We included **H****MH Into Math Grade 5 Answer Key**** PDF** **Module 7 Lesson 2 Assess Reasonableness of Fraction Sums and Differences**Â to make students experts in learning maths.

## HMH Into Math Grade 5 Module 7 Lesson 2 Answer Key Assess Reasonableness of Fraction Sums and Differences

I Can add and subtract fractions with unlike denominators using a common denominator and assess reasonableness.

**Step It Out**

1. Jaime is building a bird feeder. He connects two metal rods together to make a stand. The blueprint for the project shows the lengths of the rods. What is the total length of the rods?

A. Write an expression to model the situation.

____________________

B. Find a common denominator for the fractions in this expression.

____________________

C. Write equivalent fractions using the common denominator.

____________________

D. Write an expression using fractions with a common denominator. Then find the total length of the rods.

____________________

E. Explain how you know your answer is reasonable.

Answer:

Given,

Jaime is building a bird feeder. He connects two metal rods together to make a stand.

The blueprint for the project shows the lengths of the rods.

\(\frac{1}{6}\) + \(\frac{2}{3}\)

\(\frac{1}{6}\) + \(\frac{4}{6}\) = \(\frac{5}{6}\)

The total length of the rods is \(\frac{5}{6}\) yards.

**Turn and Talk** Jon says you have to rewrite fractions with common denominators before you can estimate. Sarah says you can estimate without finding a common denominator first. Who do you think is correct and why?

**Step It Out**

2. Jaime fastens the bottom of the bird feeder to the pole. He has four boards that are each \(\frac{5}{6}\)-foot long. How much must Jaime cut from each board to make each side of the feeder \(\frac{3}{4}\)-foot long?

A. Write an expression you can use to solve the problem.

B. Write an expression using fractions with a common denominator to model the problem. Then find how much Jaime must cut from each board.

C. Explain how you know your answer is reasonable.

Answer:

\(\frac{5}{6}\) – \(\frac{3}{4}\)

The fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 6 and 4 is 12.

\(\frac{10}{12}\) – \(\frac{9}{12}\) = \(\frac{1}{12}\)

**Turn and Talk** Look at the denominators of the given fractions. Note that neither denominator is a multiple of the other. How does this indicate that both fractions need to be renamed for them to have a common denominator?

**Check Understanding Math Board**

Question 1.

Jaime starts with \(\frac{7}{8}\) ounce of glue. After a project, \(\frac{1}{4}\) ounce of glue is left. Write an expression that can be used to find how much glue Jaime uses. Solve the problem. Show that your answer is reasonable.

Answer:

Given,

Jaime starts with \(\frac{7}{8}\) ounce of glue.

After a project, \(\frac{1}{4}\) ounce of glue is left.

\(\frac{7}{8}\) – \(\frac{1}{4}\)

\(\frac{7}{8}\) – \(\frac{2}{8}\) = \(\frac{5}{8}\) ounce

**Write the expression using fractions with a common denominator. Then find the sum or difference.**

Question 2.

\(\frac{2}{3}\) – \(\frac{1}{5}\) ____________________

Answer:

\(\frac{2}{3}\) – \(\frac{1}{5}\)

The fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 3 and 5 is 15.

\(\frac{10}{15}\) – \(\frac{3}{15}\) = \(\frac{7}{15}\)

Question 3.

\(\frac{1}{6}\) + \(\frac{3}{4}\) ____________________

Answer:

\(\frac{1}{6}\) + \(\frac{3}{4}\)

The fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 6 and 4 is 12.

\(\frac{2}{12}\) + \(\frac{9}{12}\) = \(\frac{11}{12}\)

**On Your Own**

Question 4.

**Critique Reasoning** Kyle is stringing a necklace with beads. He puts black beads on \(\frac{5}{8}\) of the string and white beads on \(\frac{1}{4}\) of the string. Kyle thinks that he will cover \(\frac{6}{12}\) of the string with beads. Is Kyle’s claim reasonable?

Answer:

Given,

Kyle is stringing a necklace with beads. He puts black beads on \(\frac{5}{8}\) of the string and white beads on \(\frac{1}{4}\) of the string.

\(\frac{5}{8}\) + \(\frac{1}{4}\)

LCD of 4 and 8 is 8.

\(\frac{5}{8}\) + \(\frac{2}{8}\) = \(\frac{7}{8}\)

Thus Kyle’s Claim is not reasonable.

Question 5.

**STEM** Precipitation can be in the form of rain, snow, sleet, or hail. In Sarasota, Florida, it rains about \(\frac{2}{3}\) inch on May 22 and about \(\frac{5}{12}\) inch on May 25.

- What expression represents the difference in the amount of rainfall for the two days?
- Write an expression using fractions with a common denominator. Then find the difference.

Answer:

Given,

Florida, it rains about \(\frac{2}{3}\) inch on May 22 and about \(\frac{5}{12}\) inch on May 25.

\(\frac{2}{3}\) – \(\frac{5}{12}\)

LCD of 3 and 12 is 12.

\(\frac{8}{12}\) – \(\frac{5}{12}\) = \(\frac{3}{12}\) = \(\frac{1}{4}\)

**Write the expression using fractions with a common denominator. Then find the sum or difference.**

Question 6.

\(\frac{3}{8}\) + \(\frac{1}{6}\)

Answer:

\(\frac{3}{8}\) + \(\frac{1}{6}\)

The fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 8 and 6 is 24.

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD.

\(\frac{3}{8}\) Ă— \(\frac{3}{3}\) + \(\frac{1}{6}\) Ă— \(\frac{4}{4}\)

\(\frac{9}{24}\) + \(\frac{4}{24}\) = \(\frac{13}{24}\)

Question 7.

