac{3}{4}\) = 5 \(\frac{3}{4}\)

Performance Task

Question 22.
For a family gathering, Marcos uses the recipe below to make a lemon-lime punch.

A). How would you decide the size of a container you need for one batch of the Lemon-Lime Punch?
Type below:
________

Answer: He may use \(\frac{1}{4}\) gallon lime juice for one batch of the lemon-lime punch.

Question 22.
B). If Marcos needs to make two batches of the recipe, how much of each ingredient will he need? How many gallons of punch will he have? Show your math solution and explain your thinking when you solve both questions.
Type below:
________

Answer: \(\frac{2}{3}\) gallon lime juice

Question 22.
C). Marcos had 1 \(\frac{1}{3}\) gallons of punch left over. He poured all of it into several containers for family members to take home. Use fractional parts of a gallon to suggest a way he could have shared the punch in three different-sized containers.
Type below:
________

Answer: 1 \(\frac{1}{12}\)

Conclusion:

Real-time learning is very important for students. By following the concepts given in the Go Math Grade 5 Chapter 6 Solution Key the students can solve the questions easily in the exam. If you understand the concept you can solve any type of question. Try to solve the questions given at the end of the chapter to test your knowledge. Get Chapter-wise Solutions in our Go Math Answer Key.

Go Math Grade 5 Chapter 7 Answer Key Pdf: Students who are in search of Chapter 7 Go Math Grade 5 Answer Key can get them here. We provide Go Math Grade 5 Answer Key Chapter 7 Multiply Fractions with a clear cut explanation. Parents who are unable to understand the logic in fraction can go through our Go Math 5th Grade Answer Key Chapter 7 Multiply Fractions and help their child. Enhance your mathematical skills by learning the concepts from HMH Go Math Grade 5 Answer Key.

Multiply Fractions Go Math Grade 5 Chapter 7 Answer Key Pdf

Most of the students feel that fractions are very difficult. Don’t worry we will help you out by providing the pictures and step by step multiplication for better understanding. With the help of this Go Math Answer Key Grade 5 Chapter 7 Multiply Fractions you can learn the concept quickly and can score the highest marks in your exams. You need to learn the basics at the primary level itself. So learn all the basics of fractions in our Go Math Grade 5 Key Chapter 7 Multiply Fractions.

Before you start your preparation we suggest you go through the topics covered in this chapter. Get the Answer Key topic wise. Thus, make use of all the links and improve your skills. Test your knowledge by solving the problems in the Review test and check the answers provided at the end of the chapter. By this, you can know how much you gained the knowledge in this chapter.

Chapter 7 – Lesson 1: Find Part of a Group

• Share and Show – Page No. 293
• Problem Solving – Page No. 294

Chapter 7 – Lesson 2: Investigate • Multiply Fractions and Whole Numbers

• Share and Show – Page No. 297
• Problem Solving – Page No. 298

Chapter 7 – Lesson 3: Fraction and Whole Number Multiplication

• Share and Show – Page No. 301
• UNLOCK the Problem – Page No. 302

Chapter 7 – Lesson 4: Investigate • Multiply Fractions

• Share and Show – Page No. 304
• Share and Show – Page No. 305
• Problem Solving – Page No. 306

Chapter 7 – Lesson 5: Compare Fraction Factors and Products

• Share and Show – Page No. 309
• Problem Solving – Page No. 310

Chapter 7 – Lesson 6: Fraction Multiplication

• Share and Show – Page No. 313
• Problem Solving – Page No. 314

Chapter 7 – Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 315
• Mid-Chapter Checkpoint – Page No. 316

Chapter 7 – Lesson 7: Investigate • Area and Mixed Numbers

• Share and Show – Page No. 319
• Problem Solving – Page No. 320

Chapter 7 – Lesson 8: Compare Mixed Number Factors and Products

• Share and Show – Page No. 323
• Problem Solving – Page No. 324

Chapter 7 – Lesson 9: Multiply Mixed Numbers

• Share and Show – Page No. 327
• Share and Show Connect to health – Page No. 328

Chapter 7 – Lesson 10: Problem Solving • Find Unknown Lengths

• Share and Show – Page No. 331
• On Your Own – Page No. 332

Chapter 7 – Chapter 7 Review/Test

• Chapter Review/Test – Page No. 333
• Chapter Review/Test – Page No. 334
• Chapter Review/Test – Page No. 335
• Chapter Review/Test – Page No. 336

Share and Show – Page No. 293

Question 1.
Complete the model to solve.

\(\frac{7}{8}\) of 16, or \(\frac{7}{8}\) × 16
How many rows of counters are there?
_____ rows

Answer: 8
By seeing the above figure we can say that the number of counters is 8 rows.

Question 1.
How many counters are in each row?
_____ counters

Answer: 2
There are 2 counters in each row.

Question 1.
Circle ____ rows to solve the problem.
_____ rows

Answer: 7

• • • • • • •
• • • • • • •
• • • • • • •
• • • • • • •
• • • • • • •
• • • • • • •
• • • • • • •
• • • • • • •

Question 1.
How many counters are circled?
\(\frac{7}{8}\) of 16=
or \(\frac{7}{8}\) × 16 =
_____ counters

Answer: 14
\(\frac{7}{8}\) × 16
8 divides 16 two times.
So, \(\frac{7}{8}\) × 16 = 7 × 2 = 14
Therefore 14 counters are circled.

Use a model to solve.

Question 2.
\(\frac{2}{3}\) × 18 = _____

Answer: 12

Explanation:
\(\frac{2}{3}\) × 18
3 divides 18 six times.
2 × 6 = 12

Question 3.
\(\frac{2}{5}\) × 15 = _____

Answer: 6

Explanation:
\(\frac{2}{5}\) × 15
5 divides 15 three times.
2 × 3 = 6
Thus \(\frac{2}{5}\) × 15 = 6

Go Math Grade 5 Chapter 7 Answer Key Pdf Question 4.
\(\frac{2}{3}\) × 6 = _____

Answer: 4

Explanation:
\(\frac{2}{3}\) × 6
3 divides 6 two times.
\(\frac{2}{3}\) × 6
2 × 2 = 4
\(\frac{2}{3}\) × 6 = 4

On Your Own

Use a model to solve.

Question 5.
\(\frac{5}{8}\) × 24 = _____

Answer: 15

Explanation:
\(\frac{5}{8}\) × 24
8 divides 24 three times.
5 × 3 = 15
\(\frac{5}{8}\) × 24 = 15

Question 6.
\(\frac{3}{4}\) × 24 = _____

Answer: 18

Explanation:
\(\frac{3}{4}\) × 24
4 divides 24 six times.
\(\frac{3}{4}\) × 24 = 3 × 6 = 18
So, \(\frac{3}{4}\) × 24 = 18

Question 7.
\(\frac{4}{7}\) × 21 = _____

Answer: 12

Explanation:
\(\frac{4}{7}\) × 21
7 divides 21 three times.
4 × 3 = 12
\(\frac{4}{7}\) × 21 = 12

Question 8.
\(\frac{2}{9}\) × 27 = _____

Answer: 6

Explanation:
\(\frac{2}{9}\) × 27
9 divides 27 three times.
2 × 3 = 6
\(\frac{2}{9}\) × 27 = 6

Question 9.
\(\frac{3}{5}\) × 20 = _____

Answer: 12

Explanation:
\(\frac{3}{5}\) × 20
5 divides 20 four times.
3 × 4 = 12
Thus \(\frac{3}{5}\) × 20 = 12

Question 10.
\(\frac{7}{11}\) × 22 = _____

Answer: 14

Explanation:
\(\frac{7}{11}\) × 22
11 divides 22 two times.
7 × 2 = 14
\(\frac{7}{11}\) × 22 = 14

Problem Solving – Page No. 294

Use the table for 11-12.

Question 11.
Four-fifths of Zack’s stamps have pictures of animals. How many stamps with pictures of animals does Zack have? Use a model to solve.
_____ stamps

Answer: 24 stamps

Explanation:
Given that, Four-fifths of Zack’s stamps have pictures of animals.
Number of stamps that Zack collected is 30
30 × \(\frac{4}{5}\)
5 divides 30 six times.
6 × 4 = 24
Zack has 24 stamps with pictures of animals.

Question 12.
Zack, Teri, and Paco combined the foreign stamps from their collections for a stamp show. Out of their collections, \(\frac{3}{10}\) of Zack’s stamps, \(\frac{5}{6}\) of Teri’s stamps, and \(\frac{3}{8}\) of Paco’s stamps were from foreign countries. How many stamps were in their display? Explain how you solved the problem.
_____ stamps

Answer: 33 stamps

Explanation:
Zack, Teri, and Paco combined the foreign stamps from their collections for a stamp show.
Out of their collections, \(\frac{3}{10}\) of Zack’s stamps, \(\frac{5}{6}\) of Teri’s stamps, and \(\frac{3}{8}\) of Paco’s stamps were from foreign countries.
Number of stamps Zack collected = 30
Number of stamps Teri collected = 18
Number of stamps Paco collected = 24
\(\frac{3}{10}\) of 30
\(\frac{3}{10}\) × 30 = 3 × 3 = 9
\(\frac{5}{6}\) × 18 = 5 × 3 = 15
\(\frac{3}{8}\) × 24 = 3 × 3 = 9
Now add all the stamps = 9 + 9 + 15 = 33

Go Math Grade 5 Chapter 7 Review/Test Answer Key Question 13.
Paula has 24 stamps in her collection. Among her stamps, \(\frac{1}{3}\) have pictures of animals. Out of her stamps with pictures of animals, \(\frac{3}{4}\) of those stamps have pictures of birds. How many stamps have pictures of birds on them?
_____ stamps

Answer: 6 stamps

Explanation:
Paula has 24 stamps in her collection. Among her stamps, \(\frac{1}{3}\) have pictures of animals.
Out of her stamps with pictures of animals, \(\frac{3}{4}\) of those stamps have pictures of birds.
\(\frac{1}{3}\) × \(\frac{3}{4}\) × 24 = 24/4 = 6
Therefore 6 stamps have pictures of birds.

Question 14.
Test Prep Barry bought 21 stamps from a hobby shop. He gave \(\frac{3}{7}\) of them to his sister. How many stamps did he have left?

Options:
a. 3 stamps
b. 6 stamps
c. 9 stamps
d. 12 stamps

Answer: 9 stamps

Explanation:
Test Prep Barry bought 21 stamps from a hobby shop. He gave \(\frac{3}{7}\) of them to his sister.
\(\frac{3}{7}\) × 21
7 divides 21 three times.
3 × 3 = 9 stamps.
Thus the correct answer is option C.

Share and Show – Page No. 297

Use the model to find the product.

Question 1.
\(\frac{5}{6}\) × 3

______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{2}\)

Explanation:
Place three whole fractions strips side by side.
Find six fraction strips all with the same denominator that fits exactly under the three whole numbers.
Circle \(\frac{5}{6}\) of 3 on the model you drew.
Complete the number sentence. \(\frac{5}{6}\) of 3
\(\frac{5}{6}\) × 3 = \(\frac{5}{2}\)
2 \(\frac{1}{2}\)

Question 2.
2 × \(\frac{5}{6}\)

______ \(\frac{□}{□}\)

Answer: 1 \(\frac{2}{3}\)

Explanation:
Place two whole fractions strips side by side.
Find six fraction strips all with the same denominator that fits exactly under the two whole numbers.
2 of \(\frac{5}{6}\) = \(\frac{5}{6}\) × 2
\(\frac{5}{3}\)
The mixed fraction of \(\frac{5}{3}\) is 1 \(\frac{2}{3}\)

Find the product.

Question 3.
\(\frac{5}{12}\) × 3 = ______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{4}\)

Explanation:
\(\frac{5}{12}\) × 3
Place three whole fractions strips side by side.
Find six fraction strips all with the same denominator that fits exactly under the two whole numbers.
\(\frac{5}{12}\) × 3
3 divides 12 four times
\(\frac{5}{12}\) × 3 = \(\frac{5}{4}\)
The mixed fraction of \(\frac{5}{4}\) is 1 \(\frac{1}{4}\)
\(\frac{5}{12}\) × 3 = 1 \(\frac{1}{4}\)

Go Math Book 5th Grade Lesson 7.2 Homework Answer Key Question 4.
9 × \(\frac{1}{3}\) = ______

Answer: 3

Explanation:
9 × \(\frac{1}{3}\)
Place nine whole fractions strips side by side.
Find three fraction strips all with the same denominator that fits exactly under the two whole numbers.
9 × \(\frac{1}{3}\)
3 divides 9 three times.
9 × \(\frac{1}{3}\) = 3
Thus 9 × \(\frac{1}{3}\) = 3

Question 5.
\(\frac{7}{8}\) × 4 = ______ \(\frac{□}{□}\)

Answer: 3 \(\frac{1}{2}\)

Explanation:
\(\frac{7}{8}\) × 4
Place four whole fractions strips side by side.
\(\frac{7}{8}\) × 4
4 divides 8 two times.
\(\frac{7}{8}\) × 4 = \(\frac{7}{2}\)
The mixed fraction of  \(\frac{7}{2}\) is 3 \(\frac{1}{2}\)
\(\frac{7}{8}\) × 4 = 3 \(\frac{1}{2}\)

Question 6.
4 × \(\frac{3}{5}\) = ______ \(\frac{□}{□}\)

Answer: 2 \(\frac{2}{5}\)

Explanation:
4 × \(\frac{3}{5}\)
Place four whole fractions strips side by side.
Place three \(\frac{1}{5}\) fraction strips all with the same denominator that fits exactly under the two whole numbers.
4 of \(\frac{3}{5}\)
4 × \(\frac{3}{5}\) = \(\frac{12}{5}\)
The mixed fraction of \(\frac{12}{5}\) is 2 \(\frac{2}{5}\)

Question 7.
\(\frac{7}{8}\) × 2 = ______ \(\frac{□}{□}\)

Answer: 1 \(\frac{3}{4}\)

Explanation:
\(\frac{7}{8}\) × 2
Place two whole fractions strips side by side.
Place seven \(\frac{1}{8}\) fraction strips all with the same denominator that fits exactly under the two whole numbers.
\(\frac{7}{8}\) of 2
\(\frac{7}{8}\) × 2 = \(\frac{7}{4}\)
The mixed fraction of \(\frac{7}{4}\) is 1 \(\frac{3}{4}\)

Question 8.
7 × \(\frac{2}{5}\) = ______ \(\frac{□}{□}\)

Answer: 2 \(\frac{4}{5}\)

Explanation:
7 × \(\frac{2}{5}\)
Place seven whole fractions strips side by side.
Place two \(\frac{1}{5}\) fraction strips all with the same denominator that fits exactly under the two whole numbers.
7 × \(\frac{2}{5}\) = \(\frac{14}{5}\)
The mixed fraction of \(\frac{14}{5}\) = 2 \(\frac{4}{5}\)

Question 9.
\(\frac{3}{8}\) × 4 = ______

Answer: \(\frac{3}{2}\)

Explanation:
\(\frac{3}{8}\) × 4
Place four whole fractions strips side by side.
Place three \(\frac{1}{8}\) fraction strips all with the same denominator that fits exactly under the two whole numbers.

Go Math Grade 5 Chapter 7 Lesson 7.2 Answer Key Question 10.
11 × \(\frac{3}{4}\) = ______ \(\frac{□}{□}\)

Answer: 8 \(\frac{1}{4}\)

Explanation:
11 × \(\frac{3}{4}\)
Place Eleven whole fractions strips side by side.
Place three \(\frac{1}{4}\) fraction strips all with the same denominator that fits exactly under the two whole numbers.
11 of \(\frac{3}{4}\)
11 × \(\frac{3}{4}\) = \(\frac{33}{4}\)
Convert the improper fraction to the mixed fraction.
\(\frac{33}{4}\) = 8 \(\frac{1}{4}\)
11 × \(\frac{3}{4}\) = 8 \(\frac{1}{4}\)

Question 11.
\(\frac{4}{15}\) × 5 = ______ \(\frac{□}{□}\)

Answer: 5 \(\frac{1}{3}\)

Explanation:
\(\frac{4}{15}\) × 5
Place five whole fractions strips side by side.
Place four \(\frac{1}{15}\) fraction strips all with the same denominator that fits exactly under the two whole numbers.
\(\frac{4}{15}\) of 5
\(\frac{4}{15}\) × 5 = \(\frac{4}{3}\)
Convert the improper fraction to the mixed fraction.
\(\frac{4}{3}\) = 5 \(\frac{1}{3}\)

Question 12.
Matt has a 5-pound bag of apples. To make a pie, he needs to use \(\frac{3}{5}\) of the bag. How many pounds of apples will he use for the pie? Explain what a model for this problem might look like.
______ pound(s)

Answer: 3 pounds

Explanation:
Given, Matt has a 5-pound bag of apples.
To make a pie, he needs to use \(\frac{3}{5}\) of the bag.
\(\frac{3}{5}\) × 5 = 3
Therefore Matt used 3 pounds of apples to make a pie.

Problem Solving – Page No. 298

Pose a Problem

Question 13.
Tarique drew the model below for a problem. Write 2 problems that can be solved using this model. One of your problems should involve multiplying a whole number by a fraction and the other problem should involve multiplying a fraction by a whole number.

Pose problems.                                       Solve your problems.
How could you change the model to give you an answer of 4 \(\frac{4}{5}\)?
Explain and write a new equation.
Type below:
_________

Answer:
The five children in the Smith family each spend 2/5 of an hour doing household chores on Saturday. How much time did they spend altogether on their chores?
Multiply the numerator with the whole number.
5 × \(\frac{2}{5}\) = \(\frac{10}{5}\) = 2

Share and Show – Page No. 301

Find the product. Write the product in the simplest form.

Question 1.
3 × \(\frac{2}{5}\) =
• Multiply the numerator by the whole number. Write the product over the denominator.

• Write the answer as a mixed number in simplest form.

______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{5}\)

Explanation:
Multiply the whole number with the numerator.
3 \(\frac{2}{5}\) = \(\frac{6}{5}\)
Now write the improper fraction in the form of the mixed fraction.
\(\frac{6}{5}\) = 1 \(\frac{1}{5}\)

Question 2.
\(\frac{2}{3}\) × 5 = ______ \(\frac{□}{□}\)

Answer: 3 \(\frac{1}{3}\)

Explanation:
Multiply the whole number with the numerator.
\(\frac{2}{3}\) × 5 = \(\frac{10}{3}\)
Now write the improper fraction in the form of the mixed fraction.
\(\frac{10}{3}\) = 3 \(\frac{1}{3}\)

Question 3.
6 × \(\frac{2}{3}\) = ______

Answer: 4

Explanation:
6 × \(\frac{2}{3}\)
Multiply the whole number with the numerator.
6 × \(\frac{2}{3}\) = \(\frac{12}{3}\)
Now write the improper fraction in the form of the mixed fraction.
\(\frac{12}{3}\) = 4

Lesson 7.3 5th Grade Homework Answers Question 4.
\(\frac{5}{7}\) × 4 = ______ \(\frac{□}{□}\)

Answer: 2 \(\frac{6}{7}\)

Explanation:
\(\frac{5}{7}\) × 4
Multiply the whole number with the numerator.
\(\frac{5}{7}\) × 4 = \(\frac{20}{7}\)
Now write the improper fraction in the form of the mixed fraction.
2 \(\frac{6}{7}\)
Thus, \(\frac{5}{7}\) × 4 = 2 \(\frac{6}{7}\)

On Your Own

Find the product. Write the product in simplest form.

Question 5.
5 × \(\frac{2}{3}\) = ______ \(\frac{□}{□}\)

Answer: 3 \(\frac{1}{3}\)

Explanation:
5 × \(\frac{2}{3}\)
Multiply the whole number with the numerator.
5 × \(\frac{2}{3}\) = \(\frac{10}{3}\)
Now write the improper fraction in the form of the mixed fraction.
3 \(\frac{1}{3}\)
5 × \(\frac{2}{3}\) = 3 \(\frac{1}{3}\)

Question 6.
\(\frac{1}{4}\) × 3 = ______ \(\frac{□}{□}\)

Answer: \(\frac{3}{4}\)

Explanation:
\(\frac{1}{4}\) × 3
Multiply the whole number with the numerator.
\(\frac{1}{4}\) × 3 = \(\frac{3}{4}\)

Question 7.
7 × \(\frac{7}{8}\) = ______ \(\frac{□}{□}\)

Answer: 6 \(\frac{1}{8}\)

Explanation:
7 × \(\frac{7}{8}\)
Multiply the whole number with the numerator.
\(\frac{49}{8}\)
Now write the improper fraction in the form of the mixed fraction.
\(\frac{49}{8}\) = 6 \(\frac{1}{8}\)
Thus, 7 × \(\frac{7}{8}\) = 6 \(\frac{1}{8}\)

Question 8.
2 × \(\frac{4}{5}\) = ______ \(\frac{□}{□}\)

Answer: 1 \(\frac{3}{5}\)

Explanation:
2 × \(\frac{4}{5}\)
Multiply the whole number with the numerator.
2 × \(\frac{4}{5}\) = \(\frac{8}{5}\)
Now write the improper fraction in the form of the mixed fraction.
\(\frac{8}{5}\) = 1 \(\frac{3}{5}\)

Question 9.
4 × \(\frac{3}{4}\) = ______

Answer: 3

Explanation:
Multiply the whole number with the numerator.
4 × \(\frac{3}{4}\) = \(\frac{12}{4}\)
4 divides 12 three times.
So, \(\frac{12}{4}\) = 3
4 × \(\frac{3}{4}\) = 3

Question 10.
\(\frac{7}{9}\) × 2 = ______ \(\frac{□}{□}\)

Answer: 1 \(\frac{5}{9}\)

Explanation:
\(\frac{7}{9}\) × 2
Multiply the whole number with the numerator.
\(\frac{7}{9}\) × 2 = \(\frac{14}{9}\)
Now write the improper fraction in the form of the mixed fraction.
\(\frac{14}{9}\) = 1 \(\frac{5}{9}\)

Practice: Copy and Solve. Find the product. Write the product in simplest form.

Question 11.
\(\frac{3}{5}\) × 11 = ______ \(\frac{□}{□}\)

Answer: 6 \(\frac{3}{5}\)

Explanation:
\(\frac{3}{5}\) × 11
Multiply the whole number with the numerator.
\(\frac{3}{5}\) × 11 = \(\frac{33}{5}\)
Now write the improper fraction in the form of the mixed fraction.
\(\frac{33}{5}\) = 6 \(\frac{3}{5}\)

Go Math Lesson 7.3 Answer Key Grade 5 Question 12.
3 × \(\frac{3}{4}\) = ______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{4}\)

Explanation:
3 × \(\frac{3}{4}\)
Multiply the whole number with the numerator.
3 × \(\frac{3}{4}\) = \(\frac{9}{4}\)
Now write the improper fraction in the form of the mixed fraction.
\(\frac{9}{4}\) = 2 \(\frac{1}{4}\)

Question 13.
\(\frac{5}{8}\) × 3 = ______ \(\frac{□}{□}\)

Answer: 1 \(\frac{7}{8}\)

Explanation:
\(\frac{5}{8}\) × 3
Multiply the whole number with the numerator.
\(\frac{5}{8}\) × 3 = \(\frac{15}{8}\)
Now write the improper fraction in the form of the mixed fraction.
\(\frac{15}{8}\) = 1 \(\frac{7}{8}\)

Algebra Find the unknown digit.

Question 14.
\(\frac{■}{2}\) × 8 = 4
■ = ______

Answer: 1

Explanation:
\(\frac{■}{2}\) × 8 = 4
\(\frac{■}{2}\) = 4/8
■ = 4 × 2/8 = 1
■ = 1

Question 15.
■ × \(\frac{5}{6}\) = \(\frac{20}{6}\) or 3 \(\frac{1}{3}\)
■ = ______

Answer: 4

Explanation:
■ × \(\frac{5}{6}\) = \(\frac{20}{6}\)
■ = 20/6 × 6/5
■ = 20/5 = 4
■ = 4

Question 16.
\(\frac{1}{■}\) × 18 = 3
■ = ______

Answer: 6

Explanation:
\(\frac{1}{■}\) × 18 = 3
\(\frac{1}{3}\) × 18 = ■
■ = 18/3 = 6
■ = 6

UNLOCK the Problem – Page No. 302

Question 17.
The caterer wants to have enough turkey to feed 24 people. If he wants to provide \(\frac{3}{4}\) of a pound of turkey for each person, how much turkey does he need?
a. What do you need to find?
Type below:
__________

Answer: I need to find How much turkey the caterer needs to provide for each person.

Question 17.
b. What operation will you use?
Type below:
__________

Answer: I will use the multiplication operation to solve the problem.

Question 17.
c. What information are you given?
Type below:
__________

I am given the information about the number of people to feed and the fraction of pounds of turkey each person gets.

Question 17.
d. Solve the problem.
Type below:
__________

Answer:
The caterer wants to serve 24 people
\(\frac{3}{4}\) × 24
4 divides 24 six times.
3 × 6 = 18
Thus the caterer needs 18 pounds of Turkey.

Question 17.
e. Complete the sentences.
The caterer wants to serve 24 people _____ of a pound of turkey each.
He will need ____ × ____ , or ______ pounds of turkey.
Type below:
__________

Answer: \(\frac{3}{4}\) × 24

Question 17.
f. Fill in the bubble for the correct answer choice.
Options:
a. 72 pounds
b. 24 pounds
c. 18 pounds
d. 6 pounds

Answer: 18 pounds

Explanation:
The caterer wants to serve 24 people
\(\frac{3}{4}\) × 24
4 divides 24 six times.
3 × 6 = 18
The correct answer is option C.

