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## Texas Go Math Grade 5 Lesson 5.6 Answer Key Add and Subtract Mixed Numbers

**Unlock the Problem**

Denise mixed 1\(\frac{4}{5}\) ounces of blue paint with 2\(\frac{1}{10}\) ounces of yellow paint. How many ounces of paint did Denise mix?

- What operation should you use to solve the problem?
- Do the fractions have the same denominator?

Add. 1\(\frac{4}{5}\) + 2\(\frac{1}{10}\)

To find the sum of mixed numbers with unequal denominators, you can use a common denominator.

STEP 1: Estimate the sum.

STEP 2: Find a common denominator. Use the common denominator to write equivalent fractions with equal denominators.

STEP 3: Add the fractions. Then add the whole numbers. Write the answer in simplest form.

So, Denise mixed __________ ounces of paint.

Answer:

So, Denise mixed \(\frac{39}{10}\) ounces of paint.

**Math Talk**

**Mathematical Processes**

Did you use the least common denominator? Explain.

Answer: yes

Explanation:

The sum of mixed numbers with unequal denominators can use a common denominator.

Question 1.

Explain how you know whether your answer is reasonable.

Answer: Yes my answer is reasonable

Because the sum of two mixed numbers is solved and it is proved

**Go Math Grade 5 Lesson 5.6 Answer Key Question 2.**

What other common denominator could you have used?

Answer: 50

multiply 5 x 10 = 50

**Example**

Subtract. 4\(\frac{5}{6}\) – 2\(\frac{3}{4}\)

You can also use a common denominator to find the difference between mixed numbers with unequal denominators.

STEP 1: Estimate the difference.

STEP 2: Find a common denominator. Use the common denominator to write equivalent fractions with equal denominators.

STEP 3: Subtract the fractions. Subtract the whole numbers. Write the answer in the simplest form.

Answer:

Question 3.

Explain how you know whether your answer is reasonable.

Answer: Used the common denominator to write equivalent fractions with equal denominators.

so, my answer is reasonable.

**Share and Show**

Question 1.

Use a common denominator to write equivalent fractions with equal denominators and then find the sum. Write your answer in simplest form.

Answer:

Explanation:

Used a common denominator and written equivalent fractions with equal denominators and then find the sum. written the answer in simplest form.

**Find the sum. Write your answer in simplest form.**

Question 2.

2\(\frac{3}{4}\) + 3\(\frac{3}{10}\)

Answer:

2\(\frac{3}{4}\) + 3\(\frac{3}{10}\) = \(\frac{11}{4}\) + \(\frac{33}{10}\) = \(\frac{55}{20}\) + \(\frac{66}{20}\) = \(\frac{121}{20}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take the least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

**Lesson 5.6 Answer Key Go Math Grade 5 Question 3.**

5\(\frac{3}{4}\) + 1\(\frac{1}{3}\)

Answer:

5\(\frac{3}{4}\) + 1\(\frac{1}{3}\) = \(\frac{23}{4}\) + \(\frac{4}{3}\) = \(\frac{69}{12}\)+ \(\frac{16}{12}\) = \(\frac{85}{12}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 4.

3\(\frac{4}{5}\) + 2\(\frac{3}{10}\)

Answer:

3\(\frac{4}{5}\) + 2\(\frac{3}{10}\) = \(\frac{19}{5}\) + \(\frac{23}{10}\) = \(\frac{38}{10}\) + \(\frac{23}{10}\) = \(\frac{61}{10}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

**Problem Solving**

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

Question 5.

1\(\frac{5}{12}\) + 4\(\frac{1}{6}\)

Answer:

1\(\frac{5}{12}\) + 4\(\frac{1}{6}\) = \(\frac{17}{12}\) + \(\frac{21}{6}\) = \(\frac{17}{12}\) + \(\frac{42}{12}\) = \(\frac{59}{12}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take the least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

**Go Math 5th Grade Lesson 5.6 Add and Subtract Mixed Numbers Question 6.**

8\(\frac{1}{2}\) + 6\(\frac{3}{5}\)

Answer:

8\(\frac{1}{2}\) + 6\(\frac{3}{5}\) = \(\frac{17}{2}\) + \(\frac{33}{5}\) = \(\frac{85}{10}\) + \(\frac{66}{10}\) = \(\frac{151}{10}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take the least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 7.

2\(\frac{1}{6}\) + 4\(\frac{5}{9}\)

Answer:

2\(\frac{1}{6}\) + 4\(\frac{5}{9}\) = \(\frac{13}{6}\) + \(\frac{36}{9}\) = \(\frac{39}{18}\) + \(\frac{72}{18}\) = \(\frac{41}{18}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 8.

