We included **HMH Into Math Grade 4 Answer Key PDF** **Module 15 Lesson 2 Rename Fractions and Mixed Numbers **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 15 Lesson 2 Answer Key Rename Fractions and Mixed Numbers

I Can rename mixed numbers as a sum of fractions with like denominators.

**Spark Your Learning**

Monique runs around a \(\frac{1}{4}\)-mile track 9 times. How many whole miles and how many quarter miles does Monique run?

Use a visual representation and write an equation modeling the problem.

Answer:

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

2 whole numbers and 1 quarter mile

Explanation:

Monique runs around a \(\frac{1}{4}\)-mile track 9 times

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

Total miles Monique run = \(\frac{9}{4}\)

= 2 \(\frac{1}{4}\)

**Turn and Talk** How would your fraction model and answer change if she ran 9 laps on a track that was a \(\frac{1}{8}\)-mile track?

Answer:

9 \(\frac{1}{8}\)

Explanation:

\(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) + \(\frac{1}{8}\) = \(\frac{72}{8}\) = 9 \(\frac{1}{8}\)

**Build Understanding**

Question 1.

Chad runs around the quarter-mile track for 1\(\frac{1}{4}\) miles. How many laps does Chad run?

How can you use the mixed number 1\(\frac{1}{4}\) to help you solve this problem?

Connect to Vocabulary

A mixed number is a number represented by a whole number and a fraction. A mixed number can be renamed as a fraction greater than 1.

Use a visual representation to help you solve the problem and then write an equation to model the problem.

Answer:

Explanation:

1 whole = 4 quarters

So, there is one whole numbers and one fourth of whole number.

= 1\(\frac{1}{4}\)

A. How did you decide how many sections to divide the whole into?

Answer:

4 section

Explanation:

1 whole = 4 quarters

So, one whole is divided into 4 sections.

B. How did you know how many parts to shade?

Answer:

5 parts

Explanation:

The quarter-mile track for 1\(\frac{1}{4}\) miles

So, total 5 laps and 5 parts

4 x \(\frac{1}{4}\) + \(\frac{1}{4}\) =1 \(\frac{1}{4}\)

C. How is your answer represented in your visual model?

Chad runs around the track _________ times.

Answer:

Chad runs around the track 5 times.

Explanation:

The quarter-mile track for 1\(\frac{1}{4}\) miles

So, total 5 laps and 5 parts

**Step It Out**

Question 2.

Puja ran around the \(\frac{1}{4}\)-mile track 15 times. Written as a mixed number, how many miles did Puja run?

A. Write a fraction greater than 1 to represent the number of miles Puja ran.

Answer:

\(\frac{15}{4}\)

Explanation:

Puja ran around the \(\frac{1}{4}\)-mile track 15 times.

As a mixed number we write = 15\(\frac{1}{4}\)

As a fraction = \(\frac{15}{4}\)

So, fraction is greater than 1 to represent the number of miles Puja ran.

B. What fraction with a denominator of 4 is equal to 1 whole?

Answer: 4

\(\frac{4}{4}\) = 1

Explanation:

1 whole = 4 quarters

So, 4 quarters with a denominator of 4 is equal to 1 whole.

C. Find the number of groups of \(\frac{4}{4}\) in \(\frac{15}{4}\). Determine how many fourths will be left over.

Answer:

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

Explanation:

\(\frac{4}{4}\) in \(\frac{15}{4}\) = 3 \(\frac{3}{4}\)

D. Write an equation modeling your answer to C.

Answer:

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

Explanation:

\(\frac{4}{4}\) in \(\frac{15}{4}\) = 3 \(\frac{3}{4}\)

E. Find how many whole miles Puja ran and what fraction of a mile is left. Then, write the number of miles as a mixed number.

Answer: 3

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

Explanation:

\(\frac{4}{4}\) in \(\frac{15}{4}\) = 3 \(\frac{3}{4}\)

**Turn and Talk** What rule could you use to describe the relationship between the numerator and denominator to determine the number of wholes there are in a fraction greater than 1?