Question 18.
Patty wants to run \(\frac{5}{6}\) of a mile every day for 5 days. How far will she run in that time?
Options:
a. 25 miles
b. 5 miles
c. 4 \(\frac{1}{6}\) miles
d. 1 \(\frac{2}{3}\) miles

Answer: 4 \(\frac{1}{6}\) miles

Explanation:
Patty wants to run \(\frac{5}{6}\) of a mile every day for 5 days.
\(\frac{5}{6}\) × 5 = \(\frac{25}{6}\)
Convert the improper fraction to the mixed fraction.
\(\frac{25}{6}\) = 4 \(\frac{1}{6}\) miles
Thus the correct answer is option C.

Question 19.
Doug has 33 feet of rope. He wants to use \(\frac{2}{3}\) of it for his canoe. How many feet of rope will he use for his canoe?
Options:
a. 11 feet
b. 22 feet
c. 33 feet
d. 66 feet

Answer: 22 feet

Explanation:
Doug has 33 feet of rope. He wants to use \(\frac{2}{3}\) of it for his canoe.
\(\frac{2}{3}\) × 33 feet
3 divides 33 eleven times.
2 × 11 = 22 feet
The correct answer is option B.

Share and Show – Page No. 304

Use the model to find the product.

Question 1.

\(\frac{3}{5} \times \frac{1}{3}=\)
\(\frac{□}{□}\)

Answer: \(\frac{1}{5}\)

Explanation:
The fraction \(\frac{3}{5}\) represents the rows and columns.
The fraction \(\frac{1}{3}\) indicates the shaded part of the figure.
\(\frac{3}{5}\) × \(\frac{1}{3}\) = \(\frac{1}{5}\)

Question 2.

\(\frac{2}{3} \times \frac{3}{5}=\)
\(\frac{□}{□}\)

Answer: \(\frac{2}{5}\)

Explanation:

The above figure shows that the circle is divided into 5 parts in which 2 parts are non shaded and 3 parts are shaded.
So, the fraction of the circle is \(\frac{2}{3}\)
The fraction for the shaded part of the circle is \(\frac{3}{5}\)
\(\frac{2}{3}\) × \(\frac{3}{5}\) = \(\frac{2}{5}\)

Share and Show – Page No. 305

Find the product. Draw a model.

Question 3.
\(\frac{2}{3} \times \frac{1}{5}=\) \(\frac{□}{□}\)

Answer: \(\frac{2}{15}\)

Explanation:
\(\frac{2}{3}\) × \(\frac{1}{5}\)
Multiply the denominators of both fractions.
\(\frac{2}{15}\)
\(\frac{2}{3} \times \frac{1}{5}=\) \(\frac{2}{15}\)

Go Math Grade 5 Lesson 7.4 Answer Key Question 4.
\(\frac{1}{2} \times \frac{5}{6}=\) \(\frac{□}{□}\)

Answer: \(\frac{5}{12}\)

Explanation:
\(\frac{1}{2}\) × \(\frac{5}{6}\)
Multiply the numerators and the denominators.
\(\frac{1}{2}\) × \(\frac{5}{6}\) = \(\frac{5}{12}\)
\(\frac{1}{2} \times \frac{5}{6}=\) \(\frac{5}{12}\)

Question 5.
\(\frac{3}{5} \times \frac{1}{3}=\) \(\frac{□}{□}\)

Answer: \(\frac{1}{5}\)

Explanation:
\(\frac{3}{5}\) × \(\frac{1}{3}\)
Multiply the denominators and the numerators of the fractions.
\(\frac{3}{5}\) × \(\frac{1}{3}\) = \(\frac{3}{15}\)
\(\frac{3}{15}\) = \(\frac{1}{5}\)
\(\frac{3}{5} \times \frac{1}{3}=\) \(\frac{1}{5}\)

Question 6.
\(\frac{3}{4} \times \frac{1}{6}=\) \(\frac{□}{□}\)

Answer: \(\frac{1}{8}\)

Explanation:
\(\frac{3}{4}\) × \(\frac{1}{6}\)
Multiply the denominators and the numerators of the fractions.
\(\frac{3}{4}\) × \(\frac{1}{6}\) = \(\frac{3}{24}\)
3 divides 24 eight times.
So, \(\frac{3}{24}\) = \(\frac{1}{8}\)
Thus, \(\frac{3}{4} \times \frac{1}{6}=\) \(\frac{1}{8}\)

Question 7.
\(\frac{2}{5} \times \frac{5}{6}=\) \(\frac{□}{□}\)

Answer: \(\frac{1}{3}\)

Explanation:
\(\frac{2}{5}\) × \(\frac{5}{6}\)
Multiply the denominators and the numerators of the fractions.
\(\frac{2}{5}\) × \(\frac{5}{6}\) = \(\frac{10}{30}\)
10 divides 30 three times.
\(\frac{10}{30}\) = \(\frac{1}{3}\)
\(\frac{2}{5} \times \frac{5}{6}=\) \(\frac{1}{3}\)

Question 8.
\(\frac{5}{6} \times \frac{3}{5}=\) \(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
\(\frac{5}{6}\) × \(\frac{3}{5}\)
Multiply the denominators and the numerators of the fractions.
\(\frac{5}{6}\) × \(\frac{3}{5}\) = \(\frac{15}{30}\)
\(\frac{5}{6}\) × \(\frac{3}{5}\) = \(\frac{15}{30}\) = \(\frac{1}{2}\)
\(\frac{5}{6} \times \frac{3}{5}=\) \(\frac{1}{2}\)

Problem Solving – Page No. 306

What’s the Error?

Question 9.
Cheryl and Marcus are going to make a two-tiered cake. The smaller tier is \(\frac{2}{3}\) the size of the larger tier. The recipe for the bottom tier calls for \(\frac{3}{5}\) cup of water. How much water will they need to make the smaller tier?

They made a model to represent the problem. Cheryl says they need \(\frac{6}{9}\) cup of water. Marcus says they need \(\frac{2}{5}\) cup water. Who is correct? Explain.

Cheryl’s answer               Marcus’ answer
Type below:
_________

Answer: Marcus’ answer is correct.

Explanation:
Cheryl and Marcus are going to make a two-tiered cake.
The smaller tier is \(\frac{2}{3}\) the size of the larger tier.
The recipe for the bottom tier calls for \(\frac{3}{5}\) cup of water.
\(\frac{3}{5}\) × \(\frac{2}{3}\) = \(\frac{2}{5}\)

Share and Show – Page No. 309

Complete the statement with equal to, greater than, or less than.

Question 1.
4 × \(\frac{7}{8}\) will be ___________ \(\frac{7}{8}\)

_________

Answer: Greater than

Explanation:
4 × \(\frac{7}{8}\) = \(\frac{7}{2}\)
The denominator with a greater number will be the smallest number.
So, \(\frac{7}{2}\) is greater than \(\frac{7}{8}\)

Question 2.
\(\frac{3}{5} \times \frac{2}{7}\) will be ___________ \(\frac{3}{5}\)

Answer: Less than

Explanation:
\(\frac{3}{5}\) × \(\frac{2}{7}\) = \(\frac{6}{35}\)
The denominator with the greatest number will be the smallest fraction.
So, \(\frac{6}{35}\) is less than \(\frac{3}{5}\)

Question 3.
\(\frac{5}{8} \times 6\) will be ___________ \(\frac{5}{8}\)

Answer: Greater than

Explanation:
\(\frac{5}{8}\) × 6 = \(\frac{15}{4}\)
\(\frac{15}{4}\) = 3 \(\frac{3}{4}\)
3 \(\frac{3}{4}\) is greater than \(\frac{5}{8}\)

Question 4.
\(\frac{2}{3} \times \frac{5}{5}\) will be ___________ \(\frac{2}{3}\)

Answer: Equal to

Explanation:
\(\frac{2}{3}\) × \(\frac{5}{5}\) = \(\frac{2}{3}\)
\(\frac{2}{3}\) is equal to \(\frac{2}{3}\)

Question 5.
\(8 \times \frac{7}{8}\) will be ___________ 8

Answer: Less than

Explanation:
8 × \(\frac{7}{8}\)= 7
7 is less than 8.
\(8 \times \frac{7}{8}\) will be less than 8.

On Your Own

Complete the statement with equal to, greater than, or less than.

Question 6.
\(\frac{4}{9} \times \frac{3}{8}\) will be ___________ \(\frac{3}{8}\)

Answer: Less than

Explanation:
\(\frac{4}{9}\) × \(\frac{3}{8}\) = \(\frac{12}{72}\)
= \(\frac{1}{6}\)
\(\frac{1}{6}\) is less than \(\frac{3}{8}\)
\(\frac{4}{9} \times \frac{3}{8}\) will be less than \(\frac{3}{8}\)

Go Math Lesson 7.5 Answer Key 5th Grade Question 7.
\(7 \times \frac{9}{10}\) will be ___________ \(\frac{9}{10}\)

Answer: Greater than

Explanation:
7 × \(\frac{9}{10}\) = \(\frac{63}{10}\)
Denominators are the same so compare the numerators.
\(\frac{63}{10}\) is greater than \(\frac{9}{10}\)

Question 8.
\(5 \times \frac{1}{3}\) will be ___________ \(\frac{1}{3}\)

Answer: Greater than

Explanation:
5 × \(\frac{1}{3}\) = \(\frac{5}{3}\)
Denominators are same so compare the numerators.
\(\frac{5}{3}\) is greater than \(\frac{1}{3}\)

Question 9.
\(\frac{6}{11} \times 1\) will be ___________ \(\frac{6}{11}\)

Answer: Equal to

Explanation:
\(\frac{6}{11}\) × 1 = \(\frac{6}{11}\)
\(\frac{6}{11}\) is equal to \(\frac{6}{11}\).

Question 10.
\(\frac{1}{6} \times \frac{7}{7}\) will be ___________ 1

Answer: Less than

Explanation:
\(\frac{1}{6}\) × \(\frac{7}{7}\) = \(\frac{1}{6}\)
\(\frac{1}{6}\) is less than 1

Question 11.
\(4 \times \frac{3}{5}\) will be ___________ \(\frac{3}{5}\)

Answer: Greater than

Explanation:
4 × \(\frac{3}{5}\) = \(\frac{12}{5}\)
Denominators are same so compare the numerators.
\(\frac{12}{5}\) is greater than \(\frac{3}{5}\)

Problem Solving – Page No. 310

Question 12.
Lola is making cookies. She plans to multiply the recipe by 3 so she can make enough cookies for the whole class. If the recipe calls for \(\frac{2}{3}\) cup of sugar, will she need more than \(\frac{2}{3}\) or less than \(\frac{2}{3}\) cup of sugar to make all the cookies?
_________ \(\frac{2}{3}\) cup of sugar

Answer: More than

Explanation:
ola is making cookies. She plans to multiply the recipe by 3 so she can make enough cookies for the whole class.
3 × \(\frac{2}{3}\) = 2
So, Lola needs more than \(\frac{2}{3}\) cup of sugar.

Question 13.
Peter is planning on spending \(\frac{2}{3}\) as many hours watching television this week as he did last week. Is Peter going to spend more hours or fewer hours watching television this week?
_________ hours

Answer: Fewer

Explanation:
Peter is planning on spending \(\frac{2}{3}\) as many hours watching television this week as he did last week.
7 × \(\frac{2}{3}\) = \(\frac{14}{3}\)
\(\frac{14}{3}\) = 4 \(\frac{2}{3}\)
Thus peter going to spend more hours or fewer hours watching television this week.

Question 14.
Test Prep Rochelle saves \(\frac{1}{4}\) of her allowance. If she decides to start saving \(\frac{1}{2}\) as much, which statement below is true?
Options:
a. She will be saving the same amount.
b. She will be saving more.
c. She will be saving less.
d. She will be saving twice as much.

Answer: She will be saving more

Explanation:
Test Prep Rochelle saves \(\frac{1}{4}\) of her allowance.
\(\frac{1}{4}\) is greater than \(\frac{1}{2}\)
So, the answer is option B.

Connect to Art

A scale model is a representation of an object with the same shape as the real object. Models can be larger or smaller than the actual object but are often smaller.

Architects often make scale models of the buildings or structures they plan to build. Models can give them an idea of how the structure will look when finished. Each measurement of the building is scaled up or down by the same factor.

Bob is building a scale model of his bike. He wants his model to be \(\frac{1}{5}\) as long as his bike.

Question 15.
If Bob’s bike is 60 inches long, how long will his model be?
_____ in.

Answer: 12 inches

Explanation:
Given that, Bob is building a scale model of his bike. He wants his model to be \(\frac{1}{5}\) as long as his bike.
If Bob’s bike is 60 inches long then multiply with the fraction \(\frac{1}{5}\)
\(\frac{1}{5}\) × 60 = 12 inches
The model will be 12 inches long.

Question 16.
If one wheel on Bob’s model is 4 inches across, how many inches across is the actual wheel on his bike? Explain.
\(\frac{□}{□}\) in.

Answer: \(\frac{4}{5}\) in.

Explanation:
Given that, one wheel on Bob’s model is 4 inches across.
4 × \(\frac{1}{5}\) = \(\frac{4}{5}\) in.

Share and Show – Page No. 313

Find the product. Write the product in simplest form.

Question 1.
\(6 \times \frac{3}{8}\)
\(\frac{6}{1} \times \frac{3}{8}\) = \(\frac{■}{■}\)
______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{4}\)

Explanation:
\(\frac{6}{1} \times \frac{3}{8}\) = \(\frac{■}{■}\)
6 × \(\frac{3}{8}\) = \(\frac{18}{8}\) = \(\frac{9}{4}\)
\(\frac{9}{4}\) = 2 \(\frac{1}{4}\)
2 \(\frac{1}{4}\) = \(\frac{■}{■}\)
\(\frac{■}{■}\) = 2 \(\frac{1}{4}\)

Question 2.
\(\frac{3}{8} \times \frac{8}{9}\) = \(\frac{□}{□}\)

Answer: \(\frac{1}{3}\)

Explanation:
\(\frac{3}{8} \times \frac{8}{9}\) = \(\frac{□}{□}\)
\(\frac{3}{8}\) × \(\frac{8}{9}\) = \(\frac{1}{3}\)
Thus, \(\frac{3}{8} \times \frac{8}{9}\) = \(\frac{1}{3}\)

Question 3.
\(\frac{2}{3} \times 27\) = ______

Answer: 18

Explanation:
27 × \(\frac{2}{3}\)
3 divides 27 nine times.
Thus, 27 × \(\frac{2}{3}\) = 18

Question 4.
\(\frac{5}{12} \times \frac{3}{5}\) = \(\frac{□}{□}\)

Answer: \(\frac{1}{4}\)

Explanation:
\(\frac{5}{12}\) × \(\frac{3}{5}\) = \(\frac{3}{12}\)
3 divides 12 four times.
\(\frac{3}{12}\) = \(\frac{1}{4}\)
\(\frac{5}{12} \times \frac{3}{5}\) = \(\frac{1}{4}\)

5th Grade Go Math Book 7.6 Answer Key Question 5.
\(\frac{1}{2} \times \frac{3}{5}\) = \(\frac{□}{□}\)

Answer: \(\frac{3}{10}\)

Explanation:
\(\frac{1}{2}\) × \(\frac{3}{5}\)
Multiply the numerators and the denominators.
\(\frac{1}{2}\) × \(\frac{3}{5}\)  = \(\frac{3}{10}\)
\(\frac{1}{2} \times \frac{3}{5}\) = \(\frac{3}{10}\)

Question 6.
\(\frac{2}{3} \times \frac{4}{5}\) = \(\frac{□}{□}\)

Answer: \(\frac{8}{15}\)

Explanation:
\(\frac{2}{3}\) × \(\frac{4}{5}\)
Multiply the numerators and the denominators.
\(\frac{2}{3}\) × \(\frac{4}{5}\) = \(\frac{8}{15}\)

Question 7.
\(\frac{1}{3} \times \frac{5}{8}\) = \(\frac{□}{□}\)

Answer: \(\frac{5}{24}\)

Explanation:
\(\frac{1}{3}\) × \(\frac{5}{8}\)
Multiply the numerators and the denominators.
\(\frac{1}{3} \times \frac{5}{8}\) = \(\frac{5}{24}\)

Question 8.
\(4 \times \frac{1}{5}\) = \(\frac{□}{□}\)

Answer: \(\frac{4}{5}\)

Explanation:
Multiply the numerator with the whole number.
4 × \(\frac{1}{5}\) = \(\frac{4}{5}\)
\(4 \times \frac{1}{5}\) = \(\frac{4}{5}\)

On Your Own

Find the product. Write the product in simplest form.

Question 9.
\(2 \times \frac{1}{8}\) = \(\frac{□}{□}\)

Answer: \(\frac{1}{4}\)

Explanation:
Multiply the whole number with the numerator.
2 × \(\frac{1}{8}\)
2 divides 8 four times.
2 × \(\frac{1}{8}\) = \(\frac{1}{4}\)
\(2 \times \frac{1}{8}\) = \(\frac{1}{4}\)

Question 10.
\(\frac{4}{9} \times \frac{4}{5}\) = \(\frac{□}{□}\)

Answer: \(\frac{16}{45}\)

Explanation:
\(\frac{4}{9}\) × \(\frac{4}{5}\)
Multiply the numerators and the denominators.
\(\frac{4}{9}\) × \(\frac{4}{5}\) = \(\frac{16}{45}\)
\(\frac{4}{9} \times \frac{4}{5}\) = \(\frac{16}{45}\)

Question 11.
\(\frac{1}{12} \times \frac{2}{3}\) = \(\frac{□}{□}\)

Answer: \(\frac{1}{18}\)

Explanation:
\(\frac{1}{12}\) × \(\frac{2}{3}\)
Multiply the numerators and the denominators.
\(\frac{1}{12}\) × \(\frac{2}{3}\) = \(\frac{2}{36}\)
\(\frac{2}{36}\) = \(\frac{1}{18}\)
\(\frac{1}{12} \times \frac{2}{3}\) = \(\frac{1}{18}\)

Question 12.
\(\frac{1}{7} \times 30\) = _____ \(\frac{□}{□}\)

Answer: 4 \(\frac{2}{7}\)

Explanation:
30 × \(\frac{1}{7}\) = \(\frac{30}{7}\)
Convert improper fraction to the mixed fraction.
\(\frac{30}{7}\) = 4 \(\frac{2}{7}\)
\(\frac{1}{7} \times 30\) = 4 \(\frac{2}{7}\)

Question 13.
Of the pets in the pet show, \(\frac{5}{6}\) are cats. \(\frac{4}{5}\) of the cats are calico cats. What fraction of the pets are calico cats?
\(\frac{□}{□}\) calico cats

Answer: \(\frac{2}{3}\)

Explanation:
Of the pets in the pet show, \(\frac{5}{6}\) are cats. \(\frac{4}{5}\) of the cats are calico cats.
\(\frac{5}{6}\) × \(\frac{4}{5}\) = \(\frac{20}{30}\) = \(\frac{2}{3}\)
\(\frac{2}{3}\) fraction of the pets are calico cats.

Question 14.
Five cats each ate \(\frac{1}{4}\) cup of food. How much food did they eat altogether?
_____ \(\frac{□}{□}\) cups of food

Answer: 1 \(\frac{1}{4}\)

Explanation:
Five cats each ate \(\frac{1}{4}\) cup of food.
5 × \(\frac{1}{4}\) = \(\frac{5}{4}\)
The mixed fraction of \(\frac{5}{4}\) is 1 \(\frac{1}{4}\)

Algebra Evaluate for the given value.

Question 15.
\(\frac{2}{5}\) × c for c = \(\frac{4}{7}\)
\(\frac{□}{□}\)

Answer: \(\frac{8}{35}\)

Explanation:
\(\frac{2}{5}\) × c = \(\frac{4}{7}\)
c = \(\frac{4}{7}\) × \(\frac{2}{5}\)
c = \(\frac{8}{35}\)

Question 16.
m × \(\frac{4}{5}\) for m = \(\frac{7}{8}\)
\(\frac{□}{□}\)

Answer: \(\frac{7}{10}\)

Explanation:
m = \(\frac{4}{5}\) × \(\frac{7}{8}\)
Multiply the numerators and denominators.
\(\frac{4}{5}\) × \(\frac{7}{8}\) = \(\frac{7}{10}\)

Question 17.
\(\frac{2}{3}\) × t for t = \(\frac{1}{8}\)
\(\frac{□}{□}\)

Answer: \(\frac{1}{12}\)

Explanation:
\(\frac{2}{3}\) × t for t = \(\frac{1}{8}\)
t = \(\frac{1}{8}\) × \(\frac{2}{3}\)
t = \(\frac{1}{12}\)

Question 18.
y × \(\frac{2}{3}\) for y = 5
_______

Answer: 4

Explanation:
y × \(\frac{2}{3}\) for y = 5
6 × \(\frac{2}{3}\) = 4

Problem Solving – Page No. 314

Speedskating is a popular sport in the Winter Olympics. Many young athletes in the U.S. participate in speedskating clubs and camps.

Question 19.
At a camp in Green Bay, Wisconsin, \(\frac{7}{9}\) of the participants were from Wisconsin. Of that group, \(\frac{3}{5}\) were 12 years old. What fraction of the group was from Wisconsin and 12 years old?
\(\frac{□}{□}\)

Answer: \(\frac{7}{15}\)

Explanation:
Given that,
At a camp in Green Bay, Wisconsin, \(\frac{7}{9}\) of the participants were from Wisconsin.
Of that group, \(\frac{3}{5}\) were 12 years old.
To find the fraction of the group was from Wisconsin and 12 years old
We have to multiply the fraction \(\frac{7}{9}\) and \(\frac{3}{5}\)
\(\frac{7}{9}\) × \(\frac{3}{5}\) = \(\frac{21}{45}\)
\(\frac{21}{45}\) = \(\frac{7}{15}\)
Thus the fraction of the group was from Wisconsin and 12 years old is \(\frac{7}{15}\).

Lesson 7.6 Go Math 5th Grade Question 20.
Maribel wants to skate 1 \(\frac{1}{2}\) miles on Monday. If she skates \(\frac{9}{10}\) mile Monday morning and \(\frac{2}{3}\) of that distance Monday afternoon, will she reach her goal? Explain.
_____

Answer: Yes

Explanation:
Maribel wants to skate 1 \(\frac{1}{2}\) miles on Monday.
To find whether Maribel reached her goal we have to multiply the fractions \(\frac{9}{10}\) and \(\frac{2}{3}\)
\(\frac{9}{10}\) × \(\frac{2}{3}\) = \(\frac{3}{5}\)
By this we can say that Maribel reaches her goal.
So, the answer is yes.

Question 21.
On the first day of camp, \(\frac{5}{6}\) of the skaters were beginners. Of the beginners, \(\frac{1}{3}\) were girls. What fraction of the skaters were girls and beginners? Explain why your answer is reasonable.
\(\frac{□}{□}\)

Answer: \(\frac{5}{18}\)

Explanation:
On the first day of camp, \(\frac{5}{6}\) of the skaters were beginners. Of the beginners, \(\frac{1}{3}\) were girls.
Multiply the fraction of the skaters were beginning and the fraction of skaters were girls.
\(\frac{5}{6}\) × latex]\frac{1}{3}[/latex] = latex]\frac{5}{18}[/latex]
The fraction of the skaters were girls and beginners are latex]\frac{5}{18}[/latex]

Question 22.
Test Prep On Wednesday, Danielle skated \(\frac{2}{3}\) of the way around the track in 2 minutes. Her younger brother skated \(\frac{3}{4}\) of Danielle’s distance in 2 minutes. What fraction of the track did Danielle’s brother finish in 2 minutes?
Options:
a. \(\frac{1}{3}\)
b. \(\frac{1}{2}\)
c. \(\frac{5}{7}\)
d. \(\frac{3}{4}\)

Answer: \(\frac{1}{2}\)

Explanation:
Test Prep On Wednesday, Danielle skated \(\frac{2}{3}\) of the way around the track in 2 minutes.
Her younger brother skated \(\frac{3}{4}\) of Danielle’s distance in 2 minutes.
Multiply the fraction of Danielle skated and her younger brother skated.
\(\frac{2}{3}\) × \(\frac{3}{4}\) = \(\frac{1}{2}\)
Thus the correct answer is option B.

Mid-Chapter Checkpoint – Page No. 315

Concept and Skills

Question 1.
Explain how you would model 5 × \(\frac{2}{3}\)
Type below:
__________

Answer: \(\frac{10}{3}\)

Question 2.
When you multiply \(\frac{2}{3}\) by a fraction less than one, how does the product compare to the factors?
Type below:
__________

Answer: \(\frac{2}{3}\) × \(\frac{1}{2}\)
= \(\frac{1}{3}\)

Find the product. Write the product in simplest form.

