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

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.

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.
$$\frac{1}{8}$$ + $$\frac{1}{8}$$ + $$\frac{1}{8}$$ + $$\frac{1}{8}$$ + $$\frac{1}{8}$$ + $$\frac{1}{8}$$ + $$\frac{1}{8}$$ + $$\frac{1}{8}$$ + $$\frac{1}{8}$$ = $$\frac{9}{8}$$ = 1$$\frac{1}{8}$$

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

A. How can you use multiplication to describe how much mix to use for 1, 2, and 3 jugs?
$$\frac{1}{4}$$ × 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.
$$\frac{1}{4}$$ × 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.
$$\frac{1}{4}$$ × 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?

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.

$$\frac{3}{10}$$

B. How did you use the number line to represent the distance Vicki runs before she stops for water?
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.
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?
$$\frac{4}{10}$$ mile.
Explanation:
d = total distance

Check Understanding

Question 1.

_______ × _________ = $$\frac{5}{6}$$
_______ + _________ + _______ + _________ + ________ = $$\frac{5}{6}$$
$$\frac{1}{6}$$ × 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.
$$\frac{3}{8}$$ = __________
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.
$$\frac{9}{4}$$ = __________
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.
$$\frac{13}{10}$$ = ___________
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$$\frac{3}{10}$$

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.

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.
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.
$$\frac{1}{4}$$; $$\frac{2}{4}$$; $$\frac{3}{4}$$; $$\frac{4}{4}$$;
$$\frac{5}{4}$$; $$\frac{6}{4}$$
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.
$$\frac{7}{8}$$ = ____________
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.
$$\frac{3}{10}$$ = _____________
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.
$$\frac{4}{3}$$ = ___________
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.
$$\frac{5}{6}$$ = _____________
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?