Answer:

A fraction has a numerator that is greater than or equal to the denominator,

then the fraction is an improper fraction.

An improper fraction is always 1 or greater than 1.

And, finally, a mixed number is a combination of a whole number and a proper fraction.

**Check Understanding**

Question 1.

Susan has 11 pieces of pizza. If each piece is \(\frac{1}{8}\) of a pizza, what mixed number describes how much pizza Susan has?

Answer:

11\(\frac{1}{8}\)

Explanation:

Susan has 11 pieces of pizza.

If each piece is \(\frac{1}{8}\) of a pizza,

In mixed number how much pizza Susan has = 11 x \(\frac{1}{8}\)

= \(\frac{89}{8}\)

Question 2.

Nick needs 3\(\frac{3}{4}\) cups of flour. He only has a \(\frac{1}{4}\)-cup measuring cup. How many times will he fill the measuring cup?

Answer:

15 times

Explanation:

Nick needs 3\(\frac{3}{4}\) cups of flour.

He only has a \(\frac{1}{4}\)-cup measuring cup.

Number of times he fill the measuring cup

3\(\frac{3}{4}\) = \(\frac{15}{4}\)

**On Your Own**

Question 3.

Nora needs 2\(\frac{1}{3}\) cups of milk for a recipe. She can only find a \(\frac{1}{3}\)-cup measuring cup. How many times will she fill the measuring cup?

Answer:

7 times

Explanation:

Nora needs 2\(\frac{1}{3}\) cups of milk for a recipe.

She can only find a \(\frac{1}{3}\)-cup measuring cup.

Number of times she fill the measuring cup

2\(\frac{1}{3}\) = \(\frac{7}{3}\)

Question 4.

**Model with Mathematics** Rename \(\frac{13}{6}\) as a mixed number. Draw a visual representation and write an equation to justify your answer.

Answer:

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

Explanation:

1 whole = 4quarters

\(\frac{13}{6}\) = 2 \(\frac{1}{6}\)

Question 5.

Write the quantity represented by the fraction model as a fraction, as a mixed number, and as a sum of fractions that are equal to 1 or less.

Answer:

2 \(\frac{1}{4}\) = \(\frac{9}{4}\)

Explanation:

1 whole = 4 quarters

There are 2 sets of wholes and 1 quarter.

So, the quantity represented by the fraction model as a fraction = \(\frac{9}{4}\)

As a mixed number = 2\(\frac{1}{4}\)

**Write the mixed number as a fraction.**

Question 6.

4\(\frac{3}{6}\) = __________

Answer:

\(\frac{27}{6}\)

Explanation:

First multiply the whole number with the denominator of the proper fraction.

Add the numerator of the proper fraction to this product.

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

= \(\frac{3+24}{6}\)

= \(\frac{27}{6}\)

Question 7.

2\(\frac{5}{8}\) = ___________

Answer:

\(\frac{21}{8}\)

Explanation:

First multiply the whole number with the denominator of the proper fraction.

Add the numerator of the proper fraction to this product.

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

= \(\frac{16+5}{8}\)

= \(\frac{21}{8}\)

**Write the fraction as a mixed number.**

Question 8.

\(\frac{36}{10}\) = ___________

Answer:

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

Explanation:

Divide the numerator by the denominator.

Write down the whole number part of the quotient.

Write the remainder as numerator.

\(\frac{36}{10}\) = 3\(\frac{6}{10}\)

Question 9.

\(\frac{19}{6}\) = _________

Answer:

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

Explanation:

Divide the numerator by the denominator.

Write down the whole number part of the quotient.

Write the remainder as numerator.

\(\frac{19}{6}\) = 3\(\frac{1}{6}\)

**I’m in a Learning Mindset!**

How did sharing strategies help me rename fractions as mixed numbers?

Answer:

Mixed number is a number which are represented by a whole number and a fraction.

Factions greater than 1 have numerators that are greater than their denominators are known as improper fractions.

Explanation:

By using the strategies number lines or fraction strips.

Renaming a mixed number as an improper fraction means to convert into equivalent fractions.