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

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.

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.
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?
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.

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?
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?
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 $$\frac{1}{4}$$

Chad runs around the track _________ times.

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.
$$\frac{15}{4}$$
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?
$$\frac{4}{4}$$ = 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.
$$\frac{3}{4}$$
Explanation:
$$\frac{4}{4}$$ in $$\frac{15}{4}$$ = 3 $$\frac{3}{4}$$

$$\frac{3}{4}$$
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.
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?
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?
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?
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$$\frac{3}{4}$$ = $$\frac{15}{4}$$

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?

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.
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.

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$$\frac{3}{6}$$ = __________
$$\frac{27}{6}$$
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$$\frac{5}{8}$$ = ___________
$$\frac{21}{8}$$
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.
$$\frac{36}{10}$$ = ___________
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.
$$\frac{19}{6}$$ = _________
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$$\frac{1}{6}$$

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