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## Texas Go Math Grade 4 Lesson 4.1 Answer Key Compare Fractions Using Benchmarks

**Essential Question**

How can you use benchmarks to compare fractions?

Answer:

A benchmark is a reference number that can be used to compare two fractions. If one fraction is less than the benchmark and a second fraction is greater, the first fraction is less than the second.

**Unlock the Problem**

Zach made a popcorn snack. He mixed \(\frac{5}{8}\) gallon of popcorn with \(\frac{1}{2}\) gallon of dried apple rings. Did he use more dried apple rings or more popcorn?

Answer:

Zach used more dried apple rings.

**Activity** Compare \(\frac{5}{8}\) and \(\frac{1}{2}\).

Materials: fraction strips

Use traction strips to compare \(\frac{5}{8}\) and \(\frac{1}{2}\). Record on the model below.

\(\frac{5}{8}\) ___________ \(\frac{1}{2}\)

So, Zach used more ______________ .

Answer:

\(\frac{5}{8}\) greater than \(\frac{1}{2}\)

So, Zach used more pop corn.

Explanation:

**Math Talk**

Mathematical Processes

Explain how the number of eighth-size parts in \(\frac{5}{8}\) is related to the number of eighth-size parts you need to make \(\frac{1}{2}\).

Answer:

Explanation:

\(\frac{4}{8}\) = \(\frac{1}{2}\)

4 eighth size parts is equal to \(\frac{1}{2}\)

**Benchmarks** A benchmark is a known size or amount that helps you understand a different size or amount. You can use \(\frac{1}{2}\) as a benchmark to help you compare fractions.

Question 1.

How many eighths are equivalent to \(\frac{1}{2}\)?

Answer:

4 eighth size parts is equal to \(\frac{1}{2}\)

Question 2.

How can you compare \(\frac{5}{8}\) and \(\frac{1}{2}\) without using a model?

Answer:

By using the bench mark.

Explanation:

By using the bench marks and compare the lengths with \(\frac{1}{2}\).

The shaded part is more than \(\frac{1}{2}\).

**Example** Use benchmarks to compare fractions.

A family hiked the same mountain trail. Evie and her father hiked \(\frac{5}{12}\) of the trail before they stopped for lunch. Jill and her mother hiked \(\frac{9}{10}\) of the trail before they stopped for lunch. Who hiked farther before lunch?

Answer:

Compare \(\frac{5}{12}\) and \(\frac{9}{10}\) to the benchmark \(\frac{1}{2}\).

Answer:

Step 1 Compare \(\frac{5}{12}\) to \(\frac{1}{2}\).

Think: Shade \(\frac{5}{12}\). \(\frac{5}{12}\) ___________ \(\frac{1}{2}\).

Answer:

Explanation:

Shaded \(\frac{5}{12}\). \(\frac{5}{12}\) lesser than \(\frac{1}{2}\).

Step 2 Compare \(\frac{9}{10}\) to \(\frac{1}{2}\).

Think: Shade \(\frac{9}{10}\). \(\frac{9}{10}\) ___________ \(\frac{1}{2}\).

Answer:

Explanation:

Shaded \(\frac{9}{10}\). \(\frac{9}{10}\) is greater than \(\frac{1}{2}\).

Since \(\frac{5}{12}\) is _____________ than \(\frac{1}{2}\) and is \(\frac{9}{10}\) than \(\frac{1}{2}\), you know that \(\frac{5}{12}\) ___________ \(\frac{9}{10}\).

So, _____________ hiked farther before lunch.

Answer:

Since \(\frac{5}{12}\) is lesser than \(\frac{1}{2}\) and \(\frac{9}{10}\) is greater than \(\frac{1}{2}\), you know that \(\frac{5}{12}\) lesser than \(\frac{9}{10}\).

So, Jill and her mother hiked farther before lunch.

**Share and show**

Question 1.

Compare \(\frac{2}{5}\) and \(\frac{1}{8}\). Write < or >.

\(\frac{2}{5}\) ______________ \(\frac{1}{8}\)

Answer:

Explanation:

\(\frac{2}{5}\) greater than \(\frac{1}{8}\)

Shaded part represent the area covered

**Compare. Write < or >.**

Question 2.

\(\frac{1}{2}\) ______________ \(\frac{4}{6}\)

Answer:

Explanation:

\(\frac{1}{2}\) is greater than \(\frac{4}{6}\)

The shaded part is more than \(\frac{1}{2}\)

Question 3.

\(\frac{3}{10}\) ______________ \(\frac{1}{2}\)

Answer:

Explanation:

\(\frac{3}{10}\) is lesser than \(\frac{1}{2}\)

The shaded part is less than \(\frac{1}{2}\)

Question 4.

