We included **HMH Into Math Grade 4 Answer Key PDF** **Module 16 Lesson 1 Understand Multiples of Unit Fractions **to make students experts in learning maths.

## HMH Into Math Grade 4 Module 16 Lesson 1 Answer Key Understand Multiples of Unit Fractions

I Can represent a fraction as the product of a whole number and a unit fraction and as an equation using repeated addition.

**Spark Your Learning**

Kam is training for a running competition. He runs on a track that is \(\frac{1}{8}\) mile around. Kam wants to run a total of \(\frac{9}{8}\) miles. How many times around the track should he run?

Write two different equations that model the problem.

Answer:

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

How many times does Kam need to run around the track to run \(\frac{9}{8}\) miles?

Answer:

9 times

Explanation:

Kam runs on a track that is \(\frac{1}{8}\) mile around.

Number of times Kam need to run around the track to run \(\frac{9}{8}\) miles.

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

He has to take 9 rounds.

**Turn and Talk** What do you notice about the relationship between the equations you wrote?

Answer:

Complete one round is 1.

Explanation:

parts are represented in fraction,

all parts are combined as whole.

**Build Understanding**

Question 1.

A track team uses this sports drink to stay hydrated. If each batch fills one jug, how much mix is needed for 1 jug of sports drink? For 2 jugs? For 3 jugs?

Show a visual representation for each amount.

Answer:

A. How can you use multiplication to describe how much mix to use for 1, 2, and 3 jugs?

Answer:

\(\frac{1}{4}\) × 1 = \(\frac{1}{4}\)

B. How tan you determine how much drink mix to use for 7 jugs of sports drink? Write a multiplication equation to find the amount.

Answer:

\(\frac{1}{4}\) × 7 = \(\frac{7}{4}\) = 1 \(\frac{3}{4}\)

C. How can you determine how much drink mix to use for 7 jugs of sports drink? Write a multiplication equation to find the amount.

Answer:

\(\frac{1}{4}\) × 7 = \(\frac{7}{4}\) = 1 \(\frac{3}{4}\)

Explanation:

If each batch fills one jug,

Total mix needed for 1 jug of sports drink = \(\frac{1}{4}\)

For 2 jugs = \(\frac{1}{4}\) + \(\frac{1}{4}\)

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

For 3 jugs = \(\frac{1}{4}\) + \(\frac{1}{4}\) + \(\frac{1}{4}\)

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

**Turn and Talk** What is another visual representation you could use to solve the problem?

Answer:

Explanation:

To fill 1 jug it need \(\frac{1}{4}\) of sport drink,

To fill 2 jugs it need \(\frac{2}{4}\) of sport drink,

To fill 3 jugs it need \(\frac{3}{4}\) of sport drink.

Question 2.

Vicki trains by running along a trail. The trail has markers every \(\frac{1}{10}\) mile. Vicki runs by 3 markers and then stops for water at the fourth marker.

A. Use the number line to find the distance she runs before she stops for water.

Answer:

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

B. How did you use the number line to represent the distance Vicki runs before she stops for water?

Answer:

She ran \(\frac{3}{4}\) of a mile.

Explanation:

Each jump represents to a mile,

she passed 3 and stopped at the 4th.

So, she ran \(\frac{3}{4}\) of a mile.

C. How can you write an addition equation and a multiplication equation to model the distance Vicki runs using the number of markers and the length of each interval? Let d = the total distance.

Answer:

d = 4\(\frac{1}{10}\)

Explanation:

d = the total distance.

d = \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\) + \(\frac{1}{10}\)

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

d = 4\(\frac{1}{10}\)

D. How far does Vicki run before stopping for water?

Answer:

\(\frac{4}{10}\) mile.

Explanation:

d = total distance

**Check Understanding**

Question 1.

Use the fraction strips to help you complete the equations.

