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Lesson 1.5- The Distributive Property, pg. 26

Lesson 1.5- The Distributive Property, pg. 26. Objectives : To use the distributive property to evaluate expressions. To use the distributive property to simplify expressions. Vocabulary. Term: a number, a variable, or a product or quotient of numbers and variables. Ex. 2x ² + 6x + 5

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Lesson 1.5- The Distributive Property, pg. 26

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  1. Lesson 1.5- The Distributive Property, pg. 26 Objectives: To use the distributive property to evaluate expressions. To use the distributive property to simplify expressions.

  2. Vocabulary • Term: a number, a variable, or a product or quotient of numbers and variables. Ex. 2x² + 6x + 5 • Like terms: terms that contain the same variables, with corresponding variables having the same exponent. Ex. 3a² + 5a² +2a • Equivalent expressions: expressions that denote the same number. Like terms

  3. Simplest form: an expression is in simplest form when it has no like terms or parentheses. • Coefficient: the numerical factor of a term. Ex. 5x + 6 coefficient constant

  4. Distributive Property • For any numbers a, b, and c, a(b + c) = ab + ac and (b + c)a = ba + ca a(b -c) = ab - ac and (b - c)a = ba - ca

  5. 5(7 + 2) 5(7) + 5(2) 35 + 10 45 (16 – 7)3 (16)3 – (7)3 Dist. prop 48 – 21 multiply 27 subtract Ex. 1: Using the distributive property. Distributive property multiply add

  6. 6(12 – 2) 6(12) - 6(2) dist. prop 72 – 12 multiply 60 subtract (5 + 7)8 (5)8 + (7)8 dist. Prop 40 + 56 multiply 96 add Your turn…..

  7. 12 × 82 12(80 + 2) 12(80) + 12(2) 960 + 24 984 24(3¾) 24(3 + ¾) 24(3) + 24(¾) 72 + 18 90 Ex. 2: Use the distributive property to find each product.

  8. 12(y + 3) 12(y) + 12(3) Dist. Prop. 12y + 36simplified 4(y² + 8y + 2) 4(y²) + 4(8y) + 4(2) 4y² + 32y + 8 Ex. 3: Re-write each product using the Distributive Property. Then simplify.

  9. 17a + 21a (17 + 21)a 38a ¼(12 – 4n) ¼(12) - ¼(4n) 3 - n 12b² - 8b² + 6b (12 – 8)b² + 6b 4b² + 6b Ex. 4: Simplify each expression.

  10. 13m + m 13m + 1m 14m 2. 3(x + 2x) 3(x) + 3(2x) 3x + 6x 9x 4(3g + 2) 4(3g) + 4(2) 12g + 8 4. 14a² + 13b² + 27 simplified You try….

  11. DINING OUT: The Ross family recently dined at an Italian restaurant. Each of the four family members ordered a pasta dish that cost $11.50, a drink that cost $1.50, and dessert that cost $2.75. a). Write an expression that could be used to calculate the cost of the Ross’ dinner before adding tax and a tip. 4(11.5 + 1.5 + 2.75) b) What was the cost of dining out for the Ross family? $63.00

  12. ORIENTATION: Madison college conducted a three-day orientation for incoming freshmen. Each day, an average of 110 students attended the morning session and an average of 160 students attended the afternoon. • Write an expression that could be used to determine the total number of incoming freshmen who attended the orientation. 3(110 + 160) • What was the attendance for all three days of orientation? 810

  13. Summary • When using the distributive property multiply the factor on the outside times every term on the inside of the parentheses. Ex. 5(x + 6) 5x + 5(6) 5x + 30 • Simplify: Remove parentheses and combine like terms. • Like terms: terms with the same variable raised to the same power

  14. NBA #5, page 30, problems 16-52 even

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