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1.7: Distributive Property

TERM: A number, a variable, or the product of the two. Ex: a, 3x, 2x, 5, . 1.7: Distributive Property. CONSTANT: a term with no variable (number ) Ex: 4, -1, 6, 2. COEFFICIENT: Is the numerical factor of the a term. Ex: 3 x, 5 w, -3 s, .

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1.7: Distributive Property

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  1. TERM: A number, a variable, or the product of the two. Ex: a, 3x, 2x, 5, 1.7: Distributive Property CONSTANT: a term with no variable (number)Ex: 4, -1, 6, 2

  2. COEFFICIENT: Is the numerical factor of the a term. Ex: 3x, 5w, -3s, LIKE TERMS: Term that have the same variable factors. Ex: 7a and -3a, 4x and 12x, etc..

  3. GOAL:

  4. Let a, b and c be real numbers. ADDITION: a( b + c ) = ab + ac 3( x + 5 ) = 3x + 15 Distributive Property ( b + c )a = ba + ca( x + 5 )3 = 3x + 15 SUBTRACTION:a( b - c ) = ab - ac 3( x - 5 ) = 3x -15 3x -15 ( b - c )a = ba - ca ( x - 5 )3 =

  5. YOU TRY IT: What is the simplified form of: -2( 2y – 3x)?

  6. SOLUTION: Remember: if there is a negative sign, it always goes with the number at the right of it. Using the distributive property we have: -2(2y – 3x) = -2(2y)-2(-3x) = -4y + 6x

  7. REAL-WORLD: The recommended hear rate for exercise, in beats per minute, is given by the expression 0.8(200 – y) where y is a person’s age in years. What is the recommended hear rate for a 14-year old student? Use the distributive property.

  8. SOLUTION: Using the given info and the distributive property we have: Given: 0.8(200 – y) 160 – 0.8y Distribute: 0.8(200 – y)  Substitute y for a 14 year old. 160 – 0.8(14)  160 – 11.2  148.8 beats/min

  9. The area is an example of distributive property Area = b ∙ h 2 Area = 2∙ (4 + 5) = 2(4) + 2(5) = 8+10 = 18 u2 Using Tiles and Models 4 5 Using Algebra we now have the following problem: Area = b ∙ h 2 Area = 2 ∙ (4 + x) = 2(4)+ 2(x) = 2x + 8 u2 x 4

  10. YOU TRY IT: What is the simplified form of: - ( -2y – 3x)?

  11. SOLUTION: Remember: if there is only a negative sign next to the parenthesis, it is understood that there is a invisible 1 next to it: Using the distributive property we have: - 1(-2y – 3x) = -1(-2y) -1(-3x) = 2y + 3x

  12. YOU TRY IT: What sum or difference is equivalent to?

  13. SOLUTION: Using the opposite procedure we see that   +

  14. SIMPLY: Put (add or subtract) like terms together to make a smaller equation. Ex: Simplify: 2n + 1 – 4m – n + 2m Solution: Re-write as: = (2n- n)+(– 4m+2m) +1 = n– 2m+1

  15. YOU TRY IT: Rewrite each expression as a sum. – 8x + 3xy – 2(3x) + 5xy

  16. SOLUTION: Given: – 8x + 3xy – 2(3x) + 5xy Doing the arithmetic (math) we have: – 8x + 3xy – 6x + 5xy Putting like terms together: – 8x – 6x + 3xy + 5xy – 14x + 8xy

  17. VIDEOS: Distributive Property Distribute: http://www.khanacademy.org/math/arithmetic/order-of-operations/ditributive_property/v/the-distributive-property

  18. Pages: 49– 52 Problems: As many as you need to master the concepts. Class Work:

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