Name ________________________________________ Date __________________ Class __________________

Holt McDougal Mathematics

Algebraic Reasoning Review for Mastery: Order of Operations

To help you remember the order of operations use the phrase “Please Excuse My Dear Aunt Sally.” Evaluate. 39 ÷ (9 + 4) + 5 − 22

Parentheses 39 ÷ 13 + 5 − 22

Exponents 39 ÷ 13 + 5 − 4

Multiply and divide from left to right 3 + 5 − 4

Add and subtract from left to right 8 − 4 = 4

Simplify each expression. 1. 12 • 4 − 2 2. 15 ÷ 3 • 5 3. 15 • 3 ÷ 5 _____ − 2 _____ • 5 _____ ÷ 5

________________________ _______________________ ________________________

4. 8 + 20 ÷ 4 5. 5 − 2 • 6 ÷ 4 + 1 6. 32 + 6 • 4 − 52

________________________ _______________________ ________________________

7. 1 + 4 • 9 ÷ 6 − 7 8. 18 ÷ (6 ÷ 3) 9. (18 ÷ 6) ÷ 3

________________________ _______________________ ________________________

(MORE PRACTICE ON BACK)

P: first, parentheses and other grouping symbols (if any) E: second, exponents (if any) M and D: then, multiplication and division, in order from left to right A and S: finally, addition and subtraction, in order from left to right

Name ________________________________________ Date __________________ Class __________________

Holt McDougal Mathematics

10. 4 • 5 + 8 ÷ 2 − 7 11. 2 • 3 − 8 ÷ 22 12. 8(7 − 6) ÷ 23

________________________ _______________________ ________________________

Algebraic Reasoning Review for Mastery: Properties of Numbers

You can use the Commutative Property, the Associative Property, and the Distributive Property with mental math to simplify expressions.

16 + 47 + 14 = 47 + 16 + 14 Commutative Property 8 • 3 • 5 = 3 • 8 • 5

= 47 + (16 + 14) Associative Property = 3 • (8 • 5)

= 47 + 30 Mental math = 3 • 40

= 77 Mental math = 120

9(28) = 9(20 + 8) 9(28) = 9(30 – 2)

= (9 • 20) + (9 • 8) Distributive Property = (9 • 30) − (9 • 2)

= 180 + 72 Mental math = 270 – 18

= 252 Mental math = 252

Simplify each expression. Tell what properties you used. 1. (45 + 39) + 25 = (39 + ______) + 25 ___________________________ Property = 39 + (______ + ______) ___________________________ Property = 39 + ______ = _________

Use the Distributive Property to simplify the following expressions

2. 5(18) = 5 • (10 + ______) 3. 6(29) = 6 • (30 − ______) = (5 • ______) + (5 • ______) = (6 • ______) − (6 • ______) = ______ + ______ = ______ − ______ = ______ = ______