\(\frac{3}{4}\) – \(\frac{7}{12}\)

Answer:

\(\frac{3}{4}\) – \(\frac{7}{12}\)

The fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 4 and 12 is 12.

Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal to the LCD.

\(\frac{3}{4}\) Ă— \(\frac{3}{3}\) – \(\frac{7}{12}\) Ă— \(\frac{1}{1}\)

\(\frac{9}{12}\) – \(\frac{7}{12}\) = \(\frac{2}{12}\) = \(\frac{1}{6}\)

Question 8.

\(\frac{1}{6}\) + \(\frac{3}{9}\)

Answer:

\(\frac{1}{6}\) + \(\frac{3}{9}\)

The fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 6 and 9 is 18.

\(\frac{3}{18}\) + \(\frac{6}{18}\) = \(\frac{9}{18}\) = \(\frac{1}{2}\)

Question 9.

\(\frac{7}{9}\) – \(\frac{1}{3}\)

Answer:

\(\frac{7}{9}\) – \(\frac{1}{3}\)

The fractions have, unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 3 and 9 is 9.

\(\frac{7}{9}\) – \(\frac{3}{9}\) = \(\frac{4}{9}\)

Question 10.

Mr. Singhâ€™s laptop memory is \(\frac{9}{10}\) full. After he deletes some files, the memory \(\frac{3}{5}\) is full.

- What faction represents the part of the laptop memory that he deletes? ______

- Is your answer reasonable? How do you know?

____________________

____________________

Answer:

Given,

Mr. Singhâ€™s laptop memory is \(\frac{9}{10}\) full.

After he deletes some files, the memory \(\frac{3}{5}\) is full.

\(\frac{9}{10}\) – \(\frac{3}{5}\)

LCD of 10 and 5 is 10.

\(\frac{9}{10}\) – \(\frac{6}{10}\) = \(\frac{3}{10}\)

The fraction \(\frac{3}{10}\) represents the part of the laptop memory that he deletes.

Question 11.

Tracy checks the digital tablets made at a factory. In one box of tablets, she finds that \(\frac{1}{20}\) have a cracked screen. In the same box, she finds that another \(\frac{1}{5}\) have the wrong software. What fraction of the tablets in the box have either a cracked screen or the wrong software?

Answer:

Given,

Tracy checks the digital tablets made at a factory. In one box of tablets, she finds that \(\frac{1}{20}\) have a cracked screen.

In the same box, she finds that another \(\frac{1}{5}\) has the wrong software.

\(\frac{1}{20}\) + \(\frac{1}{5}\)

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 5 and 20 is 20

\(\frac{1}{20}\) + \(\frac{4}{20}\) = \(\frac{5}{20}\) = \(\frac{1}{4}\)

Question 12.

**Use Structure** On Tuesday, the dance team spends \(\frac{1}{8}\) of the practice time trying on uniforms and \(\frac{1}{6}\) of the time choosing music. They spend the remaining time dancing.

- What fraction of practice time do they spend dancing?
- Explain how you found your answer.

Answer:

Given,

On Tuesday, the dance team spends \(\frac{1}{8}\) of the practice time trying on uniforms and \(\frac{1}{6}\) of the time choosing music.

1 – \(\frac{1}{8}\) = \(\frac{7}{8}\)

\(\frac{7}{8}\) – \(\frac{1}{6}\)

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 8 and 6 is 24.

\(\frac{21}{24}\) – \(\frac{4}{24}\) = \(\frac{17}{24}\)

Thus they spend \(\frac{17}{24}\) of practice time for dancing.

**Find the sum or difference.**

Question 13.

\(\frac{2}{5}\) – \(\frac{1}{10}\)

Answer:

\(\frac{2}{5}\) – \(\frac{1}{10}\)

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 5 and 10 is 10.

\(\frac{4}{10}\) – \(\frac{1}{10}\) = \(\frac{3}{10}\)

Question 14.

\(\frac{3}{4}\) – \(\frac{1}{8}\)

Answer:

\(\frac{3}{4}\) – \(\frac{1}{8}\)

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 4 and 8 is 8.

\(\frac{6}{8}\) – \(\frac{1}{8}\) = \(\frac{5}{8}\)

Question 15.

\(\frac{1}{3}\) + \(\frac{5}{12}\)

Answer:

\(\frac{1}{3}\) + \(\frac{5}{12}\)

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

LCD of 3 and 12 is 12.

\(\frac{4}{12}\) + \(\frac{5}{12}\) = \(\frac{9}{12}\)

Question 16.

\(\frac{1}{6}\) + \(\frac{3}{4}\)

Answer:

\(\frac{1}{6}\) + \(\frac{3}{4}\)

The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.

\(\frac{1}{6}\) + \(\frac{3}{4}\)

LCD of 4 and 6 is 12.

\(\frac{2}{12}\) + \(\frac{9}{12}\) = \(\frac{11}{12}\)

Question 17.

**Attend to Precision** Malcolm completes \(\frac{1}{5}\) of his new video game. After one week, he completes another \(\frac{1}{10}\) of the game. After two weeks, he completes another \(\frac{1}{2}\) of the game. How much of the game does he complete? Model with an expression and find the sum.

Answer:

Given,

Malcolm completes \(\frac{1}{5}\) of his new video game.

After one week, he completes another \(\frac{1}{10}\) of the game.

After two weeks, he completes another \(\frac{1}{2}\) of the game.

\(\frac{1}{5}\) + \(\frac{1}{10}\) + \(\frac{1}{2}\)

LCD of 5, 10, 2 is 10

\(\frac{2}{10}\) + \(\frac{1}{10}\) + \(\frac{5}{10}\) = \(\frac{8}{10}\) = \(\frac{4}{5}\)

Thus he completes \(\frac{4}{5}\) of the game.