Question 3.
\(\frac{2}{3} \times 6\)
______

Answer: 4

Explanation:
6 × \(\frac{2}{3}\)
Multiply the numerator with the whole numbers.
\(\frac{1}{3}\)

Question 4.
\(\frac{4}{5} \times 7\)
______ \(\frac{□}{□}\)

Answer: 5 \(\frac{3}{5}\)

Explanation:
Multiply the numerator with the whole numbers.
\(\frac{4}{5} \times 7\)
7 × \(\frac{4}{5}\) = \(\frac{28}{5}\)
Convert the improper fraction to the mixed fraction.
\(\frac{28}{5}\) = 5 \(\frac{3}{5}\)
\(\frac{4}{5} \times 7\) = 5 \(\frac{3}{5}\)

Question 5.
\(8 \times \frac{5}{7}\)
______ \(\frac{□}{□}\)

Answer: 5 \(\frac{5}{7}\)

Explanation:
8 × \(\frac{5}{7}\)
Multiply the numerator with the whole numbers.
8 × \(\frac{5}{7}\) = \(\frac{40}{7}\)
Convert the improper fraction to the mixed fraction.
\(\frac{40}{7}\) = 5 \(\frac{5}{7}\)

Question 6.
\(\frac{7}{8} \times \frac{3}{8}\)
\(\frac{□}{□}\)

Answer: \(\frac{21}{64}\)

Explanation:
\(\frac{7}{8}\) × \(\frac{3}{8}\)
Multiply the numerators and denominators of the fractions.
\(\frac{7}{8}\) × \(\frac{3}{8}\) = \(\frac{21}{64}\)

Question 7.
\(\frac{1}{2} \times \frac{3}{4}\)
\(\frac{□}{□}\)

Answer: \(\frac{3}{8}\)

Explanation:
Multiply the numerators and denominators of the fractions.
\(\frac{1}{2} \times \frac{3}{4}\)
\(\frac{1}{2}\) × \(\frac{3}{4}\) = \(\frac{3}{8}\)
\(\frac{1}{2} \times \frac{3}{4}\) = \(\frac{3}{8}\)

Question 8.
\(\frac{7}{8} \times \frac{4}{7}\)
\(\frac{□}{□}\)

Answer: \(\frac{1}{2}\)

Explanation:
Multiply the numerators and denominators of the fractions.
7 in the numerator and 7 in the denominator will be canceled.
4 divides 8 two times.
Thus the fraction is \(\frac{1}{2}\)
\(\frac{7}{8} \times \frac{4}{7}\) = \(\frac{1}{2}\)

Question 9.
\(2 \times \frac{3}{11}\)
\(\frac{□}{□}\)

Answer: \(\frac{6}{11}\)

Explanation:
Multiply the numerator with the whole numbers.
2 × \(\frac{3}{11}\)
2 × 3 = 6
2 × \(\frac{3}{11}\) = \(\frac{6}{11}\)
Thus, \(2 \times \frac{3}{11}\) = \(\frac{6}{11}\)

Lesson 7 Homework 5th Grade Answer Key Question 10.
\(\frac{5}{8} \times \frac{2}{3}\)
\(\frac{□}{□}\)

Answer: \(\frac{5}{12}\)

Explanation:
\(\frac{5}{8} \times \frac{2}{3}\)
Multiply the numerators and denominators of the fractions.
\(\frac{5}{8}\) × \(\frac{2}{3}\) = \(\frac{10}{24}\)
\(\frac{10}{24}\) = \(\frac{5}{12}\)
\(\frac{5}{8} \times \frac{2}{3}\) = \(\frac{5}{12}\)

Question 11.
\(\frac{7}{12} \times 8\)
______ \(\frac{□}{□}\)

Answer: 4 \(\frac{2}{3}\)

Explanation:
8 × \(\frac{7}{12}\)
Multiply the numerator with the whole numbers.
8 × \(\frac{7}{12}\) = \(\frac{56}{12}\) = \(\frac{14}{3}\)
Convert the improper fraction to the mixed fraction.
\(\frac{14}{3}\) = 4 \(\frac{2}{3}\)

Complete the statement with equal to, greater than, or less than.

Question 12.
3 × \(\frac{2}{3}\) _________ 3

Answer: Less Than

Explanation:
3 × \(\frac{2}{3}\)
Multiply the numerator with the whole numbers.
3 in the denominator will be canceled.
3 × \(\frac{2}{3}\) = 2
2 is less than 3.
3 × \(\frac{2}{3}\) less than 3.

Question 13.
\(\frac{5}{7}\) × 3 _________ \(\frac{5}{7}\)

Answer: Greater than

Explanation:
\(\frac{5}{7}\) × 3
Multiply the numerator with the whole numbers.
\(\frac{5}{7}\) × 3 = \(\frac{15}{7}\)
Convert it into mixed fraction.
\(\frac{15}{7}\) = 2 \(\frac{1}{4}\)
2 \(\frac{1}{4}\) is greater than \(\frac{5}{7}\)

Mid-Chapter Checkpoint – Page No. 316

Question 14.
There is \(\frac{5}{6}\) of an apple pie left from dinner. Tomorrow, Victor plans to eat \(\frac{1}{6}\) of the pie that was left. How much of the whole pie will be left after he eats tomorrow?
\(\frac{□}{□}\) of the whole pie

Answer: \(\frac{25}{36}\) of the whole pie

Explanation:
Gīven that,
An apple pie left from the dinner is \(\frac{5}{6}\)
Victor plans to eat pie which was left is \(\frac{1}{6}\)
The whole pie will be left after Victor eats tomorrow =?
Pie left from dinner = \(\frac{5}{6}\)
Victor plans to eat pie which was left  = \(\frac{1}{6}\)
\(\frac{5}{6}\) × \(\frac{1}{6}\) = \(\frac{5}{36}\)
To find the whole pie will be left after he eats tomorrow:
\(\frac{5}{6}\) – \(\frac{5}{36}\)
LCD = 36
\(\frac{5}{6}\) × \(\frac{6}{6}\) – \(\frac{5}{36}\)
\(\frac{30}{36}\) – \(\frac{5}{36}\) = \(\frac{25}{36}\)
Therefore, whole pie left after Victor eats tomorrow is \(\frac{25}{36}\)

Question 15.
Everett and Marie are going to make fruit bars for their family reunion. They want to make 4 times the amount the recipe makes. If the recipe calls for \(\frac{2}{3}\) cup of oil, how much oil will they need?
______ \(\frac{□}{□}\) cup of oil

Answer: 2 \(\frac{2}{3}\)

Explanation:
Everett and Marie are going to make fruit bars for their family reunion.
They want to make 4 times the amount the recipe makes.
4 × \(\frac{2}{3}\) = \(\frac{8}{3}\)
The mixed fraction of \(\frac{8}{3}\) is 2 \(\frac{2}{3}\)
Thus Everett and Marie need Everett and Marie of oil.

Go Math Chapter 7 Grade 5 Question 16.
Matt made the model below to help him solve his math problem. Write an expression that matches Matt’s model.

Type below:
__________

Answer: \(\frac{3}{4}\) × \(\frac{1}{3}\)

Explanation:
By seeing the above figure we can say that the fraction for Matt’s model is \(\frac{3}{4}\) and \(\frac{2}{3}\).
Multiply the fractions \(\frac{3}{4}\) × \(\frac{2}{3}\) = \(\frac{1}{4}\)

Share and Show – Page No. 319

Use the grid to find the area. Let each square represent \(\frac{1}{3}\) meter by \(\frac{1}{3}\) meter.

Question 1.
1 \(\frac{2}{3}\) × 1 \(\frac{1}{3}\)
• Draw a diagram to represent the dimensions.

• How many squares cover the diagram?
• What is the area of each square?
• What is the area of the diagram?
______ \(\frac{□}{□}\)

Answer: 2 \(\frac{2}{9}\)

Explanation:
20 squares cover the diagram.
Each square represents \(\frac{1}{9}\) square meter
20 × \(\frac{1}{9}\) = \(\frac{20}{9}\)
Convert the fraction into the mixed fraction.
\(\frac{20}{9}\) = 2 \(\frac{2}{9}\)
Thus the area of the diagram is 2 \(\frac{2}{9}\)

Use the grid to find the area. Let each square represent \(\frac{1}{4}\) meter by \(\frac{1}{4}\) meter.

Question 2.
1 \(\frac{3}{4}\) × 1 \(\frac{2}{4}\)

______ \(\frac{□}{□}\)

Answer: 2 \(\frac{5}{8}\)

Explanation:
42 squares cover the diagram.
Each square represents \(\frac{1}{16}\) square meters.
42 × \(\frac{1}{16}\) = \(\frac{21}{8}\)
Convert the fraction into the mixed fraction.
\(\frac{21}{8}\) = 2 \(\frac{5}{8}\)
The area of the diagram is 2 \(\frac{5}{8}\) square meter.

Question 3.
1 \(\frac{1}{4}\) × 1 \(\frac{1}{2}\)

______ \(\frac{□}{□}\)

Answer: 1 \(\frac{7}{8}\)

Explanation:
30 squares cover the diagram.
Each square represents \(\frac{1}{16}\) square meters.
30 × \(\frac{1}{16}\) = \(\frac{15}{8}\)
Convert the fraction into the mixed fraction.
\(\frac{15}{8}\) = 1 \(\frac{7}{8}\)

Use an area model to solve.

Question 4.
1 \(\frac{3}{4}\) × 2 \(\frac{1}{2}\)
______ \(\frac{□}{□}\)

Answer: 4 \(\frac{3}{8}\)

Explanation:

54 squares covers the diagram.
Each square represents \(\frac{1}{16}\) square meters.
54 × \(\frac{1}{16}\) = \(\frac{27}{8}\)
Convert the fraction into the mixed fraction.
\(\frac{27}{8}\) = 4 \(\frac{3}{8}\)

Question 5.
1 \(\frac{3}{8}\) × 2 \(\frac{1}{2}\)
______ \(\frac{□}{□}\)

Answer: 3 \(\frac{7}{16}\)

Explanation:
55 squares cover the diagram.
Each square represents \(\frac{1}{16}\) square meters.
55 × \(\frac{1}{16}\) = \(\frac{55}{16}\)
Convert the fraction into the mixed fraction.
\(\frac{55}{16}\) = 3 \(\frac{7}{16}\)

Question 6.
1 \(\frac{1}{9}\) × 1 \(\frac{2}{3}\)
______ \(\frac{□}{□}\)

Answer: 1 \(\frac{23}{27}\)

Explanation:
130 squares the diagram.
Each square represents \(\frac{1}{16}\) square meters.
1 \(\frac{1}{9}\) × 1 \(\frac{2}{3}\)
\(\frac{10}{9}\) × \(\frac{5}{3}\) = \(\frac{50}{27}\)
Convert the fraction into the mixed fraction.
\(\frac{50}{27}\) = 1 \(\frac{23}{27}\)

Question 7.
Explain how finding the area of a rectangle with whole-number side lengths compares to finding the area of a rectangle with fractional side lengths.
Type below:
__________

Answer:

15 squares cover the diagram.
Each square is \(\frac{1}{16}\) square unit.
The area of the diagram is \(\frac{15}{16}\) square units.

Problem Solving – Page No. 320

Pose a Problem

Question 8.
Terrance is designing a garden. He drew the following diagram of his garden. Pose a problem using mixed numbers that can be solved using his diagram.


Pose a Problem.                 Solve your problem.
Describe how you decided on the dimensions of Terrance’s garden.
Type below:
__________

Answer:
how finding the area of a rectangle with mixed fractions side compares to finding the area of the rectangle with the fractional side lengths.
6 × 1 \(\frac{1}{8}\) = \(\frac{□}{□}\)
Let each square represent \(\frac{1}{2}\) meter by \(\frac{1}{2}\)
From the above figure, we can say that the number of squares is 27.
So, 27 squares cover the diagram.
Each square is \(\frac{1}{4}\) square unit.
27 × \(\frac{1}{4}\)  = \(\frac{27}{4}\)
Convert the fraction into the mixed fraction.
\(\frac{27}{4}\) = 6 \(\frac{3}{4}\)

Share and Show – Page No. 323

Complete the statement with equal to, greater than, or less than.

Question 1.
\(\frac{5}{6}\) × 2 \(\frac{1}{5}\) will be __________ 2 \(\frac{1}{5}\)
Shade the model to
show \(\frac{5}{6}\) × 2 \(\frac{1}{5}\) .
__________

Answer: Less than

Explanation:
\(\frac{5}{6}\) × 2 \(\frac{1}{5}\)
Convert the mixed fraction to the improper fraction.
2 \(\frac{1}{5}\) = \(\frac{11}{5}\)
\(\frac{5}{6}\) × \(\frac{11}{5}\) = \(\frac{55}{30}\)
1 \(\frac{25}{30}\) = 1 \(\frac{5}{6}\)
Thus 1 \(\frac{5}{6}\) is less than 2 \(\frac{1}{5}\)

Question 2.
1 \(\frac{1}{5}\) × 2 \(\frac{2}{3}\) will be __________ 2 \(\frac{2}{3}\)

Answer: Greater than

Explanation:
1 \(\frac{1}{5}\) × 2 \(\frac{2}{3}\)
First, Convert the mixed fraction to the improper fraction.
\(\frac{6}{5}\) × \(\frac{8}{3}\) = \(\frac{48}{15}\)
\(\frac{48}{15}\) = 3 \(\frac{3}{15}\)
3 \(\frac{3}{15}\) is greater than 2 \(\frac{2}{3}\)

Question 3.
\(\frac{4}{5}\) × 2 \(\frac{2}{5}\) will be __________ 2 \(\frac{2}{5}\)

Answer: Less than

Explanation:
\(\frac{4}{5}\) × \(\frac{12}{5}\)
First, Convert the mixed fraction to the improper fraction.
\(\frac{4}{5}\) × \(\frac{12}{5}\) = \(\frac{48}{5}\)
\(\frac{48}{5}\) = 9 \(\frac{3}{5}\)
9 \(\frac{3}{5}\) is less than 2 \(\frac{2}{5}\)

On Your Own

Complete the statement with equal to, greater than, or less than.

Question 4.
\(\frac{2}{2}\) × 1 \(\frac{1}{2}\) will be __________ 1 \(\frac{1}{2}\)

Answer: Equal to

Explanation:
\(\frac{2}{2}\) × \(\frac{3}{2}\) = \(\frac{6}{4}\)
\(\frac{6}{4}\) = 1 \(\frac{1}{2}\)
1 \(\frac{1}{2}\) is equal to 1 \(\frac{1}{2}\)
\(\frac{2}{2}\) × 1 \(\frac{1}{2}\) will be equal to 1 \(\frac{1}{2}\)

Question 5.
\(\frac{2}{3}\) × 3 \(\frac{1}{6}\) will be __________ 3 \(\frac{1}{6}\)

Answer: Less than

Explanation:
\(\frac{2}{3}\) × 3 \(\frac{1}{6}\)
First, Convert the mixed fraction to the improper fraction.
\(\frac{2}{3}\) × \(\frac{19}{6}\) = \(\frac{38}{18}\)
\(\frac{38}{18}\) = 2 \(\frac{2}{18}\)
2 \(\frac{2}{18}\) is less than 3 \(\frac{1}{6}\)
\(\frac{2}{3}\) × 3 \(\frac{1}{6}\) will be less than 3 \(\frac{1}{6}\)

Question 6.
2 × 2 \(\frac{1}{4}\) will be __________ 2 \(\frac{1}{4}\)

Answer: Greater than

Explanation:
2 × 2 \(\frac{1}{4}\)
First, Convert the mixed fraction to the improper fraction.
2 × \(\frac{9}{4}\) = \(\frac{18}{4}\)
\(\frac{18}{4}\) = 4 \(\frac{2}{4}\)
4 \(\frac{1}{2}\) is greater than 2 \(\frac{1}{4}\)

Question 7.
4 × 1 \(\frac{3}{7}\) will be __________ 1 \(\frac{3}{7}\)

Answer: Greater than

Explanation:
4 × 1 \(\frac{3}{7}\)
First, Convert the mixed fraction to the improper fraction.
4 × \(\frac{10}{7}\) = \(\frac{40}{7}\)
4 × 1 \(\frac{3}{7}\) = 5 \(\frac{5}{7}\)
5 \(\frac{5}{7}\) is greater than 1 \(\frac{3}{7}\)

Algebra Tell whether the unknown factor is less than 1 or greater than 1.

Question 8.
■ × 1 \(\frac{2}{3}\) = \(\frac{5}{6}\)
The unknown factor is __________ 1.

Answer: Less than

Explanation:
■ × 1 \(\frac{2}{3}\) = \(\frac{5}{6}\)
■ × \(\frac{5}{3}\) = \(\frac{5}{6}\)
■ = \(\frac{1}{2}\)
Thus the unknown factor is \(\frac{1}{2}\)
\(\frac{1}{2}\) is less than 1.

Question 9.
■ × 1 \(\frac{1}{4}\) = 2 \(\frac{1}{2}\)
The unknown factor is __________ 1.

Answer: Greater than

Explanation:
■ × 1 \(\frac{1}{4}\) = 2 \(\frac{1}{2}\)
■ = 2 \(\frac{1}{2}\) ÷ 1 \(\frac{1}{4}\)
■ = 2 × 2 = 4
■ = 4
Thus the unknown factor is 4
4 is greater than 1.

Problem Solving – Page No. 324

Question 10.
Kyle is making a scale drawing of his math book. The dimensions of his drawing will be \(\frac{1}{3}\) the dimensions of his book. If the width of his book is 8 \(\frac{1}{2}\) inches, will the width of his drawing be equal to, greater than, or less than 8 \(\frac{1}{2}\) inches?
__________

Answer: Less than

Explanation:
Given that,
Kyle is making a scale drawing of his math book.
The dimensions of his drawing will be \(\frac{1}{3}\) the dimensions of his book.
\(\frac{1}{3}\) × 8 \(\frac{1}{2}\)
First, Convert the mixed fraction to the improper fraction.
\(\frac{1}{3}\) × \(\frac{17}{2}\) = \(\frac{17}{6}\)
Convert the fraction into the mixed fraction.
\(\frac{17}{6}\) = 2 \(\frac{5}{6}\)
2 \(\frac{5}{6}\) is less than 8 \(\frac{1}{2}\) inches.

Question 11.
Sense or Nonsense?
Penny wants to make a model of a beetle that is larger than life-size. Penny says she is going to use a scaling factor of \(\frac{7}{12}\). Does this make sense or is it nonsense? Explain.
Type below:
__________

Answer: It is nonsense because Penny wants to make beetle Larger than life size. So, the scaling factor \(\frac{7}{12}\) is not corresponding, because when we multiply any value with the number less than 1 we get a smaller number.

Question 12.
Shannon, Mary, and John earn a weekly allowance. Shannon earns an amount that is \(\frac{2}{3}\) of what John earns. Mary earns an amount that is 1 \(\frac{2}{3}\) of what John earns. John earns $20 a week. Who earns the greatest allowance? Who earns the least?
__________ earns the greatest allowance.
__________ earns the least allowance

Answer:
Mary earns the greatest allowance.
Shannon earns the least allowance.

Explanation:

Shannon, Mary, and John earn a weekly allowance.
Shannon earns an amount that is \(\frac{2}{3}\) of what John earns.
Mary earns an amount that is 1 \(\frac{2}{3}\) of what John earns.
John earns $20 a week.
\(\frac{2}{3}\) ________ 1 \(\frac{2}{3}\)
Convert the mixed fraction into the improper fraction.
1 \(\frac{2}{3}\) = \(\frac{5}{3}\)
\(\frac{2}{3}\) is less than 1 \(\frac{2}{3}\)
Thus Shannon earns the least allowance and Mary earns the greatest allowance.

Question 13.
Test Prep Addie’s puppy weighs 1 \(\frac{2}{3}\) times what it weighed when it was born. It weighed 1 \(\frac{1}{3}\) pounds at birth. Which statement below is true?
Options:
a. The puppy weighs the same as it did at birth.
b. The puppy weighs less than it did at birth.
c. The puppy weighs more than it did at birth.
d. The puppy weighs twice what it did at birth.

Answer: The puppy weighs more than it did at birth.

Explanation:
Test Prep Addie’s puppy weighs 1 \(\frac{2}{3}\) times what it weighed when it was born.
It weighed 1 \(\frac{1}{3}\) pounds at birth.
1 \(\frac{2}{3}\) is greater than 1 \(\frac{1}{3}\).
So, the puppy weighs more than it did at birth.
Thus the correct answer is option C.

Share and Show – Page No. 327

Find the product. Write the product in simplest form.

Question 1.
1 \(\frac{2}{3}\) × 3 \(\frac{4}{5}\) = \(\frac{■}{3}\) × \(\frac{■}{5}\)
= \(\frac{■}{■}\)
=?
_____ \(\frac{□}{□}\)

Answer: 6 \(\frac{1}{3}\)

Explanation:

1 \(\frac{2}{3}\) × 3 \(\frac{4}{5}\)
\(\frac{5}{3}\) × \(\frac{19}{5}\)
\(\frac{■}{3}\) × \(\frac{■}{5}\) = \(\frac{5}{3}\) × \(\frac{19}{5}\)
\(\frac{5}{3}\) × \(\frac{19}{5}\) = 6 \(\frac{1}{3}\)

Question 2.
\(\frac{1}{2}\) × 1 \(\frac{1}{3}\)

Shade the model to find the product.
\(\frac{□}{□}\)

Answer: \(\frac{2}{3}\)

Explanation:
\(\frac{1}{2}\) × 1 \(\frac{1}{3}\)
1 \(\frac{1}{3}\) = \(\frac{4}{3}\)
\(\frac{1}{2}\) × \(\frac{4}{3}\) = \(\frac{4}{6}\)

Question 3.
\(1 \frac{1}{8} \times 2 \frac{1}{3}\) = ______ \(\frac{□}{□}\)

Answer: 2 \(\frac{5}{8}\)

Explanation:
1 \(\frac{1}{8}\) × 2 \(\frac{1}{3}\)
\(\frac{9}{8}\) × \(\frac{7}{3}\) = \(\frac{63}{24}\)
\(\frac{63}{24}\) = 2 \(\frac{63}{24}\) = 2 \(\frac{15}{24}\)
2 \(\frac{15}{24}\) = 2 \(\frac{5}{8}\)
\(1 \frac{1}{8} \times 2 \frac{1}{3}\) = 2 \(\frac{5}{8}\)

Question 4.
\(\frac{3}{4} \times 6 \frac{5}{6}\) = ______ \(\frac{□}{□}\)

Answer: 5 \(\frac{1}{8}\)

Explanation:
\(\frac{3}{4}\) × 6 \(\frac{5}{6}\)
\(\frac{3}{4}\) × \(\frac{41}{6}\)
\(\frac{123}{24}\) = \(\frac{41}{8}\)
Convert the fraction to the mixed fraction.
\(\frac{41}{8}\) = 5 \(\frac{1}{8}\)

Question 5.
\(1 \frac{2}{7} \times 1 \frac{3}{4}\) = ______ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{4}\)

Explanation:
1 \(\frac{2}{7}\) × 1 \(\frac{3}{4}\)
Multiply the numerators and the denominators.
Convert the mixed fraction to the improper fraction.
\(\frac{9}{7}\) × \(\frac{7}{4}\) = \(\frac{63}{28}\)
\(\frac{63}{28}\) = 2 \(\frac{1}{4}\)
\(1 \frac{2}{7} \times 1 \frac{3}{4}\) = 2 \(\frac{1}{4}\)

Question 6.
\(\frac{3}{4} \times 1 \frac{1}{4}\) = ______ \(\frac{□}{□}\)

Answer: \(\frac{15}{16}\)

Explanation:
\(\frac{3}{4}\) × 1 \(\frac{1}{4}\)
\(\frac{3}{4}\) × \(\frac{5}{4}\) = \(\frac{15}{16}\)
\(\frac{3}{4} \times 1 \frac{1}{4}\) = \(\frac{15}{16}\)

Use the Distributive Property to find the product.

Question 7.
\(16 \times 2 \frac{1}{2}\) = ______

Answer: 40

Explanation:
\(16 \times 2 \frac{1}{2}\)
(16 × 2) + (16 × \(\frac{1}{2}\))
32 + 8 = 40
\(16 \times 2 \frac{1}{2}\) = 40

Question 8.
\(1 \frac{4}{5} \times 15\) = ______

Answer: 27

Explanation:
\(1 \frac{4}{5} \times 15\)
15 × 1 \(\frac{4}{5}\)
(1 × 15) + (15 × \(\frac{4}{5}\))
15 + \(\frac{60}{5}\)
15 + 12 = 27
Thus \(1 \frac{4}{5} \times 15\) = 27

On Your Own

Find the product. Write the product in simplest form.

