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

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.

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?  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?
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?
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?
$$\frac{1}{5}$$  > $$\frac{1}{8}$$ 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.
$$\frac{3}{4}$$ $$\frac{2}{3}$$
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? 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.  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.  Explanation:
$$\frac{2}{3}$$ = 0.67
$$\frac{7}{12}$$ = 0.58
$$\frac{2}{3}$$ >  $$\frac{2}{3}$$

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? _____

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. 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.  Explanation:
$$\frac{7}{10}$$ = 0.7.
$$\frac{6}{8}$$ = 0.75.

Question 7  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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