We included **HMH Into Math Grade 4 Answer Key**** PDF** **Module 11 Lesson 2 Compare Fractions Using Benchmarks** to make students experts in learning maths.

## HMH Into Math Grade 4 Module 11 Lesson 2 Answer Key Compare Fractions Using Benchmarks

I Can use benchmarks to compare two fractions and record the comparison with the symbols < or >.

**Spark Your Learning
**Abbot and Rowan go to the Climb-a-thon. They both climb ropes that are the same length. Who climbs higher than halfway up the rope?

**Show your Thinking
**

Answer:

Explanation:

Length of rope Abbot go to the Climb-a-thon = \(\frac{5}{8}\)

Length of rope Rowan go to the Climb-a-thon = \(\frac{4}{10}\)

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

\(\frac{4}{10}\) = 0.4

**Turn and Talk** How can your answer to this problem help you compare how high Abbot and Rowan climbed?

Answer:

Abbot climbs more than Rowan.

Explanation:

Length of rope Abbot go to the Climb-a-thon = \(\frac{5}{8}\)

Length of rope Rowan go to the Climb-a-thon = \(\frac{4}{10}\)

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

\(\frac{4}{10}\) = \(\frac{4}{10}\) ÷ \(\frac{2}{2}\) = \(\frac{2}{5}\) = 0.4

**Build Understanding
**1. The owner of a yogurt shop brings 1-gallon buckets of yogurt to the Climb-a-thon. At the end of the day, one bucket is \(\frac{2}{5}\) full and a second bucket is \(\frac{3}{4}\) full. Which bucket is less than \(\frac{1}{2}\) full?

A. What fractions do you need to compare to solve this problem?

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B. Use fraction strips to represent the three fractions. Draw your results.

C. Use the comparisons to the benchmark to compare the two numbers. Write> or <.

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

Use a visual model to justify your answer.

Answer:

Explanation:

Number of gallons one bucket = \(\frac{2}{5}\) = 0.4

Number of gallons second bucket = \(\frac{3}{4}\) = 0.75

Which bucket is less than \(\frac{1}{2}\) full?

\(\frac{1}{2}\) = 0.5 gallons.

\(\frac{2}{5}\) > \(\frac{3}{4}\)

Comparison:

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

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

**Check Understanding Math Board
**Question 1.

A recipe for Berry Bliss yogurt calls for \(\frac{5}{4}\) pints of strawberries and pint of raspberries. Which type of berry is there more of?

Answer:

Number of pints of raspberries are more because they size is comparatively Less than strawberries.

Explanation:

Number of pints of strawberries a recipe for Berry Bliss yogurt calls = \(\frac{5}{4}\)

Number of pints of raspberries a recipe for Berry Bliss yogurt calls = \(\frac{5}{4}\)

**Write > or < for the comparison.
**Question 2.

\(\frac{2}{3}\) \(\frac{5}{12}\)

Answer:

\(\frac{2}{3}\) > \(\frac{5}{12}\)

Explanation:

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

\(\frac{5}{12}\) = 0.42.

Question 3.

\(\frac{13}{10}\) \(\frac{8}{5}\)

Answer:

\(\frac{13}{10}\) < \(\frac{8}{5}\)

Explanation:

\(\frac{13}{10}\) = 1.3

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

Question 4.

1\(\frac{5}{6}\) 1\(\frac{3}{10}\)

Answer:

1\(\frac{5}{6}\) > 1\(\frac{3}{10}\)

Explanation:

1\(\frac{5}{6}\) = (6 + 5) ÷ 6 = \(\frac{11}{6}\) = 1.83.

1\(\frac{3}{10}\) = (10 + 3) ÷ 10 = \(\frac{13}{10}\) = 1.3.

**On Your Own
**Question 5.

How do \(\frac{5}{12}\) and \(\frac{3}{5}\) compare? Use comparison symbols to explain your thinking.

Answer:

\(\frac{5}{12}\) < \(\frac{3}{5}\)

Explanation:

1 way:

\(\frac{5}{12}\) = 0.42.

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

\(\frac{5}{12}\) < \(\frac{3}{5}\)

2 way: Equating Denominators

\(\frac{5}{12}\)

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

Multiples of 12: 12,24,36,48,60,72,84,96,108,120.

Multiples of 5: 5,10,15,20,25,30,35,40,45,50,55,60.

Common multiple of 12 n 5 = 60.

\(\frac{5}{12}\) = \(\frac{5}{12}\) × \(\frac{5}{5}\) = \(\frac{25}{60}\)

\(\frac{3}{5}\) = \(\frac{3}{5}\) × \(\frac{12}{12}\) = \(\frac{36}{60}\)

\(\frac{25}{60}\) < \(\frac{36}{60}\)

3 way: Equating Numerators.

\(\frac{5}{12}\)

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

Multiples of 3: 3,6,9,12,15,18,21,24,27,30.

Multiples of 5: 5,10,15,20,25,30,35,40,45,50,55,60.

Common multiple of 3 n 5 = 15.

\(\frac{5}{12}\) = \(\frac{5}{12}\) × \(\frac{3}{3}\) = \(\frac{15}{36}\)

\(\frac{3}{5}\) = \(\frac{3}{5}\) × \(\frac{5}{5}\) = \(\frac{15}{25}\)

\(\frac{15}{36}\) < \(\frac{15}{25}\)

**Write > or < for the comparison.
**Question 6.

\(\frac{11}{12}\) \(\frac{6}{5}\)

Answer:

\(\frac{11}{12}\) < \(\frac{6}{5}\)

Explanation:

\(\frac{11}{12}\) = 0.92.

\(\frac{6}{5}\) = 1.2.

Question 7.

\(\frac{5}{8}\) \(\frac{2}{6}\)

Answer:

\(\frac{5}{8}\) > \(\frac{2}{6}\)

Explanation:

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

\(\frac{2}{6}\) = 0.33.

Question 8.

\(\frac{11}{6}\) \(\frac{12}{10}\)

Answer:

\(\frac{11}{6}\) > \(\frac{12}{10}\)

Explanation:

\(\frac{11}{6}\) = 1.83.

\(\frac{12}{10}\) = 1.2.

Question 9.

**Use Structure** Lecia times herself climbing the wall. Her first climb takes \(\frac{5}{12}\) minute. Her second climb takes \(\frac{6}{10}\) minute. Which climb takes less time?

- Which benchmark will you use to compare the two times? Justify your choice.

____________________ - Complete the comparison. \(\frac{5}{12}\) \(\frac{6}{10}\)

The climb that takes less time is ______ minute.

Answer:

The climb that takes less time is \(\frac{5}{12}\) minute.Explanation:

Number of minutes her first climb = \(\frac{5}{12}\) = 0.42.

Number of minutes her second climb = \(\frac{6}{10}\) = 0.6.

\(\frac{5}{12}\) < \(\frac{6}{10}\)

**I’m in a Learning Mindset!
**What things should I keep in mind when comparing fractions?

___________________________________

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Answer:

Comparing fractions means determining the larger and the smaller fraction between any two or more fractions. Since fractions are made up of two parts – a numerator and a denominator, they are compared using a certain set of rules.

Explanation:

Comparing fractions means determining the larger and the smaller fraction between any two or more fractions. Since fractions are made up of two parts – a numerator and a denominator, they are compared using a certain set of rules.

Comparing fractions involves a set of rules related to the numerator and the denominator. When any two fractions are compared, we get to know the greater and the smaller fraction. We need to compare fractions in our everyday lives.