Question 9.
\(\frac{3}{4} \times 1 \frac{1}{2}\) = ______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{8}\)

Explanation:
\(\frac{3}{4}\) × 1 \(\frac{1}{2}\)
\(\frac{3}{4}\) × \(\frac{3}{2}\) = \(\frac{9}{8}\)
Now convert the improper fraction to the mixed fraction.
\(\frac{9}{8}\) = 1 \(\frac{1}{8}\)

Question 10.
\(4 \frac{2}{5} \times 1 \frac{1}{2}\) = ______ \(\frac{□}{□}\)

Answer: 6 \(\frac{3}{5}\)

Explanation:
4 \(\frac{2}{5}\) × 1 \(\frac{1}{2}\)
Convert the mixed fraction to the improper fraction.
\(\frac{22}{5}\) × \(\frac{3}{2}\) = \(\frac{66}{10}\)
The mixed fraction of \(\frac{66}{10}\) is 6 \(\frac{3}{5}\)

Question 11.
\(5 \frac{1}{3} \times \frac{3}{4}\) = ______

Answer: 4

Explanation:
5 \(\frac{1}{3}\) × \(\frac{3}{4}\)
Convert the mixed fraction to the improper fraction.
\(\frac{16}{3}\) × \(\frac{3}{4}\) = \(\frac{48}{12}\)
12 divides 48 four times.
Thus \(5 \frac{1}{3} \times \frac{3}{4}\) = 4

Question 12.
\(2 \frac{1}{2} \times 5 \frac{1}{5}\) = ______

Answer: 13

Explanation:
2 \(\frac{1}{2}\) × 5 \(\frac{1}{5}\)
\(\frac{5}{2}\) × \(\frac{26}{5}\) = \(\frac{130}{10}\)
10 divides 130 thirteen times.
\(\frac{130}{10}\) = 13
\(2 \frac{1}{2} \times 5 \frac{1}{5}\) = 13

Question 13.
\(12 \frac{3}{4} \times 2 \frac{2}{3}\) = ______

Answer: 34

Explanation:
12 \(\frac{3}{4}\) × 2 \(\frac{2}{3}\)
\(\frac{51}{4}\) × \(\frac{6}{3}\)
3 divides 51 seventeen times.
17 × 2 = 34

Question 14.
\(3 \times 4 \frac{1}{2}\) = ______ \(\frac{□}{□}\)

Answer: 13 \(\frac{1}{2}\)

Explanation:
3 × 4 \(\frac{1}{2}\)
3 × \(\frac{9}{2}\) = \(\frac{27}{2}\)
Convert the fraction to the mixed fraction
\(\frac{27}{2}\) = 13 \(\frac{1}{2}\)

Question 15.
\(2 \frac{3}{8} \times \frac{4}{9}\) = ______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{18}\)

Explanation:
2 \(\frac{3}{8}\) × \(\frac{4}{9}\)
\(\frac{19}{8}\) × \(\frac{4}{9}\) = \(\frac{76}{72}\)
\(\frac{76}{72}\) = 1 \(\frac{1}{18}\)
\(2 \frac{3}{8} \times \frac{4}{9}\) = 1 \(\frac{1}{18}\)

Question 16.
\(1 \frac{1}{3} \times 1 \frac{1}{4} \times 1 \frac{1}{5}\) = ______

Answer: 2

Explanation:

1 \(\frac{1}{3}\) × 1 \(\frac{1}{4}\) × 1 \(\frac{1}{5}\)
\(\frac{4}{3}\) × \(\frac{5}{4}\) × \(\frac{6}{5}\) = 2
\(1 \frac{1}{3} \times 1 \frac{1}{4} \times 1 \frac{1}{5}\) = 2

Use the Distributive Property to find the product.

Question 17.
\(10 \times 2 \frac{3}{5}\) = ______

Answer: 26

Explanation:
10 × 2 \(\frac{3}{5}\)
Now use the Distributive Property to find the product.
(10 × 2) + (10 × \(\frac{3}{5}\))
20 + \(\frac{30}{5}\)
5 divides 30 6 times.
20 + 6 = 26

Question 18.
\(3 \frac{3}{4} \times 12\) = ______

Answer: 45

Explanation:
3 \(\frac{3}{4}\) × 12
Now use the Distributive Property to find the product.
(12 × 3) + (12 × \(\frac{3}{4}\))
36 + \(\frac{36}{4}\)
36 + 9 = 45
\(3 \frac{3}{4} \times 12\) = 45

Share and Show Connect to health – Page No. 328

Changing Recipes

You can make a lot of recipes more healthful by reducing the amounts of fat, sugar, and salt.

Kelly has a muffin recipe that calls for 1 \(\frac{1}{2}\) cups of sugar. She wants to use \(\frac{1}{2}\) that amount of sugar and more cinnamon and vanilla. How much sugar will she use?
Multiply 1 \(\frac{1}{2}\) by \(\frac{1}{2}\) to find what part of the original amount of sugar to use.
Write the mixed number as a fraction greater than 1. Then, multiply.
\(\frac{1}{2} \times 1 \frac{1}{2}=\frac{1}{2} \times \frac{3}{2}\)
= \(\frac{3}{4}\)
So, Kelly will use \(\frac{3}{4}\) cup of sugar.

Question 19.
Michelle has a recipe that calls for 2 \(\frac{1}{2}\) cups of vegetable oil. She wants to use \(\frac{2}{3}\) that amount of oil and use applesauce to replace the rest. How much vegetable oil will she use?
______ \(\frac{□}{□}\) cups

Answer: 1 \(\frac{2}{3}\)

Explanation:
Michelle has a recipe that calls for 2 \(\frac{1}{2}\) cups of vegetable oil.
She wants to use \(\frac{2}{3}\) that amount of oil and use applesauce to replace the rest
Multiply 2 \(\frac{1}{2}\) by \(\frac{2}{3}\) to find how much vegetable oil she will use.
2 \(\frac{1}{2}\) × \(\frac{2}{3}\)
Convert the mixed fractions into the fractions.
\(\frac{5}{2}\) × \(\frac{2}{3}\) = \(\frac{10}{6}\)
\(\frac{10}{6}\) = \(\frac{5}{3}\) = 1 \(\frac{2}{3}\)
She will use 1 \(\frac{2}{3}\) cups of vegetable oil.

Question 20.
Tony’s recipe for soup calls for 1 \(\frac{1}{4}\) teaspoons of salt. He wants to use \(\frac{1}{2}\) that amount. How much salt will he use?
\(\frac{□}{□}\) teaspoon

Answer: \(\frac{5}{8}\)

Explanation:
Tony’s recipe for soup calls for 1 \(\frac{1}{4}\) teaspoons of salt.
He wants to use \(\frac{1}{2}\) that amount.
Multiply the fractions to find how much salt he will use in the recipe for soup.
1 \(\frac{1}{4}\) × \(\frac{1}{2}\)
Convert the mixed fractions to the improper fractions.
\(\frac{5}{4}\) × \(\frac{1}{2}\) = \(\frac{5}{8}\)
Thus Tony use \(\frac{5}{8}\) teaspoon of salt for soup.

Question 21.
Jeffrey’s recipe for oatmeal muffins calls for 2 \(\frac{1}{4}\) cups of oatmeal and makes one dozen muffins. If he makes 1 \(\frac{1}{2}\) dozen muffins for a club meeting, how much oatmeal will he use?
_____ \(\frac{□}{□}\) cups

Answer: 3 \(\frac{3}{8}\)

Explanation:
Jeffrey’s recipe for oatmeal muffins calls for 2 \(\frac{1}{4}\) cups of oatmeal and makes one dozen muffins.
To find how much oatmeal he will use we need to multiply the fractions.
2 \(\frac{1}{4}\) × 1 \(\frac{1}{2}\)
Convert the mixed fractions to the improper fractions.
\(\frac{9}{4}\) × \(\frac{3}{2}\)
\(\frac{27}{8}\) = 3 \(\frac{3}{8}\)
Thus he will use 3 \(\frac{3}{8}\) cups of oatmeal to make oatmeal muffins.

Question 22.
Cara’s muffin recipe calls for 1 \(\frac{1}{2}\) cups of flour for the muffins and \(\frac{1}{4}\) cup of flour for the topping. If she makes \(\frac{1}{2}\) of the original recipe, how much flour will she use?
\(\frac{□}{□}\) cup of flour

Answer: \(\frac{7}{8}\)

Explanation:
Convert mixed fractions into improper fractions.
1 \(\frac{1}{2}\) = \(\frac{3}{2}\)
\(\frac{3}{2}\) + \(\frac{1}{4}\) = \(\frac{7}{4}\)
Now we can find how much flour she will use to make \(\frac{1}{2}\) of the original recipe, when multiply
\(\frac{7}{4}\) by \(\frac{1}{2}\)
\(\frac{7}{4}\) × \(\frac{1}{2}\) = \(\frac{7}{8}\)

Share and Show – Page No. 331

Question 1.
When Pascal built a dog house, he knew he wanted the floor of the house to have an area of 24 square feet. He also wanted the width to be \(\frac{2}{3}\) the length. What are the dimensions of the dog house?
First, choose two numbers that have a product of 24.
Guess: ____ feet and ____ feet
Then, check those numbers. Is the greater number \(\frac{2}{3}\) of the other number?
Check: \(\frac{2}{3}\) × _____ = _____
My guess is ______.
Finally, if the guess is not correct, revise it and check again. Continue until you find the correct answer.
_____ feet by _____ feet

Answer: 4 feet by 6 feet

Explanation:
When Pascal built a dog house, he knew he wanted the floor of the house to have an area of 24 square feet.
He also wanted the width to be \(\frac{2}{3}\) the length.
My guess for 24 square feet is 4 feet and 6 feet.
Now let us check the numbers.
6 × \(\frac{2}{3}\) = 4
So my guess is correct.
Thus the dimensions are 4 feet by 6 feet

Question 2.
What if Pascal wanted the area of the floor to be 54 square feet and the width still to be \(\frac{2}{3}\) the length? What would the dimensions of the floor be?
_____ feet by _____ feet

Answer: 6 feet by 9 feet

Explanation:
My guess for 54 square feet is  6 feet and 9 feet.
9 × \(\frac{2}{3}\)
3 divides 9 three times.
9 × \(\frac{2}{3}\) = 6
So, my guess is correct.
Therefore the dimensions of the will be 6 feet by 9 feet

Question 3.
Leo wants to paint a mural that covers a wall with an area of 1,440 square feet. The height of the wall is \(\frac{2}{5}\) of its length. What is the length and the height of the wall?
_____ feet by _____ feet

Answer: 24 feet by 60 feet

Explanation:
Leo wants to paint a mural that covers a wall with an area of 1,440 square feet. The height of the wall is \(\frac{2}{5}\) of its length.
Guess: 1,440 square feet = 24 feet × 60 feet
\(\frac{2}{5}\) × 60 = 24
So, our guess is correct.
.Thus the dimensions of the wall are 24 feet by 60 feet.

On Your Own – Page No. 332

Question 4.
Barry wants to make a drawing that is \(\frac{1}{4}\) the size of the original. If a tree in the original drawing is 14 inches tall, how tall will the tree in Barry’s drawing be?
_____ \(\frac{□}{□}\) inches

Answer: 3 \(\frac{1}{2}\) inches

Explanation:
Given:
Barry wants to make a drawing that is \(\frac{1}{4}\) the size of the original.
The tree is 14 inches tall in the drawing.
14 × \(\frac{1}{4}\) = \(\frac{14}{4}\) = \(\frac{7}{2}\)
Convert the fraction to the mixed fraction.
\(\frac{7}{2}\) = 3 \(\frac{1}{2}\) inches

Go Math Lesson 7.10 5th Grade Answers Question 5.
A blueprint is a scale drawing of a building. The dimensions of the blueprint for Penny’s doll house are \(\frac{1}{4}\) of the measurements of the actual doll house. The floor of the doll house has an area of 864 square inches. If the width of the doll house is \(\frac{2}{3}\) the length, what are the dimensions of the floor on the blueprint of the doll house?
_____ inches by _____ inches

Answer: 9 inches by 6 inches

Explanation:
A blueprint is a scale drawing of a building.
The dimensions of the blueprint for Penny’s dollhouse are \(\frac{1}{4}\) of the measurements of the actual dollhouse.
The floor of the dollhouse has an area of 864 square inches.
The area of the dollhouse is 54 square inches.
My guess is 9 inches by 6 inches
Let us check the numbers
9 × \(\frac{2}{3}\) = 6
My guess is correct.
Therefore the dimensions of the floor on the blueprint of the dollhouse is 9 inches by 6 inches

Question 6.
Pose a Problem Look back at Exercise 4. Write a similar problem using a different measurement and a different fraction. Then solve your problem.
Type below:
__________

Answer:
Kyle is making reusable grocery bags and lunch bags. She used a 3/4 yard of cloth to make the grocery bag. A lunch bag requires 2/3 of the amount of cloth of a grocery bag’s needs. How much does she need to make the lunch bag?
\(\frac{3}{4}\) × \(\frac{2}{3}\) = \(\frac{1}{2}\)
Thus Kyle needs \(\frac{1}{2}\) of the grocery bag to make the lunch bag.

Question 7.
Test Prep Albert’s photograph has an area of 80 square inches. The length of the photo is 1 \(\frac{1}{4}\) the width. Which of the following could be the dimensions of the photograph?
Options:
a. 5 inches by 16 inches
b. 12 inches by 10 inches
c. 6 inches by 5 inches
d. 10 inches by 8 inches

Answer: 10 inches by 8 inches

Explanation:
Albert’s photograph has an area of 80 square inches.
The length of the photo is 1 \(\frac{1}{4}\) the width.
My guess for 80 square inches is 10 inches by 8 inches.
Now let us check the numbers.
8 × 1 \(\frac{1}{4}\) = 8 × \(\frac{5}{4}\) = 10
Thus the correct answer is option D.

Chapter Review/Test – Page No. 333

Concepts and Skills

Question 1.
When you multiply 3 \(\frac{1}{4}\) by a number greater than one, how does the product compare to 3 \(\frac{1}{4}\)? Explain.
Type below:
__________

Answer:
Your product will be greater than 3 1/4 because anytime you multiply a fraction times a whole number less than 1 you get a fraction less than one and any time you multiply by a fraction and a whole number greater than 1 your answer is greater than 1.

Use a model to solve.

Question 2.
\(\frac{2}{3}\) × 6 = _____

Answer: 4

Explanation:
\(\frac{2}{3}\) × 6
3 divides 6 two times.
2 × 2 = 4
\(\frac{2}{3}\) × 6 = 4

Question 3.
\(\frac{3}{7}\) × 14 = _____

Answer: 6

Explanation:
\(\frac{3}{7}\) × 14
7 divides 14 two times.
3 × 2 = 6
\(\frac{3}{7}\) × 14 = 6

Go Math Lesson 7.10 5th Grade Answer Key Question 4.
\(\frac{5}{8}\) × 24 = _____

Answer: 15

Explanation:

\(\frac{5}{8}\) × 24
8 divides 24 three times.
5 × 3 = 15
\(\frac{5}{8}\) × 24 = 15

Find the product. Write the product in simplest form.

Question 5.
\(\frac{3}{5}\) × 8 = _____ \(\frac{□}{□}\)

Answer: 4 \(\frac{4}{5}\)

Explanation:
\(\frac{3}{5}\) × 8 = \(\frac{24}{5}\)
The mixed fraction of \(\frac{24}{5}\) is 4 \(\frac{4}{5}\)
\(\frac{3}{5}\) × 8 = 4 \(\frac{4}{5}\)

Question 6.
\(\frac{1}{4}\) × 10 = _____ \(\frac{□}{□}\)

Answer: 2 \(\frac{1}{2}\)

Explanation:
\(\frac{1}{4}\) × 10
2 divides 10 five times.
\(\frac{1}{2}\) × 5 = \(\frac{5}{2}\)
The mixed fraction of \(\frac{5}{2}\) is 2 \(\frac{1}{2}\)
\(\frac{1}{4}\) × 10 = 2 \(\frac{1}{2}\)

Question 7.
\(\frac{7}{5}\) × 15 = _____

Answer: 21

\(\frac{7}{5}\) × 15
5 divides 15 three times.
\(\frac{7}{5}\) × 15 = 7 × 3 = 21
\(\frac{7}{5}\) × 15 = 21

Question 8.
\(\frac{5}{6}\) × \(\frac{2}{3}\) = \(\frac{□}{□}\)

Answer: \(\frac{5}{9}\)

Explanation:
\(\frac{5}{6}\) × \(\frac{2}{3}\) = \(\frac{10}{18}\)
\(\frac{10}{18}\) = \(\frac{5}{9}\)
Thus \(\frac{5}{6}\) × \(\frac{2}{3}\) = \(\frac{5}{9}\)

Question 9.
\(\frac{1}{5}\) × \(\frac{5}{7}\) = \(\frac{□}{□}\)

Answer: \(\frac{1}{7}\)

Explanation:
\(\frac{1}{5}\) × \(\frac{5}{7}\)
5 in the numerator and 5 in the denominator gets canceled.
= \(\frac{1}{7}\)
Thus \(\frac{1}{5}\) × \(\frac{5}{7}\) = \(\frac{1}{7}\)

Question 10.
\(\frac{3}{8}\) × \(\frac{1}{6}\) = \(\frac{□}{□}\)

Answer: \(\frac{1}{16}\)

Explanation:
\(\frac{3}{8}\) × \(\frac{1}{6}\)
3 divides 6 two times
\(\frac{3}{8}\) × \(\frac{1}{6}\) = \(\frac{1}{8}\) × \(\frac{1}{2}\)
Multiply the denominators.
= \(\frac{1}{16}\)
Thus \(\frac{3}{8}\) × \(\frac{1}{6}\) = \(\frac{1}{16}\)

Complete the statement with equal to, greater than, or less than.

Question 11.
\(\frac{7}{8}\) × \(\frac{6}{6}\) will be __________ \(\frac{7}{8}\)

Answer: Equal to

Explanation:
\(\frac{7}{8}\) × \(\frac{6}{6}\)
\(\frac{6}{6}\) = 1
\(\frac{7}{8}\) × 1 = \(\frac{7}{8}\)
\(\frac{7}{8}\) = \(\frac{7}{8}\)
Thus \(\frac{7}{8}\) × \(\frac{6}{6}\) will be equal to \(\frac{7}{8}\)

Question 12.
\(\frac{1}{2}\) × \(\frac{8}{9}\) will be __________ \(\frac{8}{9}\)

Answer: Less than

Explanation:
\(\frac{1}{2}\) × \(\frac{8}{9}\)
Multiply the numerators and denominators
\(\frac{1}{2}\) × \(\frac{8}{9}\) = \(\frac{4}{9}\)
\(\frac{4}{9}\) is less than \(\frac{8}{9}\)
So, \(\frac{1}{2}\) × \(\frac{8}{9}\) will be less than \(\frac{8}{9}\)

Chapter Review/Test – Page No. 334

Fill in the bubble completely to show your answer.

Question 13.
Wolfgang wants to enlarge a picture he developed. Which factor listed below would scale up (enlarge) his picture the most if he used it to multiply its current dimensions?
Options:
a. \(\frac{7}{8}\)
b. \(\frac{14}{14}\)
c. 1 \(\frac{4}{9}\)
d. \(\frac{3}{2}\)

Answer: 1 \(\frac{4}{9}\)

Explanation:
The greatest fraction among all the fractions is 1 \(\frac{4}{9}\).
1 \(\frac{4}{9}\) is greater than 1.
Thus the correct answer is option C.

Question 14.
Rachel wants to reduce the size of her photo. Which factor listed below would scale down (reduce) the size of her picture the most?
Options:
a. \(\frac{5}{8}\)
b. \(\frac{11}{16}\)
c. 1 \(\frac{3}{4}\)
d. \(\frac{8}{5}\)

Answer: \(\frac{5}{8}\)

Explanation:
Compared to all the fractions \(\frac{5}{8}\) is smaller.
So, Rachel would reduce the size of her picture to \(\frac{5}{8}\)
So, the correct answer is option A.

Question 15.
Marteen wants to paint \(\frac{2}{3}\) of her room today. She wants to paint \(\frac{1}{4}\) of that before lunch. How much of her room will she paint today before lunch?
Options:
a. \(\frac{1}{12}\)
b. \(\frac{1}{6}\)
c. 1 \(\frac{5}{12}\)
d. \(\frac{11}{12}\)

Answer: \(\frac{1}{6}\)

Explanation:
Marteen wants to paint \(\frac{2}{3}\) of her room today.
She wants to paint \(\frac{1}{4}\) of that before lunch.
\(\frac{2}{3}\) × \(\frac{1}{4}\) = \(\frac{1}{6}\)
So, the answer is option B.

Chapter Review/Test – Page No. 335

Fill in the bubble completely to show your answer.

Question 16.
Gia’s bus route to school is 5 \(\frac{1}{2}\) miles. The bus route home is 1 \(\frac{3}{5}\) times as long. How long is Gia’s bus route home?
Options:
a. 5 \(\frac{3}{10}\) miles
b. 8 miles
c. 8 \(\frac{4}{5}\) miles
d. 17 \(\frac{3}{5}\) miles

Answer: 8 \(\frac{4}{5}\) miles

Explanation:
Gia’s bus route to school is 5 \(\frac{1}{2}\) miles. The bus route home is 1 \(\frac{3}{5}\) times as long.
5 \(\frac{1}{2}\) × 1 \(\frac{3}{5}\)
Convert the mixed fractions to improper fractions.
\(\frac{11}{2}\) × \(\frac{8}{5}\) = \(\frac{88}{10}\) = \(\frac{44}{5}\)
The mixed fraction of \(\frac{44}{5}\) is 8 \(\frac{4}{5}\) miles
Therefore the answer is option C.

Go Math Grade 5 Chapter 7 Mid Chapter Checkpoint Question 17.
Carl’s dog weighs 2 \(\frac{1}{3}\) times what Judy’s dog weighs. If Judy’s dog weighs 35 \(\frac{1}{2}\) pounds, how much does Carl’s dog weigh?
Options:
a. 88 \(\frac{3}{4}\) pounds
b. 82 \(\frac{5}{6}\) pounds
c. 81 \(\frac{2}{3}\) pounds
d. 71 pounds

Answer: 82 \(\frac{5}{6}\) pounds

Explanation:
Carl’s dog weighs 2 \(\frac{1}{3}\) times what Judy’s dog weighs.
To find the weigh of Carl’s dog we need to multiply the fractions
2 \(\frac{1}{3}\) and 35 \(\frac{1}{2}\)
\(\frac{7}{3}\) × \(\frac{71}{2}\) = \(\frac{497}{6}\)
The mixed fraction of \(\frac{497}{6}\) is 82 \(\frac{5}{6}\) pounds.
Thus the correct answer is option B.

Question 18.
In a fifth grade class, \(\frac{4}{5}\) of the girls have brown hair. Of the brown-haired girls, \(\frac{3}{5}\) of the girls have long hair. What fraction of the girls in the class have long brown hair?
Options:
a. \(\frac{1}{20}\)
b. \(\frac{1}{5}\)
c. \(\frac{3}{5}\)
d. \(\frac{1}{4}\)

Answer: \(\frac{1}{5}\)

Explanation:
In a fifth grade class, \(\frac{4}{5}\) of the girls have brown hair. Of the brown-haired girls, \(\frac{3}{5}\) of the girls have long hair.
\(\frac{4}{5}\) – \(\frac{3}{5}\) = \(\frac{1}{5}\)
The correct answer is option B.

Chapter Review/Test – Page No. 336

Constructed Response

Question 19.
Tasha plans to tile the floor in her room with square tiles that are \(\frac{1}{4}\) foot long. Will she use more or fewer tiles if she is only able to purchase square tiles that are \(\frac{1}{3}\) foot long? Explain.
_________ tiles

Answer: Fewer

Explanation:
\(\frac{1}{4}\) is less than \(\frac{1}{3}\)
So, Tasha will use fewer tiles if she is only able to purchase square tiles that are \(\frac{1}{3}\) long.

Performance Task

Question 20.
For a bake sale, Violet wants to use the recipe below.

A). If she wants to double the recipe, how much flour will she need?
_____ \(\frac{□}{□}\) cups flour

Answer: 5 \(\frac{1}{2}\) cups flour

Explanation:
To bake the sugar cookies she needs 2 \(\frac{3}{4}\) cups flour.
If she wants to double the recipe, she needs to multiply the 2 \(\frac{3}{4}\) cups flour by 2.
2 \(\frac{3}{4}\) + 2 \(\frac{3}{4}\) = 5 \(\frac{1}{2}\) cups flour

Question 20.
B). Baxter wants to make 1 \(\frac{1}{2}\) times the recipe. Will he need more or less sugar than Violet needs if she doubles the recipe? Explain.
__________ sugar

Answer: less

Explanation:
If violet doubles the recipe he need 2 × 1 \(\frac{1}{2}\) = 3 cups of sugar
Baxter wants to make 1 \(\frac{1}{2}\) times the recipe.
1 \(\frac{1}{2}\) × \(\frac{1}{2}\) = 1 \(\frac{3}{4}\)
Baxter needs less sugar when compared to Violet’s recipe.

Question 20.
C). As shown, the recipe makes 60 cookies. Jorge wants to bring 150 cookies. How much flour will he need to make 150 cookies? Explain how you got your answer. (Hint: what can you multiply 60 by to get 150?)
_____ \(\frac{□}{□}\) cups flour

Answer: 2 \(\frac{1}{2}\) cups flour

Explanation:
The recipe makes 60 cookies. Jorge wants to bring 150 cookies.
Let the amount of flour be x.
60 × x = 150
x = 150/60 = 5/2
The mixed fraction of \(\frac{5}{2}\) is 2 \(\frac{1}{2}\)
Thus, Jorge need 2 \(\frac{1}{2}\) cups flour to make 150 cookies.

Conclusion:

Browse Grade 5 Chapter wise Resources on Go Math Answer Key. Students can get the Solutions for all the grades in Go Math Answer Key. So, keep following to get the Pdf of all Go Math Grade 5 Answer Key with a brief explanation. It helps not only students but also the teachers to explain to the students in an easy manner. I wish the information given in this chapter is helpful for all the 5th-grade students. Feel free to post your queries in the below box so that we can clarify your doubts as early as possible.

Go Math Grade 5 Chapter 8 Answer Key Pdf: Students can grab the complete knowledge on Divide Fractions on Go Math Grade 5 Answer Key Chapter 8. This article consists of the solutions to practice problems, mid-chapter, and review tests along with answers and explanations for students to have more practice. So, the students who are in search of Go Math Grade 5 Answer Key can Download pdf from here.

