We included **HMH Into Math Grade 4 Answer Key**** PDF** **Module 11 Lesson 1 Compare Fractions Using Visual Models** to make students experts in learning maths.

## HMH Into Math Grade 4 Module 11 Lesson 1 Answer Key Compare Fractions Using Visual Models

I Can use visual models to compare two fractions with different numerators and denominators.

**Spark Your Learning
**Liz and Alvin have the same type of go-kart in different colors. The fuel tank in Liz’s go-kart is \(\frac{3}{5}\) full. The fuel tank in Alvin’s go-kart is \(\frac{1}{3}\) full. Whose go-kart has more fuel?

**Show your Thinking**

Answer:

Liz’s go-kart has more fuel.

Explanation:

The fuel tank in Liz’s go-kart = \(\frac{3}{5}\) full.

The fuel tank in Alvin’s go-kart = \(\frac{1}{3}\) full.

\(\frac{3}{5}\) full = 1\(\frac{3}{5}\) = (5 + 3) ÷ 5

= \(\frac{8}{5}\) = 1.6.

\(\frac{1}{3}\) full = 1\(\frac{1}{3}\) = (3 + 1) ÷ 3

= \(\frac{4}{3}\) = 1.33.

**Turn and Talk** Why is it important that the size of the fuel tanks in the go-karts is the same?

Answer:

It is important that the size of the fuel tanks in the go-karts is the same because the maximum size of a fuel tank is limited by the weight allowed and the space available on a vehicle.

Explanation:

The maximum size of a fuel tank is limited by the weight allowed and the space available on a vehicle.

**Build Understanding
**1. There are two go-kart tracks. Which is the shorter track?

Use a fraction model to represent the length of each track. Then draw visual models for your representations.

A. How does your fraction model represent \(\frac{4}{5}\) mile?

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B. How does your fraction model represent \(\frac{7}{8}\) mile?

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C. How can you use your fraction models to compare the lengths of the tracks?

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D. Which track is shorter?

Answer:

Track A is shorter.

Explanation:

Length of track A = \(\frac{4}{5}\) mile = 0.8 mile.

Length of track B = \(\frac{7}{8}\) mile = 0.875 mile.

**Turn and Talk** The fractions \(\frac{4}{5}\) and \(\frac{7}{8}\) each have one piece missing from the whole. How can you use the sizes of the missing pieces to compare the two fractions?

Answer:

\(\frac{1}{5}\) > \(\frac{1}{8}\) because numerators are same, denominators are consider. lesser number becomes greater than the bigger number.

Explanation:

fractions \(\frac{4}{5}\) and \(\frac{7}{8}\)

Missing pieces:

\(\frac{4}{5}\) + ?? = 1

=> ?? = 1 – \(\frac{4}{5}\)

=> ?? = (5 -4) ÷ 5

=> ?? = \(\frac{1}{5}\)

\(\frac{7}{8}\) + ?? = 1

=> ?? = 1 – \(\frac{7}{8}\)

=> ?? = (8 – 7) ÷ 8

=> ?? = \(\frac{1}{8}\)

2. It takes Jack \(\frac{3}{4}\) hour to fix a tire. It takes Renee \(\frac{2}{3}\) hour to fix a tire. Who takes a longer time to fix a tire?

A. Complete the visual model to show the time for each person.

B. How do the lengths of the visual models for \(\frac{3}{4}\) hour and \(\frac{2}{3}\) hour compare? Who takes a longer time?

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C. Use the symbols < or > to write a statement comparing the two fractions.

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

Answer:

Renee takes a longer time.

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

Explanation:

Number of hours Jack takes to a tire = \(\frac{3}{4}\) = 0.75.

Number of hours Renee takes to a tire = \(\frac{2}{3}\) = 0.67.

**Check Understanding Math Board
**Question 1.

Emma fills \(\frac{3}{5}\) of a jug with water. She fills \(\frac{4}{6}\) of a same-sized jug with sports drink. Does Emma pour more water or more sports drink?

Complete the visual models to solve. Justify your answer.

Answer:

Emma pours more sports drink than water.

Explanation:

Amount of water Emma fills in a jug = \(\frac{3}{5}\)

Amount of sports drink Emma fills in a jug = \(\frac{4}{6}\)

\(\frac{4}{6}\) = \(\frac{4}{6}\) ÷ \(\frac{2}{2}\) = \(\frac{2}{3}\)

\(\frac{3}{5}\) = 0.6

\(\frac{4}{6}\) = 0.67.

\(\frac{3}{5}\) < \(\frac{4}{6}\)

**Complete the visual model to show each fraction. Then write < or > to compare.
**Question 2.

Answer:

Explanation:

\(\frac{3}{8}\) = 0.375.

\(\frac{2}{4}\) = \(\frac{2}{4}\) ÷ \(\frac{2}{2}\) = \(\frac{1}{2}\) = 0.5.

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

Question 3.

Answer:

Explanation:

\(\frac{2}{3}\) = 0.67

\(\frac{7}{12}\) = 0.58

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

**On Your Own
**Question 4.

Use Tools Marc eats \(\frac{5}{8}\) of a granola bar. Harold eats \(\frac{4}{6}\) of the same-sized granola bar.

- Use fraction strips to show the amount each person eats. Draw the fraction strips used for each person.

- Who eats less of his granola bar? _____

Answer:

Marc eats less of his granola bar.

Explanation:

Amount of a granola bar Marc eats = \(\frac{5}{8}\)

Amount of a granola bar Harold eats = \(\frac{4}{6}\)

\(\frac{4}{6}\) = \(\frac{4}{6}\) ÷ \(\frac{2}{2}\) = \(\frac{2}{3}\)

\(\frac{5}{8}\) = 0.625.

\(\frac{4}{6}\) = 0.67

\(\frac{5}{8}\) < \(\frac{4}{6}\)

Question 5.

**Reason** Quinn and Kelly are painting a wall. Quinn paints \(\frac{1}{2}\) of the wall. Kelly paints less than Quinn.

- Draw a visual model to show the part of the wall that Kelly could paint. Write the fraction it shows.
- Explain how you know your answer is correct.

Answer:

Length of the wall Kelly paints = \(\frac{1}{2}\) – x => 0 to 0.49.

Explanation:

Length of the wall Quinn paints = \(\frac{1}{2}\) = 0.5.

Length of the wall Kelly paints be x.

=> Length of the wall Kelly paints = \(\frac{1}{2}\) – x.

=> 0 to 0.49.

**Complete the visual model to show each fraction. Then write < or > to compare.
**Question 6.

Answer:

Explanation:

\(\frac{7}{10}\) = 0.7.

\(\frac{6}{8}\) = 0.75.

Question 7

Answer:

Explanation:

\(\frac{5}{6}\) = 0.83.

\(\frac{4}{5}\) = 0.8.

**I’m in a Learning Mindset
**Which strategy did you prefer for comparing fractions—using visual models or using concrete models? Why?

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Answer:

I would prefer for visual models for comparing fractions because they are easier to understand and to solve the problem in no time than concrete models.

Explanation:

I would prefer for visual models for comparing fractions because they are easier to understand and to solve the problem in no time.