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

Example 1.
Expressions with Only Addition, Subtraction, Multiplication, and Division

What operations are evaluated first?
Multiplication and division are evaluated first, from left to right.

What operations are always evaluated last?
Addition and subtraction are always evaluated last, from left to right.

Example 2.
Expressions with Four Operations and Exponents
4 + 92 ÷ 3 × 2 – 2

What operation is evaluated first?
Exponents (92 = 9 × 9 = 81)

What operations are evaluated next?
Multiplication and division, from left to right (81 ÷ 3 = 27; 27 × 2 = 54)

What operations are always evaluated last?
Addition and subtraction, from left to right (4 + 54 = 58; 58 – 2 = 56)

56

Example 3. Expressions with Parentheses
Consider a family of 4 that goes to a soccer game. Tickets are $5.00 each. The mom also buys a soft drink for$2.00. How would you write this expression?
4 × 5 + 2

How much will this outing cost?
$22 Consider a different scenario: The same family goes to the game as before, but each of the family members wants a drink. How would you write this expression? Answer: 4 × (5 + 2) Why would you add the 5 and 2 first? Answer: We need to determine how much each person spends. Each person spends$7; then, we multiply by 4 people to figure out the total cost.

How much will this outing cost?
$28 How many groups are there? Answer: 4 What does each group comprise? Answer:$5 + $2, or$7

Example 4.
Expressions with Parentheses and Exponents
2 × (3 + 4)2
Which value will we evaluate first within the parentheses? Evaluate.
First, evaluate 42 which is 16; then, add 3.The value of the parentheses is 19.
2 × (3 + 42)
2 × (3 + 16)
2 × 19

Evaluate the rest of the expression.
2 × 19 = 38

What do you think will happen when the exponent in this expression is outside of the parentheses?
2 × (3 + 4)2

Will the answer be the same?

Which should we evaluate first? Evaluate.
Parentheses
2 × (3 + 4)2
2 × (7)2

What happened differently here than in our last example?
The 4 was not raised to the second power because it did not have an exponent. We simply added the values inside the parentheses.

What should our next step be?

We need to evaluate the exponent next.
72 = 7 × 7 = 49

Evaluate to find the final answer.
2 × 49
98

The final answers were not the same.

What was different between the two expressions?
Answers may vary. In the first problem, a value inside the parentheses had an exponent, and that value was evaluated first because it was inside of the parentheses. In the second problem, the exponent was outside of the parentheses, which made us evaluate what was in the parentheses first; then, we raised that value to the power of the exponent.

What conclusions can you draw about evaluating expressions with parentheses and exponents?
Answers may vary. Regardless of the location of the exponent in the expression, evaluate the parentheses first. Sometimes there will be values with exponents inside the parentheses. If the exponent is outside the parentheses, evaluate the parentheses first, and then evaluate to the power of the exponent.

Exercise 1.
4 + 2 × 7
4 + 14
18

Exercise 2.
36 ÷ 3 × 4
12 × 4
48

Exercise 3.
20 − 5 × 2
20 − 10
10

Exercise 4.
90 − 52 × 3
90 − 25 × 3
90 − 75
15

Exercise 5.
43 + 2 × 8
64 + 2 × 8
64 + 16
80

Exercise 6.
2 + (92)
2 + (81 – 4)
2 + 77
79

Exercise 7.
2 . (13 + 5 – 14 ÷ (3 + 4)
2 . (13 + 5 – 14 ÷ 7)
2 . (13 + 5 – 2)
2 . 16
32

Exercise 8.
7 + (12 – 32)
7 + (12 – 9)
7 + 3
10

Exercise 9.
7 + (12 – 3)2
7 + 92
7 + 81
88

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

Evaluate each expression.

Question 1.
3 × 5 + 2 × 8 + 2
15 + 16 + 2
33

Question 2.
($1.75 + 2 ×$0.25 + 5 × $0.05) × 24 Answer: ($1.75 + $0.50 +$0.25) × 24
$2.50 × 24$60.00

Question 3.
(2 × 6) + (8 × 4) + 1
12 + 32 + 1
45

Question 4.
((8 × 1.95) + (3 × 2.95) + 10.95) × 1.06
(15.6 + 8.85 + 10.99) × 1.06
35.4 × 1.06
37.54

Question 5.
((12 ÷ 3)2 – (18 ÷ 32)) × (4 ÷ 2)
(42 − (18 ÷ 9)) × (4 ÷ 2)
(16 – 2) × 2
14 × 2
28

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

Question 1.
Evaluate this expression: 39 ÷ (2 + 1) – 2 × (4 + 1).
39 ÷ 3 − 2 × 5
13 − 10
3

Question 2.
Evaluate this expression: 12 × (3 + 22 ÷ 2 − 10
12 × (3 + 4) ÷2 − 10
12 × 7 ÷ 2 − 10
84 ÷ 2 − 10
42 − 10
32

Question 3.
Evaluate this expression: 12 × (3 + 2)2 ÷ 2 – 10.