\(\frac{1}{2}\) ______________ \(\frac{4}{8}\)

Answer:

Explanation:

\(\frac{1}{2}\) is equal to \(\frac{4}{8}\)

Question 5.

\(\frac{5}{8}\) ______________ \(\frac{2}{5}\)

Answer:

Explanation:

\(\frac{5}{8}\) is greater than \(\frac{2}{5}\)

**H.O.T.** Algebra Find a numerator that makes the statement true.

Question 6.

\(\frac{2}{4}\) < \(\frac{}{6}\)

Answer:

\(\frac{2}{4}\) < \(\frac{5}{6}\)

Explanation:

\(\frac{2}{4}\) is equal to \(\frac{1}{2}\) and \(\frac{5}{6}\) is greater than \(\frac{1}{2}\)

Question 7.

\(\frac{8}{10}\) < \(\frac{}{8}\)

Answer:

\(\frac{8}{10}\) < \(\frac{8}{8}\)

Explanation:

\(\frac{8}{10}\) is greater than \(\frac{1}{2}\) and \(\frac{8}{8}\) is equal to 1 so greater than \(\frac{8}{10}\)

Question 8.

\(\frac{10}{12}\) < \(\frac{}{4}\)

Answer:

\(\frac{10}{12}\) < \(\frac{4}{4}\)

Explanation:

\(\frac{10}{12}\) is greater than \(\frac{1}{2}\) and \(\frac{4}{4}\) is equal to 1 so greater than \(\frac{10}{12}\)

Question 9.

\(\frac{2}{5}\) < \(\frac{}{10}\)

Answer:

\(\frac{2}{5}\) < \(\frac{6}{10}\)

Explanation:

\(\frac{8}{10}\) is greater than \(\frac{1}{2}\) and \(\frac{8}{8}\) is equal to so greater than \(\frac{8}{10}\)

Question 10.

When two fractions are between 0 and \(\frac{1}{2}\) how do you know which fraction is greater? Explain.

Answer:

The lesser fraction is less than \(\frac{1}{2}\)

Explanation:

The greater fraction is more than \(\frac{1}{2}\) or equal to 1

**Problem Solving**

Question 11.

A group of students ate \(\frac{5}{12}\) of a large pepperoni pizza and \(\frac{8}{10}\) of a large cheese pizza. Did they eat more pepperoni pizza or cheese pizza?

Answer:

They eat more cheese pizza

Explanation:

\(\frac{8}{10}\) is greater than \(\frac{5}{12}\) compared with \(\frac{1}{2}\)

Question 12.

H.O.T. Saundra ran \(\frac{7}{12}\) of a mile. Lamar ran \(\frac{3}{4}\) of a mile. Who ran farther? Explain.

Answer:

Lamar ran farther than Saundra

Explanation:

\(\frac{3}{4}\) is greater than \(\frac{7}{12}\)

Question 13.

H.O.T. What’s the Question? Selena ran farther than Manny.

Answer:

Salena ran \(\frac{8}{10}\) and Manny ran \(\frac{4}{10}\)

Explanation:

The statement says that Selena ran more than Manny

\(\frac{8}{10}\) and \(\frac{4}{10}\) both the equations are compared with \(\frac{1}{2}\)

Question 14.

Mary made a small pan of ziti and a small pan of lasagna. She cut the ziti into 8 equal parts and the lasagna into 9 equal parts. Her family ate \(\frac{2}{3}\) of the lasagna. If her family ate more lasagna than ziti, what fraction of the ziti could have been eaten?

Answer:

\(\frac{2}{3}\) is the simplest form for \(\frac{6}{9}\)

so, they eat \(\frac{6}{9}\) of lasagna

Explanation:

They could have eaten \(\frac{3}{8}\)

\(\frac{6}{9}\) is greater than \(\frac{1}{2}\) and \(\frac{3}{8}\) is lesser than \(\frac{1}{2}\)

**Daily Assessment Task**

Fill in the bubble completely to show your answer.

Question 15.

Use Diagrams Some monkeys live high up in trees. Two monkeys are climbing a tree. One monkey climbed up \(\frac{5}{6}\) of the tree. The other monkey climbed up \(\frac{7}{8}\) of the tree. Which statement about \(\frac{5}{6}\) and \(\frac{7}{8}\) is true?

(A) \(\frac{5}{6}\) > \(\frac{7}{8}\)

(B) \(\frac{7}{8}\) < \(\frac{5}{6}\)

(C) \(\frac{5}{6}\) < \(\frac{7}{8}\)

(D) \(\frac{5}{6}\) = \(\frac{7}{8}\)

Answer: D

Explanation:

\(\frac{5}{6}\) = \(\frac{7}{8}\) is the statement true

because their shaded parts are equal

Question 16.

