# Eureka Math Grade 6 Module 4 Lesson 3 Answer Key

## Engage NY Eureka Math 6th Grade Module 4 Lesson 3 Answer Key

### Eureka Math Grade 6 Module 4 Lesson 3 Exercise Answer Key

Exercise 1.
Write the addition sentence that describes the model and the multiplication sentence that describes the model.

Answer:
5 + 5 + 5 and 3 × 5

Exercise 2.
Write an equivalent expression to demonstrate the relationship of multiplication and addition.
a. 6 + 6
Answer:
2 × 6

b. 3 + 3 + 3 + 3 + 3 + 3
Answer:
6 × 3

c. 4 + 4 + 4 + 4 + 4
Answer:
5 × 4

d. 6 × 2
Answer:
2 + 2 + 2 + 2 + 2+ 2

e. 4 × 6
Answer:
6 + 6 + 6 + 6

f. 3 × 9
Answer:
9 + 9 + 9

g. h + h + h + h + h
Answer:
5h

h. 6y
Answer:
y + y + y + y + y + y

Exercise 3.
Roberto is not familiar with tape diagrams and believes that he can show the relationship of multiplication and addition on a number line. Help Roberto demonstrate that the expression 3 × 2 is equivalent to 2 + 2 + 2 on a number line.
Answer:
Possible answer: The first number line shows that there are 3 groups of 2, resulting in 6. The second number line shows the sum of 2 + 2 + 2, resulting in 6.

Since both number lines start at 0 and end at 6, the expressions are equivalent.

Exercise 4.
Tell whether the following equations are true or false. Then, explain your reasoning.
a. x + 6g − 6g = x
The equation is true because it demonstrates the addition identity.

b. 2f − 4e + 4e = 2f
Answer:
The equation is true because it demonstrates the subtraction identity.

Exercise 5.
Write an equivalent expression to demonstrate the relationship between addition and multiplication.
a. 6 + 6 + 6 + 6 + 6 + 6 + 6
Answer:
4 × 6 + 3 × 4

b. d + d + d + w + w + w + w + w
Answer:
3d + 5w

c. a + a + b + b + b + c + c + c + c
Answer:
2a + 3b + 4c

### Eureka Math Grade 6 Module 4 Lesson 3 Problem Set Answer Key

Write an equivalent expression to show the relationship of multiplication and addition.

Question 1.
10 + 10 + 10
Answer:
3 × 10

Question 2.
4 + 4 + 4 + 4 + 4 + 4 + 4
Answer:
7 × 4

Question 3.
8 × 2
Answer:
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2

Question 4.
3 × 9
Answer:
9 + 9 + 9

Question 5.
6m
Answer:
m + m + m + m + m + m

Question 6.
d + d + d + d + d
Answer:
5d

### Eureka Math Grade 6 Module 4 Lesson 3 Exit Ticket Answer Key

Write an equivalent expression to show the relationship of multiplication and addition.

Question 1.
8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8
Answer:
9 × 8

Question 2.
4 × 9
Answer:
9 + 9 + 9 + 9

Question 3.
6 + 6 + 6
Answer:
3 × 6

Question 4.
7h
Answer:
h + h + h + h + h + h + h

Question 5.
j + j + j + j + j
Answer:
5j

Question 6.
u + u + u + u + u + u + u + u + u + u
Answer:
10u

### Eureka Math Grade 6 Module 4 Lesson 3 Opening Exercise Answer Key

Write two different expressions that can be depicted by the tape diagram shown. One expression should include addition, while the other should include multiplication.

a.

Answer:
Possible answers: 3 + 3 + 3 or 3 × 3

b.

Answer:
Possible answers: 8 + 8 or 2 × 8

c.

Answer:
Possible answers: 5 + 5 + 5 or 3 × 5