ALGEBRA I - SECTION 1-7 (The Distributive Property)

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Presentation transcript:

ALGEBRA I - SECTION 1-7 (The Distributive Property) @ SECTION 1-7 : THE DISTRIBUTIVE PROPERTY

DISTRIBUTIVE PROPERTY : For any numbers, a, b, and c, a( b + c) = a • b + a • c TERM : a number, a variable, or the product of a number and a variable. Examples : CONSTANT : a term with no variable. Examples :

COEFFICIENT : the number multiplying a variable. Examples : SIMILAR (LIKE) TERMS : terms with the same variables with the same exponents. Examples : SIMPLEST FORM : an expression written with no grouping symbols and no like terms. Examples :

6(2x + 5) = 6 • 2x + 6 • 5 = 12x + 30 Simplest Form Distributive Property Term Constant Coefficient

Use the distributive property to simplify each expression. ANSWER : 4x + 32 2) 5(2n – 7) ANSWER : 10n - 35 3) -6(4b – 1) ANSWER : -24b + 6 4) -(6 + a) ANSWER : -6 - a 5) -(2x – 9) ANSWER : -2x + 9

Write each fraction as a sum or difference. ANSWER : 2x – (13/2)

Simplify each expression. 8) 8p – 5p ANSWER : 3p 9) 10k2 + 6m – 5k + 2m ANSWER : 10k2 – 5k + 8m 10) 12y – 6 – 15y + 8 ANSWER : -3y + 2 11) 6(3n + 5) + 3n - 50 ANSWER : 21n - 20 12) x3 – 2x2 + 5x + 6x2 – 3x + 1 ANSWER : x3 + 4x2 + 2x + 1

Use the distributive property to solve mentally. Deli sandwiches cost $4.95 each including tax. Cody order five deli sandwiches. How much does he owe? Solution : 5(4.95) = 5(5 – 0.05) = 5 • 5 – 5 • 0.05 = 25 – 0.25 = $24.75 14) 199 X 4 ANSWER : 796