_______ × _________ = \(\frac{5}{6}\)

_______ + _________ + _______ + _________ + ________ = \(\frac{5}{6}\)

Answer:

\(\frac{1}{6}\) × 5 = \(\frac{5}{6}\)

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

Explanation:

From the above strip diagram 1 whole is divided into 6 parts equally.

5 parts are shaded = \(\frac{5}{6}\)

So, 5 parts of \(\frac{1}{6}\) = \(\frac{5}{6}\)

**Write the fraction as the product of a whole number and a unit fraction.**

Question 2.

\(\frac{3}{8}\) = __________

Answer:

3 x \(\frac{1}{8}\)

Explanation:

\(\frac{3}{8}\) means whole is divided into 8 equal parts,

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

= 3\(\frac{1}{8}\)

Question 3.

\(\frac{9}{4}\) = __________

Answer:

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

OR

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

Explanation:

\(\frac{9}{4}\) written as

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

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

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

Question 4.

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

Answer:

1 x \(\frac{3}{10}\)

OR

13\(\frac{1}{10}\)

Explanation:

\(\frac{13}{10}\) written as

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

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

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

\(\frac{1}{10}\) = 13\(\frac{1}{10}\) or 1\(\frac{3}{10}\)

**On Your Own**

Question 5.

**Use Tools** Alex runs 7 laps on a track. Each lap is \(\frac{1}{5}\) mile. How far does he run? Show each lap on the number line. Then write an equation modeling the problem and its solution.

Answer:

L = \(\frac{7}{5}\)

Explanation:

Alex runs 7 laps on a track.

L = 7\(\frac{1}{5}\)

Each lap is \(\frac{1}{5}\) mile.

L = \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\) +\(\frac{1}{5}\) + \(\frac{1}{5}\) + \(\frac{1}{5}\)

L = \(\frac{7}{5}\)

Question 6.

**Use Structure** Yanni is putting fertilizer around trees. She uses \(\frac{1}{3}\) gallon of fertilizer for each tree. There are 5 trees. How much fertilizer does she use? Write an addition equation and a multiplication equation to model how much fertilizer she uses.

Answer:

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

Explanation:

Yanni uses \(\frac{1}{3}\) gallon of fertilizer for each tree.

There are 5 trees.

Total fertilizer she use = 5\(\frac{1}{3}\) = \(\frac{5}{3}\)

Question 7.

**Use Repeated Reasoning** Fonsi is placing square tiles that are \(\frac{1}{4}\) yard long to make a path. He places 6 tiles end-to7end. Use multiples to find how long the path is.

Answer:

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

\(\frac{5}{4}\); \(\frac{6}{4}\)

Explanation:

Fonsi is placing square tiles that are \(\frac{1}{4}\) yard long to make a path.

He places 6 tiles end-to7end.

Multiples of the path are \(\frac{1}{4}\); \(\frac{2}{4}\); \(\frac{3}{4}\);

\(\frac{4}{4}\); \(\frac{5}{4}\); \(\frac{6}{4}\)

**Write the fraction as a product of a whole number and a unit fraction.**

Question 8.

\(\frac{7}{8}\) = ____________

Answer:

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

Explanation:

A unit fraction is any fraction with 1 as its numerator and a whole number for the denominator.

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

Question 9.

\(\frac{3}{10}\) = _____________

Answer:

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

Explanation:

A unit fraction is any fraction with 1 as its numerator and a whole number for the denominator.

Question 10.

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

Answer:

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

Explanation:

A unit fraction is any fraction with 1 as its numerator and a whole number for the denominator.

Question 11.

\(\frac{5}{6}\) = _____________

Answer:

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

Explanation:

A unit fraction is any fraction with 1 as its numerator and a whole number for the denominator.

**I’m in a Learning Mindset!**

How can I help my classmates understand multiples of unit fractions?

Answer:

By using fraction strips

Explanation:

A unit fraction is any fraction with 1 as its numerator and a whole number for the denominator.

Multiple is a form of skip counting, we write the multiples of a given number.