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.

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?
HMH Into Math Grade 4 Module 16 Lesson 1 Answer Key Understand Multiples of Unit Fractions 1
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?
HMH Into Math Grade 4 Module 16 Lesson 1 Answer Key Understand Multiples of Unit Fractions 2
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.
HMH Into Math Grade 4 Module 16 Lesson 1 Answer Key Understand Multiples of Unit Fractions 3
A. Use the number line to find the distance she runs before she stops for water.
HMH Into Math Grade 4 Module 16 Lesson 1 Answer Key Understand Multiples of Unit Fractions 4
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.
HMH Into Math Grade 4 Module 16 Lesson 1 Answer Key Understand Multiples of Unit Fractions 5
_______ × _________ = \(\frac{5}{6}\)
_______ + _________ + _______ + _________ + ________ = \(\frac{5}{6}\)
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.
HMH Into Math Grade 4 Module 16 Lesson 1 Answer Key Understand Multiples of Unit Fractions 6
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
HMH Into Math Grade 4 Module 16 Lesson 1 Answer Key Understand Multiples of Unit Fractions 5
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.

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