3.3: Simplify Expressions

Simplify. Explain each step. 7(9w)

7(9w) = (7•9)w Assoc. Prop. of Mult. =63w Multiplication

Simplify. Explain each step. (0 + a) + 8

(0 + a ) + 8 = 0 + 8 Add. Prop. of Zero = 0 Addition

Simplify. Explain each step. (14 + y) + 3

(14 + y) + 3 = (y + 14) + 3 Comm. Prop. of Addition = y + (14 + 3) Assoc. Prop. of Addition = y + 17 Addition.

Simplify. Explain each step. (18.6 • d) • 1

(18.6 • d) • 1 = 18.6 • (d • 1) Associative Property of Mult. = 18.6 • d Mult. Prop of One = 18.6d Multiplication

Simplify. Explain each step. (2.4 + 4n) + 9

(2.4 + 4n ) + 9 = (4n + 2.4) + 9 Comm. Prop. of Addition. = 4n + (2.4 + 9) Assoc. Prop. of Add. = 4n + 11.4 Addition

The expression 12 + x + 4 represents the perimeter of a triangle. Simplify the expression.

12 + x + 4 = 12 + 4 + x comm. prop .of addition. = (12 + 4 ) + x Assoc. Prop. of Add. = 16 + x Addition

3.2 + (x + 5.1)

3.2 + (x + 5.1) = 3.2 + (5.1 + x) Comm. Prop. of Addition = (3.2 + 5.1) + x Assoc. Prop. of Add. = 8.3 + x Addition

Simplify. Explain each step. 6 + (5 + x)

6 + (5 + x) = (6+5) + x Assoc. Prop. of Addition =11 + x Addition

Simplify. Explain each step. 6(2b)

6(2b) = (6 • 2)b Assoc. Prop. of Mult. = 12b Multiplication

Simplify. Explain each step. 9 • c • 4

9 • c • 4 = 9 • 4 • c Comm. Prop. of Mult. = 36c Multiplication

A case of girl scout cookies has 10 cartons. A carton has 12 boxes. The amount you earn on a whole case is 10(12x) dollars. a) What does x represent? b) Simplify the expression.

a) x represents the cost per box. b) 10(12x) = (10*12)x Assoc. Prop. of Mult. = 120x Multiplication