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.