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Divide Fractions Go Math Grade 5 Chapter 8 Answer Key Pdf

Get step by step solution for Go Math Grade 5 Answer Key Chapter 8 Divide Fractions For free. With the help of the HMH Go Math 5th Grade Solution Key you can score good marks in the exams. If you learn the concepts you can make the question on your own and test your knowledge.

The chapter Divide fraction includes topics such as Divide Fractions and Whole Numbers, Connect Fractions to Division, Interpret Division with Fractions and Fraction, and Whole-Number Division. Go through the solutions topic-wise in the below section.

Lesson 1: Investigate • Divide Fractions and Whole Numbers

• Share and Show – Page No. 341
• Problem Solving – Page No. 342

Lesson 2: Problem Solving • Use Multiplication

• Share and Show – Page No. 345
• On Your Own – Page No. 346

Lesson 3: Connect Fractions to Division

• Share and Show – Page No. 349
• Problem Solving – Page No. 350

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Page No. 351
• Mid-Chapter Checkpoint – Page No. 352

Lesson 4: Fraction and Whole-Number Division

• Share and Show – Page No. 355
• UNLOCK the Problem – Page No. 356

Lesson 5: Interpret Division with Fractions

• Share and Show – Page No. 359
• Problem Solving – Page No. 360

Chapter 8: Review/Test

• Chapter Review/Test – Page No. 361
• Chapter Review/Test – Page No. 362
• Chapter Review/Test – Page No. 363
• Chapter Review/Test – Page No. 364

Share and Show – Page No. 341

Divide and check the quotient.

Question 1.

3 ÷ \(\frac{1}{3}\) = _____ because _____ × \(\frac{1}{3}\) = 3

Answer: 3 ÷ \(\frac{1}{3}\) = 9 because 9 × \(\frac{1}{3}\) = 3

Explanation:
Step 1: Place a \(\frac{1}{3}\) strip under a three 1 whole strip to show the \(\frac{1}{3}\).
Step 2: Find 9 fraction strips, all with the same denominator, that fit exactly under the \(\frac{1}{3}\) strip.
Each piece is \(\frac{1}{3}\) of the whole.
Step 3: Record and check the quotient.
3 ÷ \(\frac{1}{3}\) = 9 because 9 × \(\frac{1}{3}\) = 3

Question 2.

Think: What label should I write for each tick mark?
3 ÷ \(\frac{1}{6}\) = _____ because _____ × \(\frac{1}{6}\) = 3

Answer: 18, 18

Explanation:
Step 1: Skip count by sixths from 0 to 3 and find 3 ÷ \(\frac{1}{6}\).
Step 2: There are 18 one-sixths in 3 wholes.
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Now record and check the quotient.
3 ÷ \(\frac{1}{6}\) = 18 because 18 × \(\frac{1}{6}\) = 3

Go Math Lesson 8.1 Answer Key 5th Grade Question 3.

\(\frac{1}{4}\) ÷ 2 = \(\frac{□}{□}\)

Answer: \(\frac{1}{8}\)

Explanation:
Step 1: Place a \(\frac{1}{4}\) strip under a 1 whole strip to show the \(\frac{1}{4}\) on the strip.
Step 2: Find 2 \(\frac{1}{8}\) fraction strips, all with the same denominator, that fit exactly under the \(\frac{1}{4}\) strip.
Step 3: Record and check the quotient.
\(\frac{1}{4}\) ÷ 2 = \(\frac{1}{8}\)

Divide. Draw a number line or use fraction strips.

Question 4.
1 ÷ \(\frac{1}{3}\) = _____

Answer: 3

Explanation:
Step 1: Skip count by thirds from 0 to 1 find 1 ÷ \(\frac{1}{3}\).
Step 2: There are 3 \(\frac{1}{3}\) in 1 whole.
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Now record and check the quotient.
1 ÷ \(\frac{1}{3}\) = 3

Question 5.
3 ÷ \(\frac{1}{4}\) = _____

Answer: 12

Explanation:
Step 1: Skip count by fourths from 0 to 3 find 3 ÷ \(\frac{1}{4}\).
Step 2: There are 12 one-fourths in 3 wholes.
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Now record and check the quotient.
3 ÷ \(\frac{1}{4}\) = 12 because 12 × \(\frac{1}{4}\) = 3

Question 6.
\(\frac{1}{5}\) ÷ 2 = _____

Answer: \(\frac{1}{10}\)

Explanation:
Step 1: Place a \(\frac{1}{5}\) strip under a 2 whole strip to show the \(\frac{1}{5}\) on the strip.
Step 2: Find 2 \(\frac{1}{10}\) fraction strips, all with the same denominator, that fit exactly under the \(\frac{1}{5}\) strip.
Step 3: Record and check the quotient.
\(\frac{1}{5}\) ÷ 2 = \(\frac{1}{10}\)

Question 7.
2 ÷ \(\frac{1}{2}\) = _____

Answer: 4

Explanation:
Step 1: Skip count by halves from 0 to 2 find 2 ÷ \(\frac{1}{2}\).
Step 2: There are 4 halves in 2 wholes.
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Record and check the quotient.
2 ÷ \(\frac{1}{2}\) = 4 because 4 × \(\frac{1}{2}\) = 2

Question 8.
\(\frac{1}{4}\) ÷ 3 = _____

Answer: \(\frac{1}{12}\)

Explanation:
Step 1: Place a \(\frac{1}{4}\) strip under a 3 whole strip to show the \(\frac{1}{4}\) on the strip.
Step 2: Find 3 \(\frac{1}{12}\) fraction strips, all with the same denominator, that fit exactly under the \(\frac{1}{4}\) strip.
Step 3: Record and check the quotient.
\(\frac{1}{4}\) ÷ 3 = \(\frac{1}{12}\)

Go Math Grade 5 Chapter 8 Answer Key Pdf Question 9.
5 ÷ \(\frac{1}{2}\) = _____

Answer: 10

Explanation:
Step 1: Skip count by halves from 0 to 5 find 5 ÷ \(\frac{1}{2}\).
Step 2: There are 10 halves in 5 wholes.
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Record and check the quotient.
5 ÷ \(\frac{1}{2}\) = 10 because 10 × \(\frac{1}{2}\) = 5

Question 10.
4 ÷ \(\frac{1}{2}\) = _____

Answer: 8

Explanation:
Step 1: Skip count by halves from 0 to 4 find 4 ÷ \(\frac{1}{2}\).
Step 2: There are 8 halves in 4 wholes.
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Record and check the quotient.
4 ÷ \(\frac{1}{2}\) = 8 because 8 × \(\frac{1}{2}\) = 4

Question 11.
\(\frac{1}{6}\) ÷ 2 = _____

Answer: \(\frac{1}{12}\)

Explanation:
Step 1: Place a \(\frac{1}{6}\) strip under a 2 whole strip to show the \(\frac{1}{6}\) on the strip.
Step 2: Find 2 \(\frac{1}{12}\) fraction strips, all with the same denominator, that fit exactly under the \(\frac{1}{6}\) strip.
Step 3: Record and check the quotient.
\(\frac{1}{6}\) ÷ 2 = \(\frac{1}{12}\)

Question 12.
3 ÷ \(\frac{1}{5}\) = _____

Answer: 15

Explanation:
Step 1: Skip count by fifths from 0 to 3 find 3 ÷ \(\frac{1}{5}\).
Step 2: There are 15 one-fifths in 3 wholes.
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Record and check the quotient.
3 ÷ \(\frac{1}{5}\) = 15 because 15 × \(\frac{1}{5}\) = 3

Problem Solving – Page No. 342

Sense or Nonsense?

Question 13.
Emilio and Julia used different ways to find \(\frac{1}{2}\) ÷ 4. Emilio used a model to find the quotient. Julia used a related multiplication equation to find the quotient. Whose answer makes sense? Whose answer is nonsense? Explain your reasoning.
Emilio’s Work

\(\frac{1}{2}\) ÷ 4

Julia’s Work
If \(\frac{1}{2}\) ÷ 4 = ■, then ■ × 4 = \(\frac{1}{2}\)
I know that \(\frac{1}{8}\) ÷ 4 = \(\frac{1}{2}\)
So, \(\frac{1}{2}\) ÷ 4 = \(\frac{1}{8}\) because \(\frac{1}{8}\) × 4 = \(\frac{1}{2}\)
Type below:
____________

Answer:
Julia’s Work is sense.
Emilio’s work is nonsense.

Question 13.
• For the answer that is nonsense, describe how to find the correct answer.
Type below:
____________

Answer:
Emilio’s work is nonsense because she divided \(\frac{1}{2}\) into two parts i.e., \(\frac{1}{4}\) and \(\frac{1}{4}\).
\(\frac{1}{2}\)/4 = \(\frac{1}{2}\) × \(\frac{1}{4}\)
Emilio must multiply the whole number with the denominator.
\(\frac{1}{2}\) × \(\frac{1}{4}\) = \(\frac{1}{8}\)

Question 13.
If you were going to find \(\frac{1}{2}\) ÷ 5, explain how you would find the quotient using fraction strips.
Type below:
____________

Answer: \(\frac{1}{10}\)

Explanation:
Step 1: Place a \(\frac{1}{2}\) strip under a 5 whole strip to show the \(\frac{1}{2}\) on the strip.
Step 2: Find 2 \(\frac{1}{10}\) fraction strips, all with the same denominator, that fit exactly under the \(\frac{1}{2}\) strip.
Step 3: Record and check the quotient.
\(\frac{1}{2}\) ÷ 5 = \(\frac{1}{10}\)

Share and Show – Page No. 345

Question 1.
A chef has 5 blocks of butter. Each block weighs 1 pound.
She cuts each block into fourths. How many \(\frac{1}{4}\)-pound pieces of butter does the chef have?
First, draw rectangles to represent the blocks of butter.
Then, divide each rectangle into fourths.
Finally, multiply the number of fourths in each block by the number of blocks.
So, the chef has ______ one-fourth-pound pieces of butter.
______ one-fourth-pound

Answer: 20

Explanation:
Step 1: First form 5 rectangles to represent the blocks of butter. And then divide each rectangle into fourths.
Step 2: Now we will multiply the number of fourths in each block by the number of blocks.
Multiply the fourths with the whole number.
4 × 5 = 20
Thus the chef has 20 one fourth pound pieces of butter.

Question 2.
What if the chef had 3 blocks of butter and cut the blocks into thirds? How many \(\frac{1}{3}\)-pound pieces of butter would the chef have?
______ \(\frac{1}{3}\)-pound

Answer: 9

Explanation:
Multiply the number of thirds in each block with the number of blocks.
3 × thirds = 3 × 3 = 9
Thus the chef has 9 one third pound pieces of butter.

Question 3.
Jason has 2 pizzas that he cuts into fourths. How many \(\frac{1}{4}\)-size pizza slices does he have?
______ \(\frac{1}{4}\)-size pizza slices

Answer: 8

Explanation:
Step 1: First, draw 2 circles to represent pizzas. Then divide each circle into fourths.
Step 2: Now multiply the number of fourths in each circle by the number of circles.
4 × 2 = 8
So, Jason has 8 one fourth size pizza slices.

Go Math Grade 5 Chapter 8 Mid Chapter Checkpoint Answers Question 4.
Thomas makes 5 sandwiches that he cuts into thirds. How many \(\frac{1}{3}\)-size sandwich pieces does he have?
______ \(\frac{1}{3}\)-size sandwich pieces

Answer: 15

Explanation:
Step 1: First, draw 5 rectangles to represent sandwiches. Then divide each rectangle into thirds.
Step 2: Multiply one third with the number of sandwiches.
3 × 5 = 15
Thomas has 15 one-third sandwich pieces.

Question 5.
Holly cuts 3 pans of brownies into eighths. How many \(\frac{1}{8}\)-size brownie pieces does she have?
______ \(\frac{1}{8}\)-size brownie pieces

Answer: 24

Explanation:
Step 1: First draw 3 rectangles to represent the ribbons. Then divide each rectangle into the pieces.
Step 2: Now multiply the Number of eights with the number of ribbons.
8 × 3 = 24
Thus Holy has 24 one eighths pieces of ribbon.

On Your Own – Page No. 346

Question 6.
Julie wants to make a drawing that is \(\frac{1}{4}\) the size of the original. If a tree in the original drawing is 8 inches tall, how tall will the tree in Julie’s drawing be?
______ inches

Answer: 2

Explanation:
Given, Julie wants to make a drawing that is \(\frac{1}{4}\) the size of the original.
The tree is 8 inches tall.
8 × \(\frac{1}{4}\) = 2
The height of the tree in Julie’s drawing is 2 inches.

Question 7.
Three friends go to a book fair. Allen spends $2.60. Maria spends 4 times as much as Allen. Akio spends $3.45 less than Maria. How much does Akio spend?
$ ______

Answer: $ 6.95

Explanation:
To find how much Akio spends for first we will find how much Maria spends, and then subtract 3.45 dollars from that value.
Allen spends 2.60 dollars.
Maris spends 4 times as much as Allen.
4 × 2.60 = 10.4
So, Maria spends 10.4 dollars.
Akio spends for 3.45 dollars less than Maria.
10.4 – 3.45 = 6.95
So, Akio spends 6.95 dollars.

Question 8.
Brianna has a sheet of paper that is 6 feet long. She cuts the length of paper into sixths and then cuts the length of each of these \(\frac{1}{6}\) pieces into thirds. How many pieces does she have? How many inches long is each piece?
______ pieces , each ______ inches long

Answer: 18 pieces, each 0.33 inches long

Explanation:
Brianna has a sheet of paper that is 6 feet long.
She cuts the length of paper into sixths and then cuts the length of each of these \(\frac{1}{6}\) pieces into thirds.
Then we will count the one-third pieces to find how many pieces she has.
6 feet ÷18 = 0.33 feet
So, each piece is 0.33 feet long.

Connect Fractions To Division Lesson 8.3 Question 9.
Pose a Problem Look back at Problem 8. Write a similar problem by changing the length of the paper and the size of the pieces.
Type below:
____________

Answer:

Explanation:
John has a tree that is 10 feet long. She cuts the length of the tree into tenth and then cuts the length of each of these 1/10 pieces into fourth. How many pieces does he have? How many feet long is each piece?
Answer:
First, draw one rectangle to represent the tree. Then divide this rectangle into tenths, and then we will divide each 1/10 piece into fourths.
Then we will count the one-fourth pieces to find how many pieces he has.
1 tree = 10 feet
10 feet ÷ 40 = 0.4 feet
So, each piece is 0.4 feet long.

Question 10.
Test Prep Adrian made 3 carrot cakes. He cut each cake into fourths. How many \(\frac{1}{4}\)-size cake pieces does he have?
Options:
a. 16
b. 12
c. 1 \(\frac{1}{3}\)
d. 1

Answer: 12

Explanation:
Test Prep Adrian made 3 carrot cakes.
He cut each cake into fourths.

By seeing the above figure we can say that Adrian has 12 one-quarter-size pieces of a granola bar.

Share and Show – Page No. 349

Draw lines on the model to complete the number sentence.

Question 1.
Six friends share 4 pizzas equally.

4 ÷ 6 =
Each friend’s share is _____ of a pizza.
\(\frac{□}{□}\) of a pizza.

Answer: \(\frac{2}{3}\)

Explanation:
Draw lines to divide each pizza into 4 equal pieces.
Each friend gets \(\frac{2}{3}\) of a pizza.
4 ÷ 6 = \(\frac{2}{3}\)
Each friend’s share is \(\frac{2}{3}\) of a pizza.

Question 2.
Four brothers share 5 sandwiches equally.

5 ÷ 4 =
Each brother’s share is ____ sandwiches.
\(\frac{□}{□}\) sandwiches

Answer: \(\frac{5}{4}\)

Explanation:
Draw lines to divide each sandwich into 4 equal pieces.
Divide the number of brothers by the total number of sandwiches.
5 ÷ 4 = \(\frac{5}{4}\)
Each brother’s share is \(\frac{5}{4}\) sandwiches.

Complete the number sentence to solve.

Question 3.
Twelve friends share 3 pies equally. What fraction of a pie does each friend get?
3 ÷ 12 =
Each friend’s share is _____ of a pie.
\(\frac{□}{□}\) of a pie

Answer: \(\frac{1}{4}\)

Explanation:
Twelve friends share 3 pies equally.
3 ÷ 12 = \(\frac{1}{4}\)
Each friend’s share is \(\frac{1}{4}\) of a pie.

Go Math Grade 5 Unit 8 Answer Key Question 4.
Three students share 8 blocks of clay equally. How much clay does each student get?
8 ÷ 3 =
Each student’s share is ____ blocks of clay.
\(\frac{□}{□}\) blocks of clay

Answer: 2 \(\frac{2}{3}\)

Explanation:
Three students share 8 blocks of clay equally.
Divide the number of blocks by three students.
8 ÷ 3 = \(\frac{8}{3}\)
\(\frac{8}{3}\) = 2 \(\frac{2}{3}\)
Each student’s share is 2 \(\frac{2}{3}\) blocks of clay.

On Your Own

Complete the number sentence to solve.

Question 5.
Four students share 7 oranges equally. How many oranges does each student get?
7 ÷ 4 =
Each student’s share is _____ oranges.
_____ \(\frac{□}{□}\) oranges

Answer: 1 \(\frac{3}{4}\)

Explanation:
Four students share 7 oranges equally.
Draw lines to divide each orange into 4 equal pieces.
7 ÷ 4 = \(\frac{7}{4}\)
Convert the improper fraction to the mixed fraction.
\(\frac{7}{4}\) = 1 \(\frac{3}{4}\)
Each student’s share is 1 \(\frac{3}{4}\) oranges.

Question 6.
Eight girls share 5 fruit bars equally. What fraction of a fruit bar does each girl get?
5 ÷ 8 =
Each girl’s share is _____ of a fruit bar.
\(\frac{□}{□}\) of a fruit bar

Answer: \(\frac{5}{8}\)

Explanation:
Given that,
Eight girls share 5 fruit bars equally.
5 ÷ 8 = \(\frac{5}{8}\)
Thus the fraction of the fruit bar each friend gets is \(\frac{5}{8}\).

Question 7.
Nine friends share 6 pizzas equally. What fraction of a pizza does each friend get?
6 ÷ 9 =
Each friend’s share is _ of a pizza.
\(\frac{□}{□}\) of a pizza

Answer: \(\frac{2}{3}\)

Explanation:
Nine friends share 6 pizzas equally.
Draw lines to divide each pizza into 9 pieces.
6 ÷ 9 = \(\frac{2}{3}\)
Thus each friend’s share is \(\frac{2}{3}\) of a pizza.

Question 8.
Two boys share 9 feet of rope equally. How many feet of rope does each boy get?
9 ÷ 2 =
Each boy’s share is ____ feet of rope.
______ \(\frac{□}{□}\) feet of rope

Answer: 4 \(\frac{1}{2}\)

Explanation:
Two boys share 9 feet of rope equally.
Divide nine into halves.
9 ÷ 2 = \(\frac{9}{2}\)
\(\frac{9}{2}\) = 4 \(\frac{1}{2}\)

Problem Solving – Page No. 350

Question 9.
Shawna has 3 adults and 2 children coming over for dessert. She is going to serve 2 small apple pies. If she plans to give each person, including herself, an equal amount of pie, how much pie will each person get?

\(\frac{□}{□}\) pie

Answer: \(\frac{1}{3}\) pie

Explanation:
To find how much pie each person will get, we will find when 2 small apple pies we will divide by 6 persons.
2 ÷ 6 = \(\frac{2}{6}\) = \(\frac{1}{3}\)
Therefore each person will get \(\frac{1}{3}\) pie.

Question 10.
There are 36 members in the math club. Addison brought 81 brownies to share with all the members. How many brownies does each member get?
______ \(\frac{□}{□}\) brownies

Answer: 2 \(\frac{1}{4}\)

Explanation:
Given that, There are 36 members in the math club.
Addison brought 81 brownies to share with all the members.
Dividing the number of brownies by members in the math club.
81 ÷ 36 = \(\frac{81}{36}\) = \(\frac{9}{4}\)
The mixed fraction of \(\frac{9}{4}\) is 2 \(\frac{1}{4}\)
Thus each member gets 2 \(\frac{1}{4}\) brownies.

Question 11.
Eight students share 12 oatmeal muffins equally and 6 students share 15 apple muffins equally. Carmine is in both groups of students. What is the total number of muffins Carmine gets?
______ muffins

Answer: 4 muffins

Explanation:
Since Carmine is in both groups of students, for first we will find out how many each student of each group gets.
Now we will find how many oatmeal muffins each of the 8 students get, we will divide the 12 oatmeal muffins by the 8 students.
12 ÷ 8 = \(\frac{12}{8}\) = \(\frac{3}{2}\)
\(\frac{3}{2}\) = 1 \(\frac{1}{2}\)
So, each student shares 1 \(\frac{1}{2}\) oatmeal muffins.
To find how many apple muffins each of the 6 students get we will divide the 15 apple muffins by the 6 students.
15 ÷ 6 = \(\frac{15}{6}\) = \(\frac{5}{2}\)
\(\frac{5}{2}\) = 2 \(\frac{1}{2}\)
As Carmine is in both groups we need to add the total number of muffins
1 \(\frac{1}{2}\)  + 2 \(\frac{1}{2}\) = 4
Therefore the total number of muffins Carmine gets is 4.

Question 12.
Nine friends order 4 large pizzas. Four of the friends share 2 pizzas equally and the other 5 friends share 2 pizzas equally. In which group does each member get a greater amount of pizza? Explain your reasoning.
Type below:
____________

Answer:
To find in which group each member get a greater amount of pizza, for first, we will find how many each of the friends gets.
Given that 4 friends share 2 pizzas equally, so to find how many pizzas each of the 4 students get, we will find when dividing the 2 pizzas among 4 friends.
2 ÷ 4 = 2/4 = \(\frac{1}{2}\)
In this group, each student’s share is \(\frac{1}{2}\) of the pizza.
The other 5 friends share 2 pizzas equally, so to find out how many pizzas each of the 5 students get, we will find when we divide the 2 pizza among 5 friends.
2 ÷ 5 = \(\frac{2}{5}\)
In this group, each student’s share is \(\frac{2}{5}\) of the pizza.
\(\frac{1}{2}\) > \(\frac{2}{5}\) so as a group with four members get a greater amount of pizza.

Question 13.
Test Prep Jason baked 5 cherry pies. He wants to share them equally among 3 of his neighbors. How many pies will each neighbor get?
Options:
a. \(\frac{3}{8}\)
b. \(\frac{3}{5}\)
c. 1 \(\frac{2}{3}\)
d. 2 \(\frac{2}{3}\)

Answer: 1 \(\frac{2}{3}\)

Explanation:
To find how many pies each neighbor we have to divide the number of cherry pies by a number of neighbor.
5 ÷ 3 = \(\frac{5}{3}\)
Convert the improper fraction to the mixed fraction.
\(\frac{5}{3}\) = 1 \(\frac{2}{3}\)

Mid-Chapter Checkpoint – Page No. 351

Concepts and Skills

Question 1.
Explain how you can tell, without computing, whether the quotient \(\frac{1}{2}\) ÷ 6 is greater than 1 or less than 1.
Type below:
____________

Answer:
\(\frac{1}{2}\) ÷ 6 = \(\frac{1}{12}\)
\(\frac{1}{12}\) is less than 1.

Divide. Draw a number line or use fraction strips.

Question 2.
3 ÷ \(\frac{1}{2}\)
______

Answer: 6

Explanation:
Step 1: Draw a number line from 0 to 3. Label each half on your number line.
Step 2: Skip count by halves from 0 to 3 to find 3 ÷ \(\frac{1}{2}\).
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Record and check the quotient.
3 ÷ \(\frac{1}{2}\) = 6 because 6 × \(\frac{1}{2}\) = 3

Question 3.
1 ÷ \(\frac{1}{4}\)
______

Answer: 4

Explanation:
Step 1: Draw a number line from 0 to 1. Label each fourth on your number line.
Step 2: Skip count by fourths from 0 to 1 to find 1 ÷ \(\frac{1}{4}\).
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Record and check the quotient.
1 ÷ \(\frac{1}{4}\) = 4 because 4 × \(\frac{1}{4}\) = 1

Question 4.
\(\frac{1}{2}\) ÷ 2
\(\frac{□}{□}\)

Answer: \(\frac{1}{4}\)

Explanation:
Step 1: Place a \(\frac{1}{2}\) strip under a 2 whole strip to show the \(\frac{1}{2}\) on the strip.
Step 2: Find 4 \(\frac{1}{2}\) fraction strips, all with the same denominator, that fit exactly under the \(\frac{1}{2}\) strip.
Step 3: Record and check the quotient.
\(\frac{1}{2}\) ÷ 2 = \(\frac{1}{4}\)

Question 5.
\(\frac{1}{3}\) ÷ 4
_____ \(\frac{□}{□}\)

Answer: \(\frac{1}{12}\)

Explanation:
Step 1: Place a \(\frac{1}{3}\) strip under a 4 whole strip to show the \(\frac{1}{3}\) on the strip.
Step 2: Find 12 \(\frac{1}{3}\) fraction strips, all with the same denominator, that fit exactly under the \(\frac{1}{3}\) strip.
Step 3: Record and check the quotient.
\(\frac{1}{3}\) ÷ 4 = \(\frac{1}{12}\)

Question 6.
2 ÷ \(\frac{1}{6}\)
______

Answer: 12

Explanation:
Step 1: Draw a number line from 0 to 2. Label each sixth on your number line.
Step 2: Skip count by fourths from 0 to 2 to find 2 ÷ \(\frac{1}{6}\).
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Record and check the quotient.
2 ÷ \(\frac{1}{6}\) = 12 because 12 × \(\frac{1}{6}\) = 2

Question 7.
\(\frac{1}{4}\) ÷ 3
\(\frac{□}{□}\)

Answer: \(\frac{1}{12}\)

Explanation:
Step 1: Place a \(\frac{1}{4}\) strip under a 3 whole strip to show the \(\frac{1}{4}\) on the strip.
Step 2: Find 12 \(\frac{1}{4}\) fraction strips, all with the same denominator, that fit exactly under the \(\frac{1}{4}\) strip.
Step 3: Record and check the quotient.
\(\frac{1}{4}\) ÷ 3 = \(\frac{1}{12}\)

Complete the number sentence to solve.