3\(\frac{5}{8}\) + \(\frac{5}{12}\)

Answer:

3\(\frac{5}{8}\) + \(\frac{5}{12}\) = \(\frac{29}{8}\) + \(\frac{5}{12}\) = \(\frac{87}{24}\) + \(\frac{10}{24}\) = \(\frac{97}{24}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

**Lesson 5.6 Add and Subtract Mixed Numbers Answer Key Question 9.**

3\(\frac{2}{3}\) – 1\(\frac{1}{6}\)

Answer:

3\(\frac{2}{3}\) – 1\(\frac{1}{6}\) = \(\frac{11}{3}\) – \(\frac{7}{6}\) = \(\frac{22}{6}\) – \(\frac{7}{6}\) = \(\frac{15}{6}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take the least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 10.

5\(\frac{6}{7}\) – 1\(\frac{2}{3}\)

Answer:

5\(\frac{6}{7}\) – 1\(\frac{2}{3}\) = \(\frac{41}{7}\) – \(\frac{5}{3}\) = \(\frac{123}{21}\) – \(\frac{35}{21}\) = \(\frac{88}{21}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 11.

2\(\frac{7}{8}\) – \(\frac{1}{2}\)

Answer:

2\(\frac{7}{8}\) – \(\frac{1}{2}\) = \(\frac{23}{8}\) – \(\frac{1}{2}\) = \(\frac{23}{8}\) – \(\frac{4}{8}\) = \(\frac{19}{8}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 12.

4\(\frac{7}{12}\) – 1\(\frac{2}{9}\)

Answer:

4\(\frac{7}{12}\) – 1\(\frac{2}{9}\) = \(\frac{55}{12}\) – \(\frac{7}{5}\) = \(\frac{275}{60}\) – \(\frac{72}{60}\) = \(\frac{203}{60}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

**Go Math 5th Grade Lesson 5.6 Answers Question 13.**

**Communicate** Why do you need to write equivalent fractions with common denominators to add 4\(\frac{5}{6}\) and \(\frac{11}{8}\)? Explain.

Answer: 4\(\frac{5}{6}\) + \(\frac{11}{8}\) = \(\frac{25}{24}\) + \(\frac{11}{24}\) = \(\frac{36}{24}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take the least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

**Problem-Solving**

**Use the table to solve 14-15.**

Question 14.

**H.O.T. Multi-Step** Gavin needs to make 2 batches of Mango paint. Explain how you could find the total amount of paint Gavin mixed.

Answer: \(\frac{70}{6}\)

Explanation:

Gavin needs to make 2 batches of Mango paint

5\(\frac{5}{6}\) red + 5\(\frac{5}{6}\) yellow = \(\frac{70}{6}\) mango

Question 15.

**H.O.T.** Gavin mixes the amount of red from one shade of paint with the amount of yellow from a different shade of paint. 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? Explain your answer.

Answer: The amounts of red and yellow from each shades are used in the mixture is same

Explanation:

Gavin needs to make 2 batches of Mango paint

5\(\frac{5}{6}\) red + 5\(\frac{5}{6}\) yellow = \(\frac{70}{6}\) mango

**Daily Assessment Task**

**Fill in the bubble completely to show your answer.**

Question 16.

Dr. Whether-or-Not collects two hailstones during a storm in California. One hailstone weighs 2\(\frac{3}{8}\) pounds, and the other hailstone weighs 1\(\frac{3}{10}\) pounds. How much heavier is the larger hailstone than the smaller hailstone?

(A) \(\frac{3}{40}\) pounds

(B) 1\(\frac{27}{40}\) pounds

(C) 1\(\frac{3}{40}\) pounds

(D) 3\(\frac{27}{40}\) pounds

Answer: D

Explanation:

Dr. Whether-or-Not collects two hailstones during a storm in California.

One hailstone weighs 2\(\frac{3}{8}\) pounds,

and the other hailstone weighs 1\(\frac{3}{10}\) pounds.

2\(\frac{3}{8}\) + 1\(\frac{3}{10}\) pounds

\(\frac{19}{8}\) + \(\frac{13}{10}\)

\(\frac{294}{80}\)

3\(\frac{27}{40}\) pounds

**Go Math Lesson 5.6 5th Grade Answer Key Question 17.**

Apply Jason is making a fruit salad. He mixes in 3\(\frac{1}{4}\) cups of orange melon and 2\(\frac{2}{3}\) cups of green melon. How many cups of melon does Jason put in the fruit salad?