Maggie did \(\frac{5}{12}\) of her homework before dinner. Her brother did \(\frac{4}{10}\) of his homework. Which statement is true about the fractions \(\frac{5}{12}\) and \(\frac{4}{10}\)?

(A) \(\frac{5}{12}\) < \(\frac{4}{10}\)

(B) \(\frac{4}{10}\) = \(\frac{1}{2}\)

(C) \(\frac{5}{12}\) > \(\frac{4}{10}\)

(D) \(\frac{5}{12}\) > \(\frac{1}{2}\)

Answer: C

Explanation:

\(\frac{5}{12}\) > \(\frac{4}{10}\) is the statement true

Question 17.

Multi-Step If you know that \(\frac{2}{6}\) < \(\frac{1}{2}\) and \(\frac{3}{4}\) > \(\frac{1}{2}\), what do you know

(A) \(\frac{3}{4}\) = \(\frac{1}{2}\)

(B) \(\frac{2}{6}\) > \(\frac{3}{4}\)

(C) \(\frac{2}{6}\) > \(\frac{1}{2}\)

(D) \(\frac{2}{6}\) < \(\frac{3}{4}\)

Answer: D

Explanation:

\(\frac{2}{6}\) < \(\frac{3}{4}\) is the statement

Both the fractions are compared with \(\frac{1}{2}\)

**TEXAS Test Prep**

Question 18.

Todd is using the benchmark \(\frac{1}{2}\) to compare fractions. Which statement is NOT correct?

(A) \(\frac{5}{6}\) < \(\frac{1}{2}\)

(B) \(\frac{3}{6}\) = \(\frac{1}{2}\)

(C) \(\frac{5}{6}\) > \(\frac{1}{2}\)

(D) \(\frac{5}{6}\) ≠ \(\frac{1}{2}\)

Answer: A

Explanation:

\(\frac{5}{6}\) < \(\frac{1}{2}\) is the statement which is not true

### Texas Go Math Grade 4 Lesson 4.1 Homework and Practice Answer Key

**Compare Fractions Using Benchmarks**

Question 1.

How many sixths are equivalent to \(\frac{1}{2}\)?

Answer:

Three sixths are equal to \(\frac{1}{2}\)

Explanation:

\(\frac{3}{6}\) = \(\frac{1}{2}\) we have to do the simplest form.

Question 2.

How can you compare \(\frac{7}{10}\) and \(\frac{1}{2}\) without using a model?

Answer:

By doing the simplest form

five tenths are to \(\frac{1}{2}\)

Explanation:

so we can easily compare by simplest form.

**Compare. Write < or >.**

Question 3.

\(\frac{8}{10}\) ___________ \(\frac{3}{8}\)

Answer:

\(\frac{8}{10}\) > \(\frac{3}{8}\)

Explanation:

Both the fractions are compared with \(\frac{1}{2}\)

Question 4.

latex]\frac{1}{3}[/latex] _____________ \(\frac{7}{12}\)

[Answer:

latex]\frac{1}{3}[/latex] < \(\frac{7}{12}\)

Explanation:

Both the fractions are compared with \(\frac{1}{2}\)

Question 5.

\(\frac{2}{6}\) _____________ \(\frac{7}{8}\)

Answer:

\(\frac{2}{6}\) < \(\frac{7}{8}\)

Explanation:

Both the fractions are compared with \(\frac{1}{2}\)

Question 6.

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

Answer:

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

Explanation:

Both the fractions are compared with \(\frac{1}{2}\)

Question 7.

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

Answer:

\(\frac{6}{6}\) > \(\frac{1}{3}\)

Explanation:

Both the fractions are compared with \(\frac{1}{2}\)

Question 8.

\(}[/\frac{4}{5latex] _____________ [latex]\frac{1}{6}\)

Answer:

\(}[/\frac{4}{5latex] > [latex]\frac{1}{6}[/latexExplanation:

Both the fractions are compared with [latex]\frac{1}{2}\)

**Find a numerator that makes the statement true.**

Question 9.

\(\frac{2}{4}\) > \(\frac{}{8}\)

Answer:

\(\frac{2}{4}\) > \(\frac{3}{8}\)

Explanation:

Both the fractions are compared with \(\frac{1}{2}\)

Question 10.

\(\frac{5}{10}\) > \(\frac{}{8}\)

Answer:

\(\frac{5}{10}\) > \(\frac{3}{8}\)

Explanation:

Both the fractions are compared with \(\frac{1}{2}\)

Question 11.

\(\frac{3}{6}\) > \(\frac{}{12}\)

Answer:

\(\frac{3}{6}\) > \(\frac{1}{12}\)

Explanation:

Both the fractions are compared with \(\frac{1}{2}\)

Question 12

\(\frac{2}{8}\) > \(\frac{}{10}\)

Answer:

\(\frac{2}{8}\) > \(\frac{1}{10}\)

Explanation:

Both the fractions are compared with \(\frac{1}{2}\)

**Problem Solving**

Question 13.