Question 8.
Two students share 3 granola bars equally. How many granola bars does each student get?
3 ÷ 2 = ______
Each student’s share is ______ granola bars.
_____ \(\frac{□}{□}\) granola bars

Answer: 1 \(\frac{1}{2}\)

Explanation:
Given that Two students share 3 granola bars equally.
Divide the number of granola bars by 2.
3 ÷ 2 = \(\frac{3}{2}\)
Convert the improper fraction into the mixed fraction.
\(\frac{3}{2}\) = 1 \(\frac{1}{2}\)
Thus each student’s share is 1 \(\frac{1}{2}\) granola bars.

Question 9.
Five girls share 4 sandwiches equally. What fraction of a sandwich does each girl get?
4 ÷ 5 = _____
Each girl’s share is ______ of a sandwich.
\(\frac{□}{□}\) of a sandwich

Answer: \(\frac{4}{5}\)

Explanation:
Given that, Five girls share 4 sandwiches equally.
Dividing the number of sandwiches by five girls.
4 ÷ 5 = \(\frac{4}{5}\)
Each girl’s share is \(\frac{4}{5}\) of a sandwich.

Question 10.
Nine boys share 4 pizzas equally. What fraction of a pizza does each boy get?
4 ÷ 9 = _____
Each boy’s share is _____ of a pizza.
\(\frac{□}{□}\) of a pizza

Answer: \(\frac{4}{9}\)

Explanation:
Given that nine boys share 4 pizzas equally.
Dividing 4 pizzas by the number of nine boys
4 ÷ 9 = \(\frac{4}{9}\)
Each boy’s share is \(\frac{4}{9}\) of a pizza.

Question 11.
Four friends share 10 fruit bars equally. How many fruit bars does each friend get?
10 ÷ 4 = _____
Each friend’s share is _____ fruit bars.
_____ \(\frac{□}{□}\) fruit bars

Answer: 2 \(\frac{1}{2}\)

Explanation:
Given that four friends share 10 fruit bars equally.
Dividing the number of fruit bars by the number of friends.
10 ÷ 4 = \(\frac{10}{4}\) = \(\frac{5}{2}\)
Convert the improper fraction into the mixed fraction.
\(\frac{5}{2}\) = 2 \(\frac{1}{2}\)

Mid-Chapter Checkpoint – Page No. 352

Question 12.
Mateo has 8 liters of punch for a party. Each glass holds \(\frac{1}{5}\) liter of punch. How many glasses can Mateo fill with a punch?

______ glasses

Answer: 40

Explanation:
Draw the rectangle that represents the number of liters.
Each rectangle is equal to 1 liter.
Each rectangle contains a one-fifth liter of punch.
Now multiply the fifths by the number of liters.
8 × 5 = 40
40 glasses can Mateo fill with a punch.

Question 13.
Four friends share 3 sheets of construction paper equally. What fraction of a sheet of paper does each friend get?

\(\frac{□}{□}\)

Answer: \(\frac{3}{4}\)

Explanation:
The rectangle represents the sheet of the construction paper.
Divide each rectangle into fourths.
3 × \(\frac{1}{4}\) = \(\frac{3}{4}\)
Each friend gets \(\frac{3}{4}\) sheet of paper.

Question 14.
Caleb and 2 friends are sharing \(\frac{1}{2}\) quart of milk equally. What fraction of a quart of milk does each of the 3 friends get?
\(\frac{□}{□}\) quart of milk

Answer: \(\frac{1}{6}\) quart of milk

Explanation:
Caleb and 2 friends are sharing \(\frac{1}{2}\) quart of milk equally.
\(\frac{1}{2}\) ÷ 3 = \(\frac{1}{6}\)
Therefore each of 3 friends gets \(\frac{1}{6}\) quart of milk.

Question 15.
Toni and Makayla are working on a craft project. Makayla has 3 yards of ribbon and Toni has 4 yards of ribbon. They cut all the ribbon into pieces that are \(\frac{1}{4}\) yard long. How many pieces of ribbon do they have?
Makayla: __________ pieces of ribbon
Toni: __________ pieces of ribbon

Answer:
Makayla: 12 pieces of ribbon
Toni: 16 pieces of ribbon

Explanation:
Toni and Makayla are working on a craft project.
Makayla has 3 yards of ribbon and Toni has 4 yards of ribbon.
They cut all the ribbon into pieces that are \(\frac{1}{4}\) yard long.
Now multiply the number of yards of ribbon that Makayla has with \(\frac{1}{4}\)
3 ÷ \(\frac{1}{4}\) = 12 pieces of ribbon
Multiply the number of yards of ribbon that Toni has with \(\frac{1}{4}\)
4 ÷ \(\frac{1}{4}\) = 16 pieces of ribbon

Share and Show – Page No. 355

Question 1.
Use the model to complete the number sentence.

2 ÷ \(\frac{1}{4}\) = 2 × ______ = ______

Answer: 2 × 4 = 8

Explanation:

• Draw 2 rectangles and divide each rectangle into fourths.
• When you divide 1 rectangle into fourths you are finding the number of fourths in 2 rectangles.
• There are 2 groups of rectangles. There are 8 fourths
• Complete the number sentence.

Go Math Book 5th Grade Chapter 8 Answer Key Question 2.
Use the model to complete the number sentence.

\(\frac{1}{6}\) ÷ 2 = _ × \(\frac{1}{6}\) = _
Type below:
__________

Answer: \(\frac{1}{12}\)

Explanation:

• Draw the rectangle and divide the rectangle into sixths.
• The rectangle is divided into 2 equal parts. You can find 12 sixths.
• In the figure, you can see one shaded part in the rectangle.
• Complete the number sentence.

\(\frac{1}{6}\) × \(\frac{1}{2}\) = \(\frac{1}{12}\)

Write a related multiplication sentence to solve.

Question 3.
3 ÷ \(\frac{1}{4}\)
______

Answer: 12

Explanation:

• Draw 3 rectangles and divide each rectangle into fourths.
• When you divide 1 rectangle into fourths you are finding the number of fourths in 3 rectangles.
• There are 3 groups of rectangles. There are 12 fourths
• Complete the number sentence.

3 × 4 = 12
3 ÷ \(\frac{1}{4}\) = 12

Question 4.
\(\frac{1}{5}\) ÷ 4
\(\frac{□}{□}\)

Answer: \(\frac{1}{20}\)

Explanation:

• Draw the rectangle and divide the rectangle into fifths.
• The rectangle is divided into 4 equal parts. You can find 20 fifths.
• Complete the number sentence.

\(\frac{1}{5}\) × \(\frac{1}{4}\) = \(\frac{1}{20}\)
\(\frac{1}{5}\) ÷ 4 = \(\frac{1}{20}\)

Question 5.
\(\frac{1}{9}\) ÷ 3
\(\frac{□}{□}\)

Answer: \(\frac{1}{27}\)

Explanation:

• Draw 3 rectangle and divide the rectangle into ninths.
• The rectangle is divided into 3 equal parts. You can find 27 ninths.
• Complete the number sentence.

\(\frac{1}{9}\) × \(\frac{1}{3}\) = \(\frac{1}{27}\)
\(\frac{1}{9}\) ÷ 3 = \(\frac{1}{27}\)

Question 6.
7 ÷ \(\frac{1}{2}\)
______

Answer: 14

Explanation:

• Draw 7 rectangles and divide each rectangle into halves.
• When you divide 7 rectangles into halves you are finding the number of halves in 7 rectangles.
• There are 7 groups of rectangles. There are 14 halves.
• Complete the number sentence.

7 × 2 = 14
7 ÷ \(\frac{1}{2}\) = 14

On Your Own

Write a related multiplication sentence to solve.

Question 7.
5 ÷ \(\frac{1}{3}\)
______

Answer: 15

Explanation:

• Draw 5 rectangles and divide each rectangle into thirds.
• When you divide 5 rectangles into halves you are finding the number of thirds in 5 rectangles.
• There are 5 groups of rectangles. There are 15 thirds.
• Complete the number sentence.

5 × 3 = 15
5 ÷ \(\frac{1}{3}\) = 15

Question 8.
8 ÷ \(\frac{1}{2}\)
______

Answer: 16

Explanation:

• Draw 8 rectangles and divide each rectangle into halves.
• When you divide 8 rectangles into halves you are finding the number of thirds in 8 rectangles.
• There are 8 groups of rectangles. There are 16 halves.
• Complete the number sentence.

8 × 2 = 16
8 ÷ \(\frac{1}{2}\) = 16

Question 9.
\(\frac{1}{7}\) ÷ 4
\(\frac{□}{□}\)

Answer: \(\frac{1}{28}\)

Explanation:

\(\frac{1}{7}\) ÷ 4

• Draw 4 rectangles and divide the rectangle into sevenths.
• The rectangle is divided into 4 equal parts. You can find 28 sevenths.
• Complete the number sentence.

\(\frac{1}{7}\) × \(\frac{1}{4}\) = \(\frac{1}{28}\)
Thus, \(\frac{1}{7}\) ÷ 4 = \(\frac{1}{28}\)

Go Math Grade 5 Chapter 8 Mid Chapter Checkpoint Answer Key Question 10.
\(\frac{1}{2}\) ÷ 9
\(\frac{□}{□}\)

Answer: \(\frac{1}{18}\)

Explanation:

\(\frac{1}{2}\) ÷ 9

• Draw 9 rectangles and divide the rectangle into halves.
• The rectangle is divided into 9 equal parts. You can find 18 halves.
• Complete the number sentence.

\(\frac{1}{2}\) × \(\frac{1}{9}\) = \(\frac{1}{18}\)
\(\frac{1}{2}\) ÷ 9 = \(\frac{1}{18}\)

Question 11.
\(\frac{1}{3}\) ÷ 4
\(\frac{□}{□}\)

Answer: \(\frac{1}{12}\)

Explanation:
\(\frac{1}{3}\) ÷ 4

• Draw 4 rectangles and divide the rectangle into thirds.
• The rectangle is divided into 4 equal parts. You can find 12 thirds.
• Complete the number sentence.

\(\frac{1}{3}\) × \(\frac{1}{4}\) = \(\frac{1}{12}\)
\(\frac{1}{3}\) ÷ 4 = \(\frac{1}{12}\)

Question 12.
\(\frac{1}{4}\) ÷ 12
\(\frac{□}{□}\)

Answer: \(\frac{1}{48}\)

Explanation:

• Draw 12 rectangles and divide the rectangle into fourths.
• The rectangle is divided into 12 equal parts. You can find 48 thirds.
• Complete the number sentence.
  \(\frac{1}{4}\) ÷ 12 = \(\frac{1}{4}\) × \(\frac{1}{12}\) = \(\frac{1}{48}\)

Question 13.
6 ÷ \(\frac{1}{5}\)
______

Answer: 30

Explanation:

• Draw 6 rectangles and divide each rectangle into fifths.
• When you divide 6 rectangles into fifths you are finding the number of fifths in 6 rectangles.
• There are 6 groups of rectangles. There are 30 fifths.
• Complete the number sentence.
  6 × 5 = 30
  6 ÷ \(\frac{1}{5}\) = 30

Question 14.
\(\frac{2}{3}\) ÷ 3
\(\frac{□}{□}\)

Answer: \(\frac{2}{9}\)

Explanation:
\(\frac{2}{3}\) ÷ 3

• Draw 3 rectangles and divide the rectangle into two thirds.
• The rectangle is divided into 3 equal parts.
• Complete the number sentence.
  \(\frac{2}{3}\) ÷ 3 = \(\frac{2}{3}\) × \(\frac{1}{3}\) = \(\frac{2}{9}\)

UNLOCK the Problem – Page No. 356

Question 15.
The slowest mammal is the three-toed sloth. The top speed of a three-toed sloth on the ground is about \(\frac{1}{4}\) foot per second. The top speed of a giant tortoise on the ground is about \(\frac{1}{3}\) foot per second. How much longer would it take a three-toed sloth than a giant tortoise to travel 10 feet on the ground?

a. What do you need to find?
Type below:
__________

Answer: We Need to find How much longer would it take a three-toed sloth than a giant tortoise to travel 10 feet on the ground.

Question 15.
b. What operations will you use to solve the problem?
Type below:
__________

Answer:
The operations which we will use is:
Multiplication to find how many seconds three-toed sloth tortoise need to travel 10 feet.
Subtraction to finds how second longer need three-toed to travel 10 feet.

Question 15.
c. Show the steps you used to solve the problem.
Type below:
__________

Answer:
To find how much longer would it take a three-toed sloth than a giant tortoise to travel 10 feet on the ground, for first we will find how much seconds a three-toed sloth and giant tortoise need to travel 10 feet.
The top speed of a three-toed sloth on the ground is about 1/4 foot per second, so to find how much seconds need a three-toed sloth to travel 10 feet we will find as:
10 feet ÷ 1/4 foot per second = 10 × 4 = 40 seconds
The top speed of a giant tortoise on the ground is about 1/3 foot per second, so to find how much seconds need a giant tortoise to travel 10 feet we will find as:
10 feet ÷ 1/3 foot per second = 10 × 3 = 30 seconds

Question 15.
d. Complete the sentences.
A three-toed sloth would travel 10 feet in _____ seconds.
A giant tortoise would travel 10 feet in _____ seconds.
Since _____ – _____ = _____, it would take a three-toed sloth _____ seconds longer to travel 10 feet.
Type below:
__________

Answer:
A three-toed sloth would travel 10 feet in 40 seconds.
A giant tortoise would travel 10 feet in 30 seconds.
Since 40 – 30 = 10, it would take a three-toed sloth 10 seconds longer to travel 10 feet.

Question 15.
e. Fill in the bubble for the correct answer choice.
Options:
a. 10 seconds
b. 30 seconds
c. 40 seconds
d. 70 seconds

Answer: 10 seconds

Explanation:
A three-toed sloth would travel 10 feet in 40 seconds.
A giant tortoise would travel 10 feet in 30 seconds.
Since 40 – 30 = 10, it would take a three-toed sloth 10 seconds longer to travel 10 feet.
The correct answer is option A.

Go Math Grade 5 Workbook Chapter 8 Review Answer Key Question 16.
Robert divides 8 cups of almonds into \(\frac{1}{8}\)-cup servings. How many servings does he have?
Options:
a. 1
b. 16
c. 8
d. 64

Answer: 64

Explanation:
Robert divides 8 cups of almonds into \(\frac{1}{8}\)-cup servings.
8 × \(\frac{1}{8}\)
8 × 8 = 64
Thus robert has 64 servings.
The correct answer is option D.

Question 17.
Tina cuts \(\frac{1}{3}\) yard of fabric into 4 equal parts. What is the length of each part?
Options:
a. 12 yards
b. 1 \(\frac{1}{3}\) yards
c. \(\frac{3}{4}\) yards
d. \(\frac{1}{12}\) yards

Answer: \(\frac{1}{12}\) yards

Explanation:
\(\frac{1}{3}\) ÷ 4
\(\frac{1}{3}\) × \(\frac{1}{4}\) = \(\frac{1}{12}\) yards
The correct answer is option D.

Share and Show – Page No. 359

Question 1.
Complete the story problem to represent 3 ÷ \(\frac{1}{4}\).
Carmen has a roll of paper that is ______ feet long. She cuts the paper into pieces that are each ______ foot long. How many pieces of paper does Carmen have?
Type below:
__________

Answer:
3 ÷ \(\frac{1}{4}\)
3 × 4 = 12
Carmen has a roll of paper that is 3 feet long.
She cuts the paper into pieces that are each \(\frac{1}{4}\) foot long.

Question 2.
Draw a diagram to represent the problem. Then solve. April has 6 fruit bars. She cuts the bars into halves. How many \(\frac{1}{2}\)-size bar pieces does she have?
_____ \(\frac{1}{2}\)-size bar pieces

Answer:
First, draw 6 rectangles that represent fruit bars.
Now divide each fruit bar into halves.
Dividing 6 fruit bards by halves.
6 ÷ \(\frac{1}{2}\) = 12
Thus she has 12 \(\frac{1}{2}\)-size bar pieces

Question 3.
Write an equation to represent the problem. Then solve. Two friends share \(\frac{1}{4}\) of a large peach pie. What fraction of the whole pie does each friend get?
\(\frac{□}{□}\)

Answer: \(\frac{1}{8}\)

Explanation:
Given that, Two friends share \(\frac{1}{4}\) of a large peach pie.
\(\frac{1}{4}\) ÷ 2 = \(\frac{1}{8}\)
Thus the fraction of the whole pie each friend gets is \(\frac{1}{8}\).

On Your Own

Question 4.
Write an equation to represent the problem. Then solve.
Benito has \(\frac{1}{3}\) -kilogram of grapes. He divides the grapes equally into 3 bags. What fraction of a kilogram of grapes is in each bag?
\(\frac{□}{□}\)

Answer: \(\frac{1}{9}\)

Explanation:
Given:
Benito has \(\frac{1}{3}\) -kilogram of grapes. He divides the grapes equally into 3 bags.
The equation for the division is,
\(\frac{1}{3}\) ÷ 3 = \(\frac{1}{9}\)
\(\frac{1}{9}\) of a kilogram of grapes is in each bag.

5th Grade Go Math Book Connect Fractions to Division Question 5.
Draw a diagram to represent the problem. Then solve.
Sonya has 5 sandwiches. She cuts each sandwich into fourths. How many \(\frac{1}{4}\)-size sandwich pieces does she have?
_____ \(\frac{1}{4}\)-size sandwich pieces

Answer: 20

Explanation:
Given,
Sonya has 5 sandwiches. She cuts each sandwich into fourths.
Dividing the number of sandwiches by fourths.
5 ÷ \(\frac{1}{4}\) = 5 × 4 = 20
Thus she has 20 \(\frac{1}{4}\)-size sandwich pieces.

Question 6.
Write a story problem to represent 2 ÷ \(\frac{1}{8}\). Then solve.
Type below:
__________

Answer:
Erica makes 2 sandwiches and cuts each sandwich into eighths. How many \(\frac{1}{8}\) size sandwich pieces does she have?
Answer: 2 ÷ \(\frac{1}{8}\)
2 ÷ \(\frac{1}{8}\) = 16 because 16 × \(\frac{1}{8}\) = 2

Problem Solving – Page No. 360

Pose a Problem

Question 7.
Amy wrote the following problem to represent 4 ÷ \(\frac{1}{6}\) .

Jacob has a board that is 4 feet long. He cuts the board into pieces that are each \(\frac{1}{6}\) foot long. How many pieces does Jacob have now?
Then Amy drew this diagram to solve her problem.

So, Jacob has 24 pieces.
Write a new problem using a different item to be divided and different fractional pieces. Then draw a diagram to solve your problem.
Pose a problem.                           Draw a diagram to solve your problem.
Type below:
__________

Question 8.
Test Prep Melvin has \(\frac{1}{4}\) of a gallon of fruit punch. He shares the punch equally with each of 2 friends and himself. Which equation represents the fraction of a gallon of punch that each of the friends get?
Options:
a. \(\frac{1}{4}\) ÷ \(\frac{1}{3}\) = n
b. \(\frac{1}{4}\) ÷ 3 = n
c. 3 ÷ \(\frac{1}{4}\) = n
d. 3 ÷ 4 = n

Answer: \(\frac{1}{4}\) ÷ 3 = n

Explanation:
Melvin has \(\frac{1}{4}\) of a gallon of fruit punch.
He shares the punch equally with each of 2 friends and himself.
The expressions which represents this are \(\frac{1}{4}\) ÷ 3 or \(\frac{1}{4}\) × \(\frac{1}{3}\).
So, the correct answers \(\frac{1}{4}\) ÷ 3 = n i.e., option B.

Chapter Review/Test – Page No. 361

Concepts and Skills

Divide. Draw a number line or use fraction strips.

Question 1.
2 ÷ \(\frac{1}{3}\) = ______

Answer: 6

Explanation:
Step 1: Draw a number line from 0 to 2. Divide the number line into thirds. Label each third on your number line.
Step 2: Skip count by thirds from 0 to 2 to find 2 ÷ \(\frac{1}{3}\).
There are 6 thirds in 2 wholes.
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Record and check the quotient.
2 ÷ \(\frac{1}{3}\) = 6 because 6 × \(\frac{1}{3}\) = 2

Go Math 5th Grade Chapter 8 Review Test Answer Key Question 2.
1 ÷ \(\frac{1}{5}\) = ______

Answer: 5

Explanation:
Step 1: Draw a number line from 0 to 1. Divide the number line into fifths. Label each fifth on your number line.
Step 2: Skip count by fifths from 0 to 1 to find 1 ÷ \(\frac{1}{5}\).
You can use the relationship between multiplication and division to explain and check your solution.
Step 3: Record and check the quotient.
1 ÷ \(\frac{1}{5}\) = 5 because 5 × \(\frac{1}{5}\) = 1

Question 3.
\(\frac{1}{4}\) ÷ 3 = \(\frac{□}{□}\)

Answer: \(\frac{1}{12}\)

Explanation:
Step 1: Draw a number line from 0 to 3. Divide the number line into fourths. Label each fourth on your number line.
Step 2: Skip count by fourth from 0 to 3 to find 3 ÷ \(\frac{1}{4}\).
You can use the relationship between multiplication and division to explain and check your solution.
3 ÷ \(\frac{1}{4}\) = \(\frac{1}{12}\)
Thus \(\frac{1}{4}\) ÷ 3 = \(\frac{1}{12}\)

Complete the number sentence to solve.

Question 4.
Three students share 4 sandwiches equally. How many sandwiches does each student get?
4 ÷ 3 = ______ \(\frac{□}{□}\)

Answer: 1 \(\frac{1}{3}\)

Explanation:
To find what fraction of sandwich each student gets we have to divide the number of sandwiches by the number of students.
4 ÷ 3 = \(\frac{4}{3}\)
Now convert the improper fraction to the mixed fraction.
\(\frac{4}{3}\) = 1 \(\frac{1}{3}\)

Question 5.
Six girls share 5 pints of milk equally. What fraction of a pint of milk does each girl get?
5 ÷ 6 = \(\frac{□}{□}\)

Answer: \(\frac{5}{6}\)

Explanation:
Given that, Six girls share 5 pints of milk equally.
To find the fraction of a pint of milk each girl gets, we have to divide the pints of milk by the number of girls.
5 ÷ 6 = \(\frac{5}{6}\)
Thus each girl get \(\frac{5}{6}\) pint of milk.

Write a related multiplication sentence to solve.

Question 6.
\(\frac{1}{4}\) ÷ 5
Type below:
__________

Answer: \(\frac{1}{20}\)

Explanation:
\(\frac{1}{4}\) ÷ 5
\(\frac{1}{4}\) × \(\frac{1}{5}\) = \(\frac{1}{20}\)
\(\frac{1}{4}\) ÷ 5 = \(\frac{1}{20}\)

Question 7.
\(\frac{1}{3}\) ÷ 9
Type below:
__________

Answer: \(\frac{1}{27}\)

Explanation:
\(\frac{1}{3}\) ÷ 9
\(\frac{1}{3}\) × \(\frac{1}{9}\) = \(\frac{1}{27}\)
\(\frac{1}{3}\) ÷ 9 = \(\frac{1}{27}\)

Question 8.
8 ÷ \(\frac{1}{2}\)
Type below:
__________

Answer: 16

Explanation:
8 ÷ \(\frac{1}{2}\)
8 × 2 = 16

Question 9.
5 ÷ \(\frac{1}{6}\)
Type below:
__________

Answer: 30

Explanation:
5 ÷ \(\frac{1}{6}\)
5 × 6 = 30

Question 10.
Write a story problem to represent \(\frac{1}{2}\) ÷ 3. Then solve.
Type below:
__________

Answer: \(\frac{1}{6}\)

Explanation:
\(\frac{1}{2}\) ÷ 3
\(\frac{1}{2}\) × \(\frac{1}{3}\) = \(\frac{1}{6}\)

Question 11.
Write a story problem to represent 3 ÷ \(\frac{1}{2}\). Then solve.
Type below:
__________

Answer: 6

Explanation:
3 ÷ \(\frac{1}{2}\)
3 × 2 = 6

Chapter Review/Test – Page No. 362

Fill in the bubble completely to show your answer.

Question 12.
Michelle cuts \(\frac{1}{4}\) yard of ribbon into 4 equal pieces. What is the length of each piece?
Options:
a. \(\frac{1}{16}\) yard
b. \(\frac{1}{8}\) yard
c. 1 yard
d. 16 yard

Answer: \(\frac{1}{16}\) yard

Explanation:
Michelle cuts \(\frac{1}{4}\) yard of ribbon into 4 equal pieces.
\(\frac{1}{4}\) ÷ 4
\(\frac{1}{4}\) × \(\frac{1}{4}\) = \(\frac{1}{16}\)
Thus the correct answer is option A.