(A) 5\(\frac{1}{4}\) cups

(B) 5\(\frac{1}{3}\) cups

(C) 5\(\frac{7}{12}\) cups

(D) 5\(\frac{11}{12}\) cups

Answer: A

Explanation:

Apply Jason is making a fruit salad.

He mixes in 3\(\frac{1}{4}\) cups of orange melon and 2\(\frac{2}{3}\) cups of green melon.

3\(\frac{1}{4}\) + 2\(\frac{2}{3}\)

\(\frac{13}{4}\) + \(\frac{8}{3}\)

\(\frac{39}{12}\) + \(\frac{24}{12}\)

\(\frac{63}{12}\)

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

Question 18.

**Multi-Step** Dakota makes a salad dressing by combining 6\(\frac{1}{3}\) fluid ounces of oil and 2\(\frac{3}{8}\) fluid ounces of vinegar in a jar. She then pours 2\(\frac{1}{4}\) fluid ounces of the dressing onto her salad. How much dressing remains in the jar?

(A) 6\(\frac{1}{8}\) fluid ounces

(B) 6\(\frac{3}{8}\) fluid ounces

(C) 6\(\frac{11}{24}\) fluid ounces

(D) 6\(\frac{17}{24}\) fluid ounces

Answer: C

Dakota makes a salad dressing by combining 6\(\frac{1}{3}\) fluid ounces of oil

and 2\(\frac{3}{8}\) fluid ounces of vinegar in a jar.

She then pours 2\(\frac{1}{4}\) fluid ounces of the dressing onto her salad.

6\(\frac{1}{3}\) + 2\(\frac{3}{8}\) – 2\(\frac{1}{4}\)

\(\frac{155}{24}\)

6\(\frac{11}{24}\) fluid ounces

**Texas Test Prep**

Question 19.

Yolanda walked 3\(\frac{6}{10}\) miles. Then she walked 4\(\frac{1}{2}\) more miles. How many miles did Yolanda walk?

(A) 7\(\frac{1}{10}\) miles

(B) 8\(\frac{7}{10}\) miles

(C) 8\(\frac{1}{10}\) miles

(D) 7\(\frac{7}{10}\) miles

Answer: C

Explanation:

Yolanda walked 3\(\frac{6}{10}\) miles.

Then she walked 4\(\frac{1}{2}\) more miles

3\(\frac{6}{10}\) + 4\(\frac{1}{2}\)

\(\frac{72}{20}\) + \(\frac{90}{20}\)

\(\frac{162}{20}\)

### Texas Go Math Grade 5 Lesson 5.6 Homework and Practice Answer Key

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

Question 1.

1\(\frac{1}{4}\) + 2\(\frac{2}{3}\) _____________

Answer:

1\(\frac{1}{4}\) + 2\(\frac{2}{3}\) = \(\frac{5}{4}\) + \(\frac{8}{3}\) = \(\frac{15}{12}\) + \(\frac{32}{12}\) = \(\frac{47}{12}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 2.

3\(\frac{3}{4}\) + 4\(\frac{5}{12}\) _____________

Answer:

3\(\frac{3}{4}\) + 4\(\frac{5}{12}\) = \(\frac{36}{12}\) + \(\frac{53}{12}\) = \(\frac{89}{12}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 3.

1\(\frac{1}{3}\) + 2\(\frac{1}{6}\) _____________

Answer:

1\(\frac{1}{3}\) + 2\(\frac{1}{6}\) = \(\frac{8}{6}\) + \(\frac{13}{6}\) = \(\frac{21}{6}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

**Go Math Lesson 5.6 5th Grade Add and Subtract Mixed Numbers Question 4.**

4\(\frac{1}{2}\) + 3\(\frac{4}{5}\) _____________

Answer:

4\(\frac{1}{2}\) + 3\(\frac{4}{5}\) = \(\frac{45}{10}\) + \(\frac{38}{10}\) = \(\frac{83}{10}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 5.

5\(\frac{5}{6}\) + 4\(\frac{2}{9}\) ____________

Answer:

5\(\frac{5}{6}\) + 4\(\frac{2}{9}\) = \(\frac{35}{6}\) + \(\frac{38}{9}\) = \(\frac{105}{18}\) + \(\frac{76}{18}\) = \(\frac{181}{18}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 6.

7\(\frac{1}{4}\) + 3\(\frac{2}{5}\) ___________

Answer:

7\(\frac{1}{4}\) + 3\(\frac{2}{5}\) = \(\frac{29}{4}\) + \(\frac{17}{5}\) = \(\frac{145}{20}\) + \(\frac{68}{20}\) = \(\frac{213}{20}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 7.

