Answer Keys: Order of Operations

Student Concept Worksheet Answers

1

6 + 2 x 5 = 16

First multiply: 2 x 5 = 10. Then add: 6 + 10 = 16.

2

(7 - 3) x 4 = 16

Parentheses first: 7 - 3 = 4. Then multiply: 4 x 4 = 16.

3

3² + 5 x 2 = 19

Exponent first: 3² = 9. Multiply: 5 x 2 = 10. Add: 9 + 10 = 19.

Practice Worksheet Answers

Part A: Basic Expressions

#	Expression	Answer	Work
1	7 + 3 x 4	19	3 x 4 = 12, then 7 + 12 = 19
2	20 - 8 ÷ 2	16	8 ÷ 2 = 4, then 20 - 4 = 16
3	5 x 6 - 10	20	5 x 6 = 30, then 30 - 10 = 20
4	36 ÷ 6 + 9	15	36 ÷ 6 = 6, then 6 + 9 = 15

Part B: Expressions with Parentheses

#	Expression	Answer	Work
5	(4 + 5) x 3	27	(4 + 5) = 9, then 9 x 3 = 27
6	24 ÷ (8 - 2)	4	(8 - 2) = 6, then 24 ÷ 6 = 4
7	(12 - 4) x (3 + 2)	40	8 x 5 = 40
8	50 - (6 + 4) x 3	20	(6 + 4) = 10, 10 x 3 = 30, 50 - 30 = 20

Part C: Expressions with Exponents

#	Expression	Answer	Work
9	2² + 5	9	2² = 4, then 4 + 5 = 9
10	3² x 4	36	3² = 9, then 9 x 4 = 36
11	10 + 2³	18	2³ = 8, then 10 + 8 = 18
12	(5 - 2)² + 1	10	(5 - 2) = 3, 3² = 9, 9 + 1 = 10

Part D: True or False

#	Statement	Answer	Explanation
13	In 8 + 4 x 2, add first	FALSE	Multiply first: 4 x 2 = 8
14	M and D go left to right	TRUE	Same level, work left to right
15	Parentheses are last	FALSE	Parentheses are FIRST!
16	(2+3)x4 = 2+3x4	FALSE	(2+3)x4=20, but 2+3x4=14

Part E: Matching

#	Expression	Answer	Work
17	6 + 3 x 5	C (21)	3 x 5 = 15, 6 + 15 = 21
18	(6 + 3) x 5	A (45)	9 x 5 = 45
19	4² - 6	B or D (10)	16 - 6 = 10
20	18 ÷ 3 + 4	B or D (10)	6 + 4 = 10

Challenge Questions:

#21: 2 x 3² + (12 - 4) ÷ 2 = 2 x 9 + 8 ÷ 2 = 18 + 4 = 22

#22: Many answers possible. Example: 2 + 3 x 4 = 14 or (2 + 4) + 3 x 4 = 14 (if allowed) or 2 x 4 + 3 x 2 = 14

#23: Maya added before multiplying. She did (5 + 3) x 2 = 8 x 2 = 16. Correct: 5 + (3 x 2) = 5 + 6 = 11. Multiplication comes before addition!

FAST Practice Quiz Answers

1

B) 17

5 + 3 x 4: First multiply 3 x 4 = 12, then add 5 + 12 = 17.

2

A) 30

(8 - 3) x 6: Parentheses first: 8 - 3 = 5, then 5 x 6 = 30.

3

C) 4 x 4 + 4

4 x 4 + 4 = 16 + 4 = 20. (A = 20, B = 32, D = 32)

4

Select: First, Third, and Fourth statements

Parentheses first - TRUE
Multiplication before division - FALSE (same level, left to right)
A/S left to right - TRUE
Exponents before multiplication - TRUE
Always left to right - FALSE (must follow PEMDAS)

5

A) 19

2² + 3 x 5: Exponent first: 2² = 4. Multiply: 3 x 5 = 15. Add: 4 + 15 = 19.

6

B) Step 2

Diego should have done 3 x 2 = 6 before adding. Correct: 18 ÷ 6 = 3, 3 x 2 = 6, then 3 + 6 = 9. He added 3 + 3 before multiplying by 2.

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