5th Grade Math Test and Answers Pdf Chapter 8 Test Answer Key Question 13.
Ashton picked 6 pounds of pecans. He wants to share the pecans equally among 5 of his neighbors. How many pounds of pecans will each neighbor get?
Options:
a. \(\frac{5}{11}\) pound
b. \(\frac{5}{6}\) pound
c. 1 \(\frac{1}{5}\) pounds
d. 2 \(\frac{1}{5}\) pounds

Answer: 1 \(\frac{1}{5}\) pounds

Explanation:
Ashton picked 6 pounds of pecans.
He wants to share the pecans equally among 5 of his neighbors.
Divide the number of pounds by the number of neighbors.
= \(\frac{6}{5}\)
Now convert the improper fraction to the mixed fraction.
\(\frac{6}{5}\) = 1 \(\frac{1}{5}\) pounds
Thus the correct answer is option C.

Question 14.
Isabella has 5 pounds of trail mix. She divides the mix into \(\frac{1}{4}\)-pound servings. How many \(\frac{1}{4}\)-pound servings does she have?
Options:
a. 1 \(\frac{1}{4}\)
b. 9
c. 16
d. 20

Answer: 1 \(\frac{1}{4}\)

Explanation:
Given,
Isabella has 5 pounds of trail mix.
She divides the mix into \(\frac{1}{4}\)-pound servings.
5 × \(\frac{1}{4}\) = \(\frac{5}{4}\)
Now convert the improper fraction to the mixed fraction.
\(\frac{5}{4}\) = 1 \(\frac{1}{4}\)
Thus the correct answer is option A.

Question 15.
Melvin has \(\frac{1}{2}\) of a cake. He shares the cake equally with each of 2 friends and himself. Which equation represents the fraction of the whole cake that each of the friends get?
Options:
a. \(\frac{1}{2}\) ÷ \(\frac{1}{3}\) = n
b. \(\frac{1}{2}\) ÷ 3 = n
c. 2 ÷ \(\frac{1}{3}\) = n
d. 2 ÷ 3 = n

Answer: \(\frac{1}{2}\) ÷ 3 = n

Explanation:
Melvin has \(\frac{1}{2}\) of a cake.
He shares the cake equally with each of 2 friends and himself.
\(\frac{1}{2}\) divided by 3.
\(\frac{1}{2}\) ÷ 3 = n
Thus the correct answer is option B.

Chapter Review/Test – Page No. 363

Fill in the bubble completely to show your answer.

Question 16.
Camille has 8 feet of rope. She cuts the rope into \(\frac{1}{3}\)-foot pieces for a science project. How many \(\frac{1}{3}\)-foot pieces of rope does she have?
Options:
a. 24
b. 8
c. 3
d. 2 \(\frac{2}{3}\)

Answer: 24

Explanation:
Given,
Camille has 8 feet of rope.
She cuts the rope into \(\frac{1}{3}\)-foot pieces for a science project.
8 ÷ \(\frac{1}{3}\) = 8 × 3 = 24
Thus the correct answer is option A.

Question 17.
Awan makes 3 sandwiches and cuts each sandwich into sixths. How many \(\frac{1}{6}\)-size sandwich pieces does he have?
Options:
a. \(\frac{1}{2}\)
b. 2
c. 9
d. 18

Answer: 18

Explanation:
Given that, Awan makes 3 sandwiches and cuts each sandwich into sixths.
3 ÷ \(\frac{1}{6}\)
3/ \(\frac{1}{6}\) = 3 × 6 = 18
The correct answer is option D.

Question 18.
Eight students share 5 blocks of modeling clay equally. What fraction of one block of modeling clay does each student get?
Options:
a. \(\frac{1}{40}\)
b. \(\frac{1}{8}\)
c. \(\frac{5}{8}\)
d. 1 \(\frac{3}{5}\)

Answer: 1 \(\frac{3}{5}\)

Explanation:
Eight students share 5 blocks of modeling clay equally.
Divide number of students by the number of blocks.
8 ÷ 5 = \(\frac{8}{5}\)
Convert the fraction to the mixed fraction.
\(\frac{8}{5}\) = 1 \(\frac{3}{5}\)
So, the correct answer is option D.

Lesson 8 Homework Answer Key Grade 5 Question 19.
The diagram below represents which division problem?

Options:
a. 5 ÷ \(\frac{1}{3}\)
b. \(\frac{1}{3}\) ÷ 5
c. 5 ÷ \(\frac{1}{4}\)
d. \(\frac{1}{4}\) ÷ 5

Answer: 5 ÷ \(\frac{1}{3}\)

Explanation:
The figure above shows that there are 5 rectangles. Each rectangle is divided into three parts.
So, the fraction is one third.
Divide number of blocks by the number of thirds.
5 ÷ \(\frac{1}{3}\)
Thus the correct answer is option A.

Chapter Review/Test – Page No. 364

Constructed Response

Question 20.
Dora buys one package each of the 1-pound, 2-pound, and 4-pound packages of ground beef to make hamburgers. How many \(\frac{1}{4}\)-pound hamburgers can she make? Show your work using words, pictures, or numbers.
Explain how you found your answer.
______ hamburgers

Answer: 28 hamburgers

Explanation:
Given:
Dora buys one package each of the 1-pound, 2-pound, and 4-pound packages of ground beef to make hamburgers.
Total number of pounds = 1 + 2 + 4 = 7 pounds
Now divide number of pounds by \(\frac{1}{4}\)
7 ÷ \(\frac{1}{4}\) = 28
Thus Dora can make 28 Hamburgers.

Performance Task

Question 21.
Suppose your teacher gives you the division problem 6 ÷ \(\frac{1}{5}\).
A). In the space below, draw a diagram to represent 6 ÷ \(\frac{1}{5}\).
Type below:
__________

Answer:
Draw 6 rectangles and divide each whole by one-fifths fractions.

Question 21.
B). Write a story problem to represent 6 ÷ \(\frac{1}{5}\).
Type below:
__________

Answer:
Kyra has 6 feet of rope. If she cuts the rope into \(\frac{1}{5}\) foot pieces for a project. How many \(\frac{1}{5}\)-foot pieces of rope does she have?

Question 21.
C). Use a related multiplication expression to solve your story problem.
Show your work.
Type below:
__________

Answer:
The multiplication expression to solve the above problem is
6 ÷ \(\frac{1}{5}\) = 6/\(\frac{1}{5}\) = 6 × 5 = 30

Question 21.
D). Write a division problem that shows a unit fraction divided by a whole number. Write a story problem to represent your division problem. Then solve.
Type below:
__________

Answer:
Isabella has 7 pounds of trail mix. She divides the mix into \(\frac{1}{4}\)-pound servings. How many \(\frac{1}{4}\)-pound servings does she have?

Conclusion:

Browse Go Math Grade 5 Answer Chapter 8 Divide Fractions on our Go Math Answer Key page. Students can get Chapter-wise Answer Keys for Go Math Grade 5 here. Stick to our Go Math Answer Key page to get the simple solutions for all the chapters in an easy manner.

Go Math Grade 5 Chapter 9 Answer Key Pdf: Now it is the time to redefine your true self using Go Math Answer Key for Grade 5. Students who wish to score the highest marks in the exams can get the step by steps explanations from Go Math Grade 5 Answer Key Chapter 9 Algebra: Patterns and Graphing for free. So, Download the pdf of HMH Go Math 5th Grade Solution Key Chapter 9 and start learning the simple techniques for better understanding.

Algebra: Patterns and Graphing Go Math Grade 5 Chapter 9 Answer Key Pdf

Learn the concepts and skills to draw the line plots and graphs from Go Math Answer Key. Get a topic-wise solution with a brief explanation from here. Get the solutions for exercises and homework problems on our Go Math Grade 5 Solution Key Chapter 9 Patterns and Graphing. Check whether the answers are correct or not on Go Math Grade 5 Answer Key Algebra: Patterns and Graphing.

Lesson 1: Line Plot

• Share and Show – Page No. 371
• UNLOCK the Problem – Page No. 372

Lesson 2: Ordered Pairs

• Share and Show – Page No. 375
• Problem Solving – Page No. 376

Lesson 3: Investigate • Graph Data

• Share and Show – Page No. 379
• Problem Solving – Page No. 380

Lesson 4: Line Graphs

• Share and Show – Page No. 383
• Connect to science – Page No. 384

Mid-Chapter Checkpoint

• Mid-Chapter Checkpoint – Vocabulary – Page No. 385
• Mid-Chapter Checkpoint – Page No. 386

Lesson 5: Numerical Patterns

• Share and Show – Page No. 389
• Problem Solving – Page No. 390

Lesson 6: Problem Solving • Find a Rule

• Share and Show – Page No. 393
• On Your Own – Page No. 394

Lesson 7: Graph and Analyze Relationships

• Share and Show – Page No. 397
• Problem Solving – Page No. 398

Chapter 9 Review/Test

• Chapter Review/Test – Page No. 399
• Chapter Review/Test – Page No. 400
• Chapter Review/Test – Page No. 401
• Chapter Review/Test – Page No. 402

Share and Show – Page No. 371

Use the data to complete the line plot. Then answer the questions.

Lilly needs to buy beads for a necklace. The beads are sold by mass. She sketches a design to determine what beads are needed and then writes down their sizes. The sizes are shown below.

\(\frac{2}{5} g, \frac{2}{5} g, \frac{4}{5} g, \frac{2}{5} g, \frac{1}{5} g, \frac{1}{5} g, \frac{3}{5} g, \frac{4}{5} g, \frac{1}{5} g, \frac{2}{5} g, \frac{3}{5} g, \frac{3}{5} g, \frac{2}{5} g\)
Think: There are ___ Xs above \(\frac{1}{5}\) on the line plot, so the combined mass of the beads is _____ fifths, or _____ gram.

Question 1.
What is the combined mass of the beads with a mass of 1/5 gram?
\(\frac{□}{□}\) grams

Answer: \(\frac{3}{5}\) grams

Explanation:
For first we will count the number of \(\frac{1}{5}\) grams for each amount. Draw an x for the number of times each amount is recorded to complete the line plot.
There are 3 xs above \(\frac{1}{5}\) on the line plot, so the combined mass of the beads is 3 fifths
3 × \(\frac{1}{5}\) = 3/5 gram.

5th Grade Math Lesson 9.1 Answer Key Question 2.
What is the combined mass of all the beads with a mass of \(\frac{2}{5}\) gram?
_____ grams

Answer: 2

Explanation:
For first we will count the number of \(\frac{2}{5}\) grams for each amount. Draw an x for the number of times each amount is recorded to complete the line plot.
There are 5 xs above \(\frac{2}{5}\) on the line plot, so the combined mass of the beads is 5 two fifths.
5 × \(\frac{2}{5}\) = 2 grams

Question 3.
What is the combined mass of all the beads on the necklace?
_____ grams

Answer: 6

Explanation:
Total mass of all the beads on the necklace is \(\frac{3}{5}\) + 2 + \(\frac{8}{5}\) + \(\frac{9}{5}\) = \(\frac{30}{5}\) = 6
Therefore the combined mass of all the beads on the necklace is 6.

Question 4.
What is the average weight of the beads on the necklace?
\(\frac{□}{□}\) grams

Answer: \(\frac{3}{7}\) grams

Explanation:
Divide the sum by the number of beads to find the average.
The number of beads = 3 + 5 + 3 + 2 = 14
Divide by 6.
6 ÷ 14 = 3/7
So, the average mass of the beads on the necklace is 3/7 gram.

On Your Own

Use the data to complete the line plot. Then answer the questions.

A breakfast chef used different amounts of milk when making pancakes, depending on the number of pancakes ordered. The results are shown below.
\(\frac{1}{2} c, \frac{1}{4} c, \frac{1}{2} c, \frac{3}{4} c, \frac{1}{2} c, \frac{3}{4} c, \frac{1}{2} c, \frac{1}{4} c, \frac{1}{2} c, \frac{1}{2} c\)

Question 5.
How much milk combined is used in \(\frac{1}{4}\)-cup amounts?
\(\frac{□}{□}\) cup

Answer: \(\frac{1}{2}\) cup

Explanation:
For first we will count the number of \(\frac{1}{4}\) cups for each amount.
2 × \(\frac{1}{4}\) = \(\frac{1}{2}\)

Question 6.
How much milk combined is used in \(\frac{1}{2}\)-cup amounts?
______ cups

Answer: 3 cups

Explanation:
For first we will count the number of \(\frac{1}{2}\) cups for each amount.
There are 6 \(\frac{1}{2}\) cups
6 × \(\frac{1}{2}\) = 3 cups

Question 7.
How much milk combined is used in \(\frac{3}{4}\)-cup amounts?
_____ \(\frac{□}{□}\) cups

Answer: 1 \(\frac{1}{2}\) cups

Explanation:
For first we will count the number of \(\frac{3}{4}\) cups for each amount.
There are 2 \(\frac{3}{4}\) cups of milk.
2 × \(\frac{3}{4}\) = \(\frac{3}{2}\)
Convert from improper fraction to the mixed fraction.
\(\frac{3}{2}\) = 1 \(\frac{1}{2}\) cups

Question 8.
How much milk is used in all the orders of pancakes?
_____ cups

Answer: 5 cups

Explanation:
\(\frac{1}{2} c\) + [/latex]\frac{1}{4} c[/latex] + [/latex]\frac{1}{2} c[/latex] + [/latex]\frac{3}{4} c[/latex] + [/latex]\frac{1}{2} c[/latex] + [/latex]\frac{3}{4} c[/latex] + [/latex]\frac{1}{2} c[/latex] +[/latex]\frac{1}{4} c[/latex] + [/latex]\frac{1}{2} c[/latex] + [/latex]\frac{1}{2} c[/latex]
= 3 + [/latex]\frac{1}{4} c[/latex] + [/latex]\frac{3}{4} c[/latex] + [/latex]\frac{3}{4} c[/latex] + [/latex]\frac{1}{4} c[/latex]
= 3 + 1 + 1 = 5cups
Therefore 5 cups of milk is used in all the orders of pancakes.

Question 9.
What is the average amount of milk used for an order of pancakes?
\(\frac{□}{□}\) cup of milk

Answer: \(\frac{1}{2}\) cup of milk

Explanation:
There are 6 \(\frac{1}{2}\) cups of milk.
The average amount of milk used for an order of pancakes is \(\frac{1}{2}\) cup.

Question 10.
Describe an amount you could add to the data that would make the average increase.
Type below:
_________

Answer: \(\frac{3}{4}\) cup
We can add \(\frac{3}{4}\) to the data to increase the average amount of milk.

UNLOCK the Problem – Page No. 372

Question 11.
For 10 straight days, Samantha measured the amount of food that her cat Dewey ate, recording the results, which are shown below. Graph the results on the line plot. What is the average amount of cat food that Dewey ate daily?

\(\frac{1}{2} c, \frac{3}{8} c, \frac{5}{8} c, \frac{1}{2} c, \frac{5}{8} c, \frac{1}{4} c, \frac{3}{4} c, \frac{1}{4} c, \frac{1}{2} c, \frac{5}{8} c\)
a. What do you need to know?
Type below:
_________

Answer: I need to know the average amount of cat food that Dewey ate daily.

Question 11.
b. How can you use a line plot to organize the information?

Type below:
_________

Answer:

We can draw the line plot by using the given information.

Question 11.
c. What steps could you use to find the average amount of food that Dewey ate daily?
Type below:
_________

Answer: \(\frac{1}{2}\) cup

Explanation:
Number of days = 10
1/4 + 1/4 + 3/8 + 1/2 + 1/2 + 1/2 + 5/8 + 5/8 + 5/8 + 3/4 = 1 + 1 + 1/4 + 3/8 + 1/2 + 15/8
2 + 18/8 + 3/4 = 2 + 3 = 5
The average amount of food is 5 ÷ 10 = 5/10 = \(\frac{1}{2}\) cup

Question 11.
d. Fill in the blanks for the totals of each amount measured.
\(\frac{1}{4}\) cup: __________
\(\frac{3}{8}\) cup: __________
\(\frac{1}{2}\) cup: __________
\(\frac{5}{8}\) cup: __________
\(\frac{3}{4}\) cup: __________
Type below:
_________

Answer:
There are 2 xs above \(\frac{1}{4}\) cup: 2
There is 1 x above \(\frac{3}{8}\) cup: 1
There are 3 xs above \(\frac{1}{2}\) cup: 3
There are 3 xs above \(\frac{5}{8}\) cup: 3
There is 1 x above \(\frac{3}{4}\) cup: 1

Question 11.
e. Find the total amount of cat food eaten over 10 days.
_____ + _____ + _____ + _____ + _____ = _____
So, the average amount of food Dewey ate daily was ______.
Type below:
_________

Answer:
Number of days = 10
1/4 + 1/4 + 3/8 + 1/2 + 1/2 + 1/2 + 5/8 + 5/8 + 5/8 + 3/4 = 1 + 1 + 1/4 + 3/8 + 1/2 + 15/8
2 + 18/8 + 3/4 = 2 + 3 = 5 cups

Question 12.
Test Prep How many days did Dewey eat the least amount of cat food?
Options:
a. 1 day
b. 2 day
c. 3 day
d. 4 day

Answer: 1 day
By seeing the above line plot we can say that Dewey eats the least amount of cat food on day 1.
Thus the correct answer is option A.

Share and Show – Page No. 375

Use Coordinate Grid A to write an ordered pair for the given point.

Question 1.
C( _____ , _____ )

Answer: 6, 3

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the point’s horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the point’s vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for C is (6, 3).

Question 2.
D( _____ , _____ )

Answer: 3, 0

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
Thus the ordered pair for D is (3, 0)

Question 3.
E( _____ , _____ )

Answer: 9, 9

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the point’s horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the point’s vertical distance from 0, which is its y-coordinate.
Thus the ordered pair for E (9, 9)

Go Math Grade 5 Workbook 9.2 Answer Key Question 4.
F( _____ , _____ )

Answer: 10, 5

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
Thus the ordered pair for F is (10, 5)

Plot and label the points on Coordinate Grid A.

Question 5.
M (0, 9)
Type below:
_________

Answer:

Question 6.
H (8, 6)
Type below:
_________

Answer:

Question 7.
K (10, 4)
Type below:
_________

Answer:

Question 8.
T (4, 5)
Type below:
_________

Answer:

Go Math 5 Grade Answer Key Topic 9 Lesson 9.2 Answer Key Question 9.
W (5, 10)
Type below:
_________

Answer:

Question 10.
R (1, 3)
Type below:
_________

Answer:

On Your Own

Use Coordinate Grid B to write an ordered pair for the given point.

Question 11.
G( _____ , _____ )

Answer: 6, 4

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for G is (6, 4)

Question 12.
H( _____ , _____ )

Answer: 4, 9

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for H is (4, 9)

Question 13.
I( _____ , _____ )

Answer: 0, 7

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for I is (0, 7)

Question 14.
J( _____ , _____ )

Answer: 9, 5

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for J is (9, 5)

Question 15.
K( _____ , _____ )

Answer: 3, 3

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for K is (3, 3)

Question 16.
L( _____ , _____ )

Answer: 5, 2

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for L is (5, 2)

Question 17.
M( _____ , _____ )

Answer: 1, 1

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for M is (1, 1)

Question 18.
N( _____ , _____ )

Answer: 2, 5

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for N is (2, 5)

Question 19.
O( _____ , _____ )

Answer: 7, 8

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for O is (7, 8)

Question 20.
P( _____ , _____ )

Answer: 10, 10

Explanation:
Locate the point for which you want to write an ordered pair.
Look below at the x-axis to identify the points horizontal distance from 0, which is its x-coordinate.
Look to the left at the y-axis to identify the points vertical distance from 0, which is it’s y-coordinate.
So, the ordered pair for P is (10, 10)

Plot and label the points on Coordinate Grid B.

Question 21.
W (8, 2)

Answer:

Question 22.
E (0, 4)

Answer:

Question 23.
X (2, 9)

Answer:

Question 24.
B (3, 4)

Answer:

Go Math Pre Algebra Chapter 9 Math Test 5th Grade Question 25.
R (4, 0)

Answer:

Question 26.
F (7, 6)

Answer:

Question 27.
T (5, 7)

Answer:

Question 28.
A (7, 1)

Answer:

Question 29.
S (10, 8)

Answer:

Question 30.
Y (1, 6)

Answer:

Question 31.
Q (3, 8)

Answer:

Question 32.
V (3, 1)

Answer:

Problem Solving – Page No. 376

Nathan and his friends are planning a trip to New York City. Use the map for 33–38. Each unit represents 1 city block.

Question 33.
What ordered pair gives the location of Bryant Park?
( _____ , _____ )

Answer: 4, 8

Question 34.
What’s the Error? Nathan says that Madison Square Garden is located at (0, 3) on the map. Is his ordered pair correct? Explain.
Type below:
__________

Answer: He needs to put point 3 on Y-axis but he placed on X-Axis.

Question 35.
The Empire State Building is located 5 blocks right and 1 block up from (0, 0). Write the ordered pair for this location. Plot and label a point for the Empire State Building.
Type below:
__________

Answer: 5, 1

Question 36.
Paulo walks from point B to Bryant Park. Raul walks from point B to Madison Square Garden. If they only walk along the grid lines, who walks farther? Explain.
__________

Answer: Paulo
By seeing the above graph we can say that Paulo walks farther along the grid lines.

Question 37.
Explain how to find the distance between Bryant Park and a hot dog stand at the point (4, 2).
_____ city blocks

Answer: 6

Question 38.
Test Prep Use the map above. Suppose a pizzeria is located at point B. What ordered pair describes this point?
Options:
a. (4,2)
b. (3,4)
c. (2,4)
d. (4,4)

Answer: (2,4)

Share and Show – Page No. 379

Graph the data on the coordinate grid.

Question 1.
a. Write the ordered pairs for each point.
Type below:
__________

Answer: A(1, 30), B (2, 35), C (3, 38), D (4, 41), E (5, 44)

Question 1.
b. What does the ordered pair (3, 38) tell you about Ryan’s age and height?
Type below:
__________

Answer: The ordered pair tells that the age of Ryan is 3 and height is 38 inches.

Question 1.
c. Why would the point (6, 42) be nonsense?
Type below:
__________

Answer: The point (6, 42) be nonsense because the height will be increased. In the above-ordered pair the height is decreased. So, the statement is nonsense.

5th Grade Math Problems Lesson 9.3 Answer Key Question 2.
a. Write the ordered pairs for each point.
Type below:
__________

Answer: We can write the ordered pairs by using the above table Day is the x-axis and height is the y-axis. The coordinates are A (5,1), B (10,3), C (15, 8), D (20,12), E (25,16), F(30,19).

Question 2.
b. How would the ordered pairs be different if the heights of the plants were measured every 6 days for 30 days instead of every 5 days?

Answer:
If the heights of the plants were measured every 6 days for 30 days instead of every 5 days the coordinates will be A (6,1), B (12,3), C (18, 8), D (24,12), E (30,16)

Problem Solving – Page No. 380

What’s the Error?

Question 3.
Mary places a miniature car onto a track with launchers. The speed of the car is recorded every foot. Some of the data is shown in the table. Mary graphs the data on the coordinate grid below.

Look at Mary’s graphed data.
Find her error.


Graph the data and correct
the error.

• Describe the error Mary made.
Type below:
__________

Answer:

Graph the data and correct the error

Share and Show – Page No. 383

Use the table at the right for 1–3.

Question 1.
What scale and intervals would be appropriate to make a graph of the data?
Type below:
__________

Answer:
Scale is 1 cm = 10°F
Months will be on the x-axis.
The temperature will be on the y-axis.

Question 2.
Write the related pairs as ordered pairs.
Type below:
__________

Answer: The related pairs are A (Jan, 40), B (Feb, 44), C (Mar, 54), D (Apr, 62), E (May, 70)

Question 3.
Make a line graph of the data.
Type below:
__________

5th Grade Problem Solving Go Math Lesson 9.4 Question 4.
Use the graph to determine between which two months the least change in average temperature occurs.
Type below:
__________

Answer: By seeing the above graph we can say that Jan and Feb have the least change in the average temperature.

On Your Own

Use the table at the right for 5–7.

Question 5.
Write the related number pairs for the plant height as ordered pairs.
Type below:
__________

Answer: The related number pairs of the above table are A (1, 20), B(2, 25), C (3, 29), D (4, 32)

Question 6.
What scale and intervals would be appropriate to make a graph of the data?
Type below:
__________

Answer: The above table says that the X-Axis is Month and Y-Axis is Height in inches.
Scale is 1 cm = 5 inches.

Explanation:
The horizontal axis could represent months from 1 to 4. In this case, the scale interval is one month.
The vertical axis could represent height from 20 inches to 32 inches but we can show a break in the scale between 1 inch and 16 inches since there are no heights between 0 inches and 20 inches, the scale interval is 1 inch.

Question 7.
Make a line graph of the data.
Type below:
__________

Question 8.
Use the graph to find the difference in height between Month 1 and Month 2.
Type below:
__________

Answer: By observing the above graph we can say that the difference between months 1 and 2 is 5 inches.
25 – 20 = 5 inches
From the graph we can see that the plant grew the most between 1 and 2 months (about 5 inches), the least change is between 3 and 4 months (about 3 inches).

