1.7: Distributive Property

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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,. - PowerPoint PPT Presentation

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1.7: Distributive Property TERM: A number, a variable, or the product of the two.

Ex: a, 3x, 2x, 5, CONSTANT: a term with no variable (number)

Ex: 4, -1, 6, 2COEFFICIENT: 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..GOAL:

Distributive Property Let a, b and c be real numbers.ADDITION: a( b + c ) = ab + ac3( x + 5 ) = ( b + c )a = ba + ca( x + 5 )3 = SUBTRACTION:a( b - c ) = ab - ac3( x - 5 ) = ( b - c )a = ba - ca( x - 5 )3 =3x + 153x + 153x - 153x - 15YOU TRY IT:

What is the simplified form of: -2( 2y 3x)?- 2(2y 3x) = -2(2y) -2(-3x) = -4y + 6xSOLUTION: Remember: if there is a negative sign, it always goes with the number at the right of it. Using the distributive property we have: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 persons age in years. What is the recommended hear rate for a 14-year old student? Use the distributive property. 7SOLUTION:Using the given info and the distributive property we have:Given: 0.8(200 y) Substitute y for a 14 year old.160 0.8(14) Distribute: 0.8(200 y) 160 11.2 148.8 beats/min 160 0.8y 8Using Tiles and ModelsThe area is an example of distributive property245Area = b h Area = 2 (4 + 5) = 2(4) + 2(5) = 8+10 = 18 u2Using Algebra we now have the following problem:2Area = b h Area = 2 (4 + x) = 2(4)+ 2(x) = 2x + 8 u2 4xYOU TRY IT:

What is the simplified form of: - ( -2y 3x)?- 1(-2y 3x) = -1(-2y) -1(-3x) = 2y + 3xSOLUTION: 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:SOLUTION:

Using the opposite procedure we see thatSIMPLY: 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 YOU TRY IT:

Rewrite each expression as a sum. 8x + 3xy 2(3x) + 5xySOLUTION:Doing the arithmetic (math) we have: Given: 8x + 3xy 2(3x) + 5xy 8x + 3xy 6x + 5xyPutting like terms together: 8x 6x + 3xy + 5xy 14x + 8xyVIDEOS:Distributive PropertyDistribute:http://www.khanacademy.org/math/arithmetic/order-of-operations/ditributive_property/v/the-distributive-property

Class Work:Pages: 49 52

Problems: As many as you need to master the concepts.