Leticia read \(\frac{4}{5}\) other book and Grace read \(\frac{6}{10}\) of her book. Who read more of her book, Leticia or Grace? Explain.

Answer:

Leticia read more

Explanation:

Both the fractions are compared with \(\frac{1}{2}\)

\(\frac{6}{10}\) is made as simplest form of \(\frac{3}{5}\)

\(\frac{3}{5}\) and \(\frac{4}{5}\) are compared so \(\frac{6}{10}\) is lesser and \(\frac{4}{5}\) is greater

Question 14.

Kyle made brownies and a cake. He cut the brownies into 6 equal parts and the cake into 8 equal parts. His family ate \(\frac{3}{4}\) of the cake. If his family ate more cake than brownies, what fraction of the brownies could have been eaten?

Answer:

\(\frac{3}{6}\)

Explanation:

\(\frac{3}{6}\) is equal to \(\frac{1}{2}\)

and \(\frac{3}{4}\) is greater than \(\frac{1}{2}\)

**Lesson Check**

Fill in the bubble completely to show your answer.

Question 15.

Which symbol completes the following statement?

\(\frac{5}{8}\) __________ \(\frac{9}{10}\)

(A) =

(B) ≠

(C) <

(D) >

Answer: C

Explanation:

\(\frac{5}{8}\) < \(\frac{9}{10}\)

lesser than symbol is used

Question 16.

Garrett is using the benchmark \(\frac{1}{2}\) to compare fractions. Which statement is NOT true?

(A) \(\frac{4}{8}\) = \(\frac{1}{2}\)

(B) \(\frac{3}{8}\) ≠ \(\frac{1}{2}\)

(C) \(\frac{3}{8}\) < \(\frac{1}{2}\)

(D) \(\frac{3}{8}\) > \(\frac{1}{2}\)

Answer: D

Explanation:

\(\frac{3}{8}\) > \(\frac{1}{2}\) is not correct statement.

Question 17.

Rob’s paper route is \(\frac{8}{10}\) mile long. Lin’s route is \(\frac{3}{4}\) mile long. What is true about \(\frac{8}{10}\) and \(\frac{3}{4}\)?

(A) \(\frac{3}{4}\) > \(\frac{8}{10}\)

(B) \(\frac{8}{10}\) < \(\frac{3}{4}\)

(C) \(\frac{8}{10}\) > \(\frac{3}{4}\)

(D) \(\frac{8}{10}\) = \(\frac{3}{4}\)

Answer: C

Explanation:

\(\frac{8}{10}\) > \(\frac{3}{4}\) is the statement true about \(\frac{8}{10}\) and \(\frac{3}{4}\)

Question 18.

Tia compares \(\frac{11}{12}\) and \(\frac{2}{3}\). Which statement

is true?

(A) \(\frac{2}{3}\) = \(\frac{11}{12}\)

(B) \(\frac{2}{3}\) > \(\frac{11}{12}\)

(C) \(\frac{11}{12}\) = \(\frac{2}{3}\)

(D) \(\frac{2}{3}\) < \(\frac{11}{12}\)

Answer: D

Explanation:

\(\frac{2}{3}\) < \(\frac{11}{12}\) is true about the statement of \(\frac{11}{12}\) and \(\frac{2}{3}\)

Question 19.

Multi-Step Sandra is making crafts from leftover ribbons. She needs a ribbon longer than \(\frac{2}{3}\) yard to make a bow. Which length of ribbon could she use for the bow?

(A) \(\frac{3}{4}\) yard

(B) \(\frac{2}{6}\) yard

(C) \(\frac{1}{5}\) yard

(D) \(\frac{4}{7}\) yard

Answer: A

Explanation:

\(\frac{3}{4}\) yard of ribbon she use for the bow

Question 20.

Multi-Step Jessie has several bottles of used paint. He has three bottles of blue paint. The first bottle is \(\frac{1}{8}\) full, the second bottle is \(\frac{1}{4}\) full, and the third bottle \(\frac{1}{4}\) is full He has one bottle of yellow paint that is \(\frac{1}{2}\) full. Which of the following correctly compares the blue paint to the yellow paint?

(A) \(\frac{3}{8}\) = \(\frac{1}{2}\)

(B) \(\frac{5}{8}\) > \(\frac{1}{2}\)

(C) \(\frac{3}{8}\) > \(\frac{1}{2}\)

(D) \(\frac{3}{8}\) < \(\frac{1}{2}\)

Answer: B

Explanation:

\(\frac{5}{8}\) > \(\frac{1}{2}\)

we make the unlike denominator to like denominators

and the added the numerators

and compared with \(\frac{1}{2}\)