Question 9.
Use the graph to estimate the height at 1 \(\frac{1}{2}\) months.
_____ in.

Answer: The estimated height at 1 \(\frac{1}{2}\) months is 22.5 inches.
The average of month 1 and month 2 is (20 + 25) ÷ 2 = 45/2 = 22.5 inches.

Connect to science – Page No. 384

Evaporation changes water on Earth’s surface into water vapor. Water vapor condenses in the atmosphere and returns to the surface as precipitation. This process is called the water cycle. The ocean is an important part of this cycle. It influences the average temperature and precipitation of a place.

The overlay graph below uses two vertical scales to show monthly average precipitation and temperatures for Redding, California.

Use the graph for 10–13.

Question 10.
About how much precipitation falls in Redding, California, in February?
_____ inches

Answer: From the graph, we can see that the precipitation in February is 4.2 inches.

Question 11.
What is the average temperature for Redding, California, in February?
_____ °F

Answer: From the graph, we can see that the temperature in February is 50°F.

Question 12.
Explain how the overlay graph helps you relate precipitation and temperature for each month.
Type below:
__________

Answer: The average temperature for each month is plotted on the graph with the blue line and the red bar graph represents the precipitation. As the temperature increases the precipitation decreases.

Question 13.
Describe how the average temperature changes in the first 5 months of the year.
Type below:
__________

Answer: From the graph, we can see that the temperature in the first 5 months of the year but the amount of precipitation is decreasing. It’s logical because when the temperature is increasing the amount of precipitation is decreasing.

Go Math Grade 5 Chapter 9 Review/Test Answer Key Pdf Question 14.
Test Prep Which day had an increase of 3 feet of snow from the previous day?

Options:
a. Day 2
b. Day 3
c. Day 5
d. Day 6

Answer: Day 5

Explanation:
By seeing the above graph we can say that the snow level has increased 3 feet from day 4 to Day 5.
Thus the correct answer is option C.

Mid-Chapter Checkpoint – Vocabulary – Page No. 385

Choose the best term from the box.

Question 1.
The ______ is the horizontal number line on the coordinate grid.
__________

Answer: X-Axis
The X-Axis is the horizontal number line on the coordinate grid.

Question 2.
A ______ is a graph that uses line segments to show how data changes over time.
__________

Answer: Line graph
A Line graph is a graph that uses line segments to show how data changes over time.

Concepts and Skills

Use the line plot at the right for 3–5.

Question 3.
How many kittens weigh at least \(\frac{3}{8}\) of a pound?
______ kittens

Answer: 9

Explanation:
The line plot shows that there are 4 xs above \(\frac{3}{8}\), 3 xs above \(\frac{1}{2}\), and 2 xs on \(\frac{5}{8}\).
To find the kittens weigh at least \(\frac{3}{8}\) we need to add all above \(\frac{3}{8}\)
= 4 + 3 + 2 = 9

Question 4.
What is the combined weight of all the kittens?
______ lb

Answer: 5

Explanation:
There are 3 xs above 1/4 on the line plot, so the combined weight of Kitten in the animal shelter is 3 fourths
3 × 1/4 = 3/4.
There are 4 xs above 3/8 on the line plot, so the combined weight of kittens in the animal shelter is 4 three eights or
4 × 3/8 = 12/8 = 3/2
There are 3 xs above 1/2 on the line plot, so the combined weight of kittens in the animal shelter is 3 halves = 3/2
There are 2 xs above 5/8 on the line plot, so the combined weight of kittens in the animal shelter is 10/8
3/4 + 1 4/8 + 1 1/2 + 1 2/8
= 3/4 + 12/8 + 3/2 + 10/8 = 6/8 + 12/8 + 12/8 + 10/8 = 40/8 = 5 lb

Question 5.
What is the average weight of the kittens in the shelter?
______ lb

Answer: 5/12

Explanation:
Divide the sum you found in example 4. 5 lb by the number of the kittens to find the average. The number of kittens is 12 so we will divide 5 lb by 12.
5 ÷ 12 = 5/12.
Thus the average weight of the kittens in the shelter as 5/12 lb.

Use the coordinate grid at the right for 6–13.

Write an ordered pair for the given point.

Question 6.
A( ______ , ______ )

Answer: 1, 6
The ordered pair for A is (1,6)

Question 7.
B( ______ , ______ )

Answer: 2, 2
The ordered pair for B is (2, 2)

Question 8.
C( ______ , ______ )

Answer: 4, 4
The ordered pair for C is (4, 4)

Question 9.
D( ______ , ______ )

Answer: 0, 3
The ordered pair for D is (0, 3)

Plot and label the point on the coordinate grid.

Question 10.
E(6, 2)
Type below:
__________

Answer:

Question 11.
F(5, 0)
Type below:
__________

Answer:

Question 12.
G(3, 4)
Type below:
__________

Answer:

Question 13.
H(3, 1)
Type below:
__________

Answer:

Mid-Chapter Checkpoint – Page No. 386

Question 14.
Jane drew a point that was 1 unit to the right of the y-axis and 7 units above the x-axis. What is the ordered pair for this location?
( ______ , ______ )

Answer: (1, 7)
The ordered pair for the location is (1, 7).

Question 15.
The graph below shows the amount of snowfall in a 6-hour period.

Between which hours did the least amount of snowfall?
between hour ______ and hour ______

Answer: From the graph, we can see that the least amount of snowfall between 2 hours and 4 hours, 0 inches.

Question 16.
Joy recorded the distances she walked each day for five days. How far did she walk in 5 days?

______ \(\frac{□}{□}\) miles

Answer: 2 \(\frac{1}{6}\) miles

Explanation:
There are 3 xs above \(\frac{1}{3}\) = 3 × \(\frac{1}{3}\) = 1
There are 1 x above \(\frac{1}{2}\) = 1 × \(\frac{1}{2}\) = \(\frac{1}{2}\)
There is 1 x above \(\frac{2}{3}\) = 1 × \(\frac{2}{3}\) = \(\frac{2}{3}\)
1 + \(\frac{2}{3}\) + \(\frac{1}{2}\) = (6 + 3 + 4)/6 = 13/6
The mixed fraction of 13/6 is 2 \(\frac{1}{6}\) miles
Thus she walked 2 \(\frac{1}{6}\) miles in 5 days.

Share and Show – Page No. 389

Use the given rules to complete each sequence. Then, complete the rule that describes how nickels are related to dimes.

Question 1.

Type below:
__________

Answer: The number of Dimes is 2 times the number of Nickels.
We need to add 5 to Nickels = 5 + 5 + 5 + 5 + 5 = 25
We need to add 10 to Dimes = 10 + 10 + 10 + 10 + 10 = 50

Complete the rule that describes how one sequence is related to the other. Use the rule to find the unknown term.

Question 2.
Multiply the number of books by ______ to find the amount spent.

______
Explain:
__________

Answer: The amount spent is 4 times the number of books so we multiply the number of books by 4 to find the amount spent.
Multiply 4 to the amount spent = 24 × 4 = 96

Question 3.
Divide the weight of the bag by _____ to find the number of marbles.

______
Explain:
__________

Answer: The weight of Bag is 3 times the number of marbles So, we divide the weight of Bag by 3 to find the number of marbles.
Divide 360 by 3
360/3 = 120

On Your Own

Complete the rule that describes how one sequence is related to the other. Use the rule to find the unknown term.

Question 4.
Multiply the number of eggs by _______ to find the number of muffins.

Type below:
__________

Answer: The muffins is 6 times the number of eggs so we multiply the number of eggs by 6 to find the muffins.
The unknown term in the table we will find when multiplying 18 by 6.
18 × 6 = 108
The unknown term is 108.

Go Math Book 5th Grade Chapter 9 Review Test Question 5.
Divide the number of meters by _______ to find the number of laps.

Type below:
__________

Answer: The number of meters is 400 times the number of laps so we divide the number of meters by 400 to find the number of laps.
The unknown term in the table we will find when divide 6400 by 400.
6400 ÷ 400 = 16
The unknown term is 16.

Question 6.
Suppose the number of eggs used in Exercise 4 is changed to 3 eggs for each batch of 12 muffins, and 48 eggs are used. How many batches and how many muffins will be made?
______ batches
______ muffins

Answer: 16 batches 192 muffins will be made.

Explanation:
If we change to 3 eggs for each batch of 12 muffins and 48 eggs are used we will have 16 batches.
16 × 3 = 48
The muffins are 4 times the number of eggs so we multiply the number of eggs by 4 to fins the number of muffins.
If the number of batches is 16 and there are 48 eggs to find the number of muffins we will multiply the number of eggs 48 with 4:
48 × 4 = 192
192 muffins will be made.

Problem Solving – Page No. 390

Question 7.
Emily has a road map with a key that shows an inch on the map equals 5 miles of actual distance. If a distance measured on the map is 12 inches, what is the actual distance? Write the rule you used to find the actual distance.
______ miles

Answer: 60 miles

Explanation:
For first the total length of roads is 5 inches + 7 inches = 12 inches
1 inch on the map represents 5 miles of actual distance so to find what actual distance corresponding to 12 inches we will find with using proportion.
1 inch : 5 inches = 12 inches: x inches
1 × x = 5 × 12
x = 60 miles
The actual distance which Emily will drive is 60 miles.
The rule which we used to find the actual distance is multiplied by 5 which is a mark in solution.

Question 8.
To make a shade of lavender paint, Jon mixes 4 ounces of red tint and 28 ounces of blue tint into one gallon of white paint. If 20 gallons of white paint and 80 ounces of red tint are used, how much blue tint should be added? Write a rule that you can use to find the amount of blue tint needed.
______ oz

Answer: 560 oz

Explanation:
For one gallon of white paint, Jon mixed 28 ounces of blue tint so to find how much tint corresponding to 20 gallons of white paint we will find with using proportion.
1 gallon of white paint:28 ounces of blue tint = 20 gallons of white paint:x ounces of the blue tint.
1 × x = 28 × 20
x = 560
560 ounces of blue tint should be added.
The rule which we used to find the amount of blue tint needed is to multiply by 28 which is the mark in solution.

Question 9.
In the cafeteria, tables are arranged in groups of 4, with each table seating 8 students. How many students can sit at 10 groups of tables? Write the rule you used to find the number of students.
______ students

Answer: 320 students

Explanation:
Tables are arranged in groups of 4, with each table seating 8 students, so in one group sit
4 × 8 = 32 students
To find how many students can sit at 10 groups of tables, we will find when multiplying 32 students with 10.
32 × 10 = 320
Finally, 320 students can sit at 10 groups of tables. The rule which we used to find the number of students is to multiply by 32 which is marked is a solution.

5th Grade Go Math Book Chapter 9 Test Answer Key Question 10.
Test Prep What is the unknown number in Sequence 2 in the chart? What rule could you write that relates Sequence 1 to Sequence 2?

Options:
a. 70; Multiply by 2.
b. 100; Add 25.
c. 105; Multiply by 3.
d. 150; Add 150.

Answer: 105; Multiply by 3.

Explanation:
The unknown number in Sequence number 7 we will get when multiply 35 with 3 because the rule that releases the number of miles to the number of runners is multiplying by 3.
The unknown number is: 35 × 3 = 105
Thus the correct answer is option C.

Share and Show – Page No. 393

Question 1.
Max builds rail fences. For one style of fence, each section uses 3 vertical fence posts and 6 horizontal rails. How many posts and rails does he need for a fence that will be 9 sections long?



First, think about what the problem is asking and what you know. As each section of fence is added, how does the number of posts and the number of rails change?

Next, make a table and look for a pattern. Use what you know about 1, 2, and 3 sections. Write a rule for the number of posts and rails needed for 9 sections
of fence.

Possible rule for posts: _____________
Possible rule for rails: ______________
Finally, use the rule to solve the problem.
Type below:
__________

Answer:
Possible rule for posts: 27
Possible rule for rails: 54

Explanation:
The number of posts is 3 times the number of sections. So, we multiply the number of posts by 3.
With using the rule the unknown number is 9 × 3 = 27
Thus the possible rule for posts is 27.
Now multiply the number of rails by 2.
With using the rule the unknown number is 27 × 2 = 54
Thus the possible rule for rails is 54.

Question 2.
What if another style of rail fencing has 6 rails between each pair of posts? How many rails are needed for 9 sections of this fence?

Possible rule for rails: ____________________
______ rails

Answer: 108 rails

Explanation:
The number of posts is 3 times the number of sections. So, we multiply the number of posts by 3.
With using the rule the unknown number is 9 × 3 = 27
Thus the possible rule for posts is 27.
Now multiply the number of rails by 4.
With using the rule the unknown number is 27 × 4 = 108
Thus the possible rule for rails is 108.

Question 3.
Leslie is buying a coat on layaway for $135. She will pay $15 each week until the coat is paid for. How much will she have left to pay after 8 weeks?

$ ______

Answer: $15

Explanation:
Leslie is buying a coat on layaway for $135. She will pay $15 each week until the coat is paid for.
Multiply the number of weeks by 15.
15 × 8 = $120
Now subtract $120 from $135
= $135 – $120 = $15

On Your Own – Page No. 394

Question 4.
Jane works as a limousine driver. She earns $50 for every 2 hours that she works. How much does Jane earn in one week if she works 40 hours per week? Write a rule and complete the table.
Possible rule: _____________

$ ______

Answer: 1000

Explanation:
The possible rule for hours worked: We can see that the difference between terms is 2.
So, the rule that describes this is Add 2.
The possible rule for Jane’s Pay: We can see that the difference between terms is 50.
So, the rule that describes this is Add 50.
Jane’s Pay is 25 times the hours worked so, we will multiply the hours worked by 25 to find Jane’s Pay.
The unknown number Jane’s Pay we will find when multiplying 40 with 25:
40 × 25 = 1000
She earns 1000 dollars.

Go Math Grade 5 Chapter 9 Answer Key Pdf Question 5.
Rosa joins a paperback book club. Members pay $8 to buy 2 tokens and can trade 2 tokens for 4 paperback books. Rosa buys 30 tokens and trades them for 60 paperback books. How much money does she spend? Write a rule and complete the table.
Possible rule: _______________

$ ______

Answer: 120

Explanation:
Possible rule for Tokens: We can see that the difference between terms is 8.
So, the rule which describes this is Add 8.
Possible rule for Games: We can see that the difference between terms is 4.
So, the rule which describes this is Add 4.
Tokens are 2 times the games so, we will divide the tokens by 2 to find how many games can she3 play.
The unknown number of games we will find when dividing 120 with 2:
120 ÷ 2 = 60
She can play 60 games for 120 tokens.

Question 6.
Paul is taking a taxicab to a museum. The taxi driver charges a $3 fee plus $2 for each mile traveled. How much does the ride to the museum cost if it is 8 miles away?

Answer: $40

Explanation:
Paul is taking a taxicab to a museum. The taxi driver charges a $3 fee plus $2 for each mile traveled.
That means the driver charged $5 per mile.
For 8 miles = 8 × $5 = $40.

Question 7.
Test Prep Which expression could describe the next figure in the pattern, Figure 4?

Options:
a. 2 × 5
b. 2 + 4 + 4
c. 2 + 4 + 4 + 4
d. 16

Answer: 2 + 4 + 4 + 4

Explanation:
We can see that the difference between two consecutive figures is 4 squares.
So, the rule which describes this is Add 4.
Thus figure 4 has 14 squares.
Thus the correct answer is option C.

Share and Show – Page No. 397

Graph and label the related number pairs as ordered pairs.
Then complete and use the rule to find the unknown term.

Question 1.
Multiply the number of tablespoons by ___ to find its weight in ounces.


Type below:
_________

Answer: Multiply the number of tablespoons by 2 to find its weight in ounces.
5 × 2 = 10

Question 2.
Multiply the number of hours by ____ to find the distance in miles.


Type below:
_________

Answer: Multiply the number of hours by 3 to find the distance in miles.
4 × 3 = 12 miles

On Your Own

Graph and label the related number pairs as ordered pairs.
Then complete and use the rule to find the unknown term.

Question 3.
Multiply the number of inches by ____ to find the distance in miles.


Type below:
_________

Answer: Multiply the number of inches by 5 to find the distance in miles.
10 × 5 = 50

Go Math Grade 5 Chapter 9 Review Test Answer Key Question 4.
Multiply the number of centiliters by ____ to find the equivalent number of milliliters.

Answer:
Multiply the number of centiliters by 10 to find the equivalent number of milliliters.
5 × 10 = 50 milliliters

Problem Solving – Page No. 398

Sense or Nonsense?

Question 5.
Elsa solved the following problem.

Lou and George are making chili for the Annual Firefighter’s Ball. Lou uses 2 teaspoons of hot sauce for every 2 cups of chili that he makes, and George uses 3 teaspoons of the same hot sauce for every cup of chili in his recipe. Who has the hotter chili, George or Lou?

Write the related number pairs as ordered pairs and then graph them. Use the graph to compare who has the hotter chili, George or Lou.

Lou’s chili: (2, 2), (4, 4), (6, 6), (8, 8)
George’s chili: (1, 3), (2, 6), (3, 9), (4, 12)

Elsa said that George’s chili was hotter than Lou’s because the graph showed that the amount of hot sauce in George’s chili was always 3 times as great as the amount of hot sauce in Lou’s chili.

Does Elsa’s answer make sense, or is it nonsense?
Explain.

Answer: Elsa’s Answer makes sense.

Explanation:
Elsa’s answer makes sense because the amount of hot sauce in George’s chili was always 3 times as great as the amount of hot sauce in Lou’s chili. To prove this we will take two points from the graph which has an equal amount of cups of chili and compare the amount of hot sauce in George’s chili with the amount of hot sauce in Lou’s chili.
If we take 4 cups of George’s chili and Lou’s chili the amount of hot sauce in George’s chili is 12 teaspoons and the amount of hot sauce in Lou’s chili is 4 teaspoons.
12 is 3 times greater than 4 so Elsa’s answer makes sense.

Chapter Review/Test – Vocabulary – Page No. 399

Choose the best term from the box.

Question 1.
The __________ is the point where the x-axis and y-axis meet. Its __________ is 0, and its __________ is 0.
The ________ is the point where the x-axis and y-axis meet.
Its ________ is 0,
and its ________ is 0.

Answer:
The Origin is the point where the x-axis and y-axis meet.
Its x-coordinate is 0,
and its y-coordinate is 0.

Go Math 5th Grade 11.9 Answer Key Chapter 9 Question 2.
A __________ uses line segments to show how data changes over time.

Answer: A line graph uses line segments to show how data changes over time.

Check Concepts

Use the table for 3–4.

Question 3.
Write related number pairs of data as ordered pairs.
Type below:
__________

Answer:
The ordered pair for week 1 is (1, 2)
The ordered pair for week 2 is (2, 6)
The ordered pair for week 3 is (3, 14)
The ordered pair for week 4 is (4, 16)

Question 4.
Make a line graph of the data.

Type below:
__________

Answer:

The ordered pair for week 1 is (1, 2)
The ordered pair for week 2 is (2, 6)
The ordered pair for week 3 is (3, 14)
The ordered pair for week 4 is (4, 16)

Complete the rule that describes how one sequence is related to the other. Use the rule to find the unknown term.

Question 5.
Multiply the number of eggs by ________ to find the number of cupcakes.

_______

Answer:
Multiply the number of eggs by 6 to find the number of cupcakes.
The unknown number in batches 6 we will get when multiply 18 with 6 because the rule that releases the number of eggs to the number of cupcakes is multiplying by 6.
The number of eggs is multiple of 3 and the number of cupcakes is multiple of 6.

Chapter Review/Test – Page No. 400

Fill in the bubble completely to show your answer.

Question 6.
The letters on the coordinate grid represent the locations of the first four holes on a golf course.

Which ordered pair describes the location of the hole labeled T?
Options:
a. (0, 7)
b. (1, 7)
c. (7, 0)
d. (7, 1)

Answer: (0, 7)
By seeing the above graph we can find the location of the hole label T i.e., (0, 7)

Use the line plot at the right for 7–8.

Go Math Grade 5 Chapter 9 Mid Chapter Checkpoint Answer Key Question 7.
What is the average of the data in the line plot?
Options:
a. \(\frac{1}{2}\) pound
b. 1 pound
c. 6 pounds
d. 6 \(\frac{3}{4}\) pounds

Answer: 6 pounds

Explanation:
There are 3 xs above \(\frac{1}{2}\) pound = 3 × \(\frac{1}{2}\) = 3/2
There are 4 xs above \(\frac{2}{3}\) pound = 4 × \(\frac{2}{3}\) = 8/3
There is 1 x above \(\frac{5}{6}\) pound = 5/6
There are 2 xs above \(\frac{1}{6}\) = 2/6
There are 2 xs above \(\frac{1}{3}\) = 2/3
3/2 + 8/3 + 5/6 + 2/6 + 2/3 = 6 pounds
Thus the correct answer is option C.

Question 8.
How many bags of rice weigh at least \(\frac{1}{2}\) pound?
Options:
a. 2
b. 3
c. 5
d. 8

Answer: 8

Explanation:
By seeing the above line plot we can find the number of bags of rice weigh at least \(\frac{1}{2}\) pound
There are 3 xs above \(\frac{1}{2}\) pound = 3 × \(\frac{1}{2}\) = 3/2
There are 4 xs above \(\frac{2}{3}\) pound = 4 × \(\frac{2}{3}\) = 8/3
There is 1 x above \(\frac{5}{6}\) pound = 5/6
Total number of bags of rice weigh at least \(\frac{1}{2}\) pound = 3 + 4 + 1 = 8
Thus the correct answer is option D.

Chapter Review/Test – Page No. 401

Fill in the bubble completely to show your answer.

Use the table for 9–10.

Question 9.
Compare Tori’s and Martin’s savings. Which of the following statements is true?
Options:
a. Tori saves 4 times as much per week as Martin.
b. Tori will always have exactly $15 more in savings than Martin has.
c. Tori will save 15 times as much as Martin will.
d. On week 5, Martin will have $30 and Tori will have $90.

Answer: Tori saves 4 times as much per week as Martin.

Explanation:
By seeing the above table we can say that Tori saves 4 times as much per week as Martin.
Thus the correct answer is option A.

Go Math 5th Grade Chapter 9 Review Test Question 10.
What rule could you use to find Tori’s savings after 10 weeks?
Options:
a. Add 10 from one week to the next.
b. Multiply the week by 2.
c. Multiply Martin’s savings by 4.
d. Divide Martin’s savings by 4.

Answer: Multiply Martin’s savings by 4.

Explanation:
We can find the savings of Tori by multiplying the savings of Martins by 4.
Thus the suitable statement is Multiply Martin’s savings by 4.
Therefore the correct answer is option C.

Question 11.
In an ordered pair, the x-coordinate represents the number of hexagons and the y-coordinate represents the total number of sides. If the x-coordinate is 7, what is the y-coordinate?
Options:
a. 6
b. 7
c. 13
d. 42

Answer: 6

Explanation:
Given that x-coordinate represents the number of hexagons.
Thus x-coordinate is 6.
And also given that the y-coordinate represents the number of sides.
The figure hexagon contains 6 sides.
So, the y-coordinate is 6.
Thus the ordered pair is (7, 6)
Therefore the correct answer is option A.

Question 12.
Point A is 2 units to the right and 4 units up from the origin. What ordered pair describes point A?
Options:
a. (2, 0)
b. (2, 4)
c. (4, 2)
d. (0, 4)

Answer: (2, 4)

Explanation:
Point A is 2 units to the right and 4 units up from the origin.
2 units will be located on the x-axis and 4 units will be on the y-axis.
Thus the ordered pair for point A is (2, 4)
Therefore the correct answer is option B.

Chapter Review/Test – Page No. 402

Constructed Response

Question 13.
Mr. Stevens drives 110 miles in 2 hours, 165 miles in 3 hours, and 220 miles in 4 hours. How many miles will he drive in 5 hours?
Explain how the number of hours he drives is related to the number of miles he drives.
_____ miles

Answer: 275 miles

Explanation:
Given that, Mr. Stevens drives 110 miles in 2 hours, 165 miles in 3 hours, and 220 miles in 4 hours.
We have to divide the number of miles by number of hours
That means, 110/2, 165/3, 220/4
The distance gone in 5 hours can be found with this equation
110/2 x ?/5
multiply 110 by 5 then divide the product by 2
110 × 5= 550
550/2 =275
Thus the answer is Mr. Stevens goes 275 miles in 5 hr.

Performance Task

Go Math Grade 5 Chapter 9 Test Pdf Question 14.
Tim opens the freezer door and measures the temperature of the air inside. He continues to measure the temperature every 2 minutes, as the door stays open, and records the data in the table.

A). On the grid below, make a line graph showing the data in the table.

Type below:
__________

Question 14.
B). Use the graph to estimate the temperature at 7 minutes.
Estimate: _____ °F

Answer: By seeing the above graph we can say that the estimated temperature at 7 minutes is 15°F.

Question 14.
C). Write a question that can be answered by making a prediction. Then answer your question and explain how you made your prediction.
Type below:
__________

Question: Estimate the temperature at 5 minutes by using the graph.
Answer: By seeing the above table we can say that the estimated temperature at 5 minutes is 13°F

Conclusion:

Fall in love with Math by solving the sums from Go Math Answer Key. Click on the above link to get the step by step explanation for the problems. Check out the solution for the mid-chapter checkpoint and Review test from this article. No fee required to refer Go Math 5th standard 5 Answer Key. Just make use of the links and Download Go Math Grade 5 Answer Key Chapter 9 Algebra: Patterns and Graphing pdf.