3\(\frac{2}{7}\) + 8\(\frac{1}{3}\) _____________

Answer:

3\(\frac{2}{7}\) + 8\(\frac{1}{3}\) = \(\frac{23}{7}\) + \(\frac{25}{3}\) = \(\frac{69}{21}\) + \(\frac{175}{21}\) = \(\frac{244}{21}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 8.

4\(\frac{3}{7}\) + 3\(\frac{1}{2}\) ____________

Answer:

4\(\frac{3}{7}\) + 3\(\frac{1}{2}\) = \(\frac{31}{7}\) + \(\frac{7}{2}\) = \(\frac{62}{14}\) + \(\frac{49}{14}\) = \(\frac{114}{14}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 9.

2\(\frac{4}{5}\) – 1\(\frac{1}{2}\) ____________

Answer:

2\(\frac{4}{5}\) – 1\(\frac{1}{2}\) = \(\frac{14}{5}\) – \(\frac{3}{2}\) = \(\frac{28}{10}\) – \(\frac{15}{10}\) = \(\frac{13}{10}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 10.

5\(\frac{3}{8}\) – 1\(\frac{1}{4}\) ____________

Answer:

5\(\frac{3}{8}\) – 1\(\frac{1}{4}\) = \(\frac{43}{8}\) – \(\frac{5}{4}\) = \(\frac{43}{8}\) – \(\frac{10}{8}\) = \(\frac{33}{8}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 11.

4\(\frac{1}{3}\) – 3\(\frac{1}{6}\) _____________

Answer:

4\(\frac{1}{3}\) – 3\(\frac{1}{6}\) = \(\frac{13}{3}\) – \(\frac{19}{6}\) = \(\frac{26}{6}\) – \(\frac{19}{6}\) = \(\frac{7}{6}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 12.

6\(\frac{5}{6}\) – 5\(\frac{7}{9}\) _____________

Answer:

6\(\frac{5}{6}\) – 5\(\frac{7}{9}\) = \(\frac{41}{6}\) – \(\frac{53}{9}\) = \(\frac{123}{18}\) – \(\frac{106}{18}\) = \(\frac{17}{18}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

**Go Math Grade 5 Practice and Homework Lesson 5.6 Answer Key Question 13.**

4\(\frac{1}{3}\) – 2\(\frac{1}{4}\) ____________

Answer:

4\(\frac{1}{3}\) – 2\(\frac{1}{4}\) = \(\frac{13}{3}\) – \(\frac{9}{4}\) = \(\frac{52}{12}\) – \(\frac{27}{12}\) = \(\frac{25}{12}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 14.

3\(\frac{1}{4}\) – 1\(\frac{1}{6}\) _____________

Answer:

3\(\frac{1}{4}\) – 1\(\frac{1}{6}\) = \(\frac{13}{4}\) – \(\frac{7}{6}\) = \(\frac{39}{12}\) – \(\frac{14}{12}\) = \(\frac{25}{12}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 15.

6\(\frac{3}{4}\) – 2\(\frac{5}{16}\) _____________

Answer:

6\(\frac{3}{4}\) – 2\(\frac{5}{16}\) = \(\frac{23}{4}\) – \(\frac{37}{16}\)= \(\frac{92}{16}\) – \(\frac{37}{16}\) = \(\frac{55}{16}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 16.

7\(\frac{3}{5}\) – 2\(\frac{1}{4}\) _____________

Answer:

7\(\frac{3}{5}\) – 2\(\frac{1}{4}\) = \(\frac{38}{5}\) – \(\frac{9}{4}\) = \(\frac{152}{20}\) – \(\frac{45}{20}\) = \(\frac{107}{20}\)

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

Question 17.

Use two mixed numbers to write an equation with a sum of 4\(\frac{1}{4}\).

Answer:

Explanation:

Step I: We add the whole numbers, separately. We change the mixed fractions into improper fractions.

Step II: To add fractions, we take least common denominators and change the fractions into like fractions.

Step III: We find the sum of the whole numbers and the fractions in the simplest form.

**Problem Solving**

Question 18.

Lucas says his twin baby brothers have a total weight of 15\(\frac{1}{8}\) pounds. Jackson weighs pounds, and Jeremy weighs 8\(\frac{7}{8}\) pounds. Explain how you can use estimation to tell if the total weight is reasonable.

Answer:

Question 19.

The gas tank in Rebecca’s old car held 14\(\frac{1}{5}\) gallons. The gas tank in Rebecca’s new car holds 18\(\frac{1}{2}\) gallons. How many more gallons will the tank in Rebecca’s new car hold than her old car?

Answer: 4\(\frac{3}{10}\)

Explanation:

18\(\frac{1}{2}\) – 14\(\frac{1}{5}\)

= 4\(\frac{3}{10}\)

**Lesson Check**

**Fill in the bubble completely to show your answer.**

**Use the table for 20-21.**

Four students made paper chains to decorate the community center. The table at the right shows the lengths of the paper chains.

Question 20.

If Ioana attaches her chain to the end of Gabrielle’s chain, what will be the length of the combined chain?

(A) 13\(\frac{3}{4}\) feet

(B) 13\(\frac{1}{4}\) feet

(C) 12\(\frac{1}{4}\) feet

(D) 12\(\frac{1}{2}\) feet

Answer: B

Explanation:

the length of the combined chain is 13\(\frac{1}{4}\) feet

7\(\frac{1}{2}\) feet + 5\(\frac{3}{4}\) feet=

\(\frac{30+23}{4}\) feet

\(\frac{53}{4}\)

Question 21.

How much longer is Oksana’s chain than Gabrielle’s chain?

(A) 15\(\frac{7}{12}\) feet

(B) 14\(\frac{1}{12}\) feet

(C) 4\(\frac{1}{4}\) feet

(D) 4\(\frac{1}{12}\) feet

Answer: D

4\(\frac{1}{12}\) feet is longer than Oksana’s chain than Gabrielle’s chain

Explanation:

9\(\frac{5}{6}\) feet + 5\(\frac{3}{4}\) feet=

\(\frac{118-69}{12}\) feet

\(\frac{49}{12}\)

4\(\frac{1}{12}\)

Question 22.

Mia hiked 2\(\frac{1}{2}\) miles farther than Jacob. Which could be the two distances each person hiked?

(A) Mia: 2\(\frac{1}{2}\) miles; Jacob: 1\(\frac{1}{4}\) miles

(B) Mia: 2\(\frac{1}{2}\) miles; Jacob: 7\(\frac{1}{2}\) miles

(C) Mia: 3\(\frac{2}{5}\) miles; Jacob: 5\(\frac{9}{10}\) miles

(D) Mia: 5\(\frac{9}{10}\) miles; Jacob: 3\(\frac{2}{5}\) miles

Answer: A

Explanation:

2\(\frac{1}{2}\) than jacob

if Mia: 2\(\frac{1}{2}\) miles; Jacob: 1\(\frac{1}{4}\) miles

Question 23.

**Multi-Step** Mr. Carter owned a ranch with 7\(\frac{1}{4}\) acres. Last year, he bought 3\(\frac{1}{5}\) acres of land from his neighbor. Then he sold 2\(\frac{1}{4}\) acres. How many acres does Mr. Carter own now?

(A) 10\(\frac{9}{20}\) acres

(B) 8\(\frac{1}{5}\) acres

(C) 12\(\frac{7}{10}\) acres

(D) 6\(\frac{3}{10}\) acres

Answer: B

Mr. Carter owned a ranch with 7\(\frac{1}{4}\) acres.

Last year, he bought 3\(\frac{1}{5}\) acres of land from his neighbor

Then he sold 2\(\frac{1}{4}\) acres.

7\(\frac{1}{4}\) + 3\(\frac{1}{5}\) – 2\(\frac{1}{4}\)

\(\frac{164}{20}\)

= 8\(\frac{1}{5}\) acres

Question 24.

**Multi-Step** This week, Maddie worked 2\(\frac{1}{2}\) hours on Monday, 2\(\frac{2}{3}\) hours on Tuesday, and 3\(\frac{1}{4}\) hours on Wednesday. How many more hours will Maddie need to work this week to make her goal of 10\(\frac{1}{2}\) hours a week?

(A) 2\(\frac{1}{12}\) hours

(B) 8\(\frac{5}{12}\) hours

(C) 18\(\frac{11}{12}\) hours

(D) 5\(\frac{1}{3}\) hours

Answer: A

Explanation:

This week, Maddie worked 2\(\frac{1}{2}\) hours on Monday,

2\(\frac{2}{3}\) hours on Tuesday,

and 3\(\frac{1}{4}\) hours on Wednesday.

2\(\frac{1}{2}\)+2\(\frac{2}{3}\) + 3\(\frac{1}{4}\) -10\(\frac{1}{2}\)

\(\frac{25}{12}\)

=2\(\frac{1}{12}\) hours