Distributive Property (Algebra 1)

Slide 2: The Distributive Property  Use the Distributive Property to evaluate expressions.  Use the Distributive Property to simplify expressions. 1) term 2) like terms 3) equivalent expressions 4) simplest form 5) coefficient

Slide 3: The Distributive Property Eight customers each bought a bargain game and a new release. Calculate the total sales for these customers.

Slide 4: The Distributive Property Eight customers each bought a bargain game and a new release. Calculate the total sales for these customers. There are two methods you could use to calculate the video game sales. number of each customer' s sales of sales of  customers purchase price bargain games new releases X           

Slide 5: The Distributive Property Eight customers each bought a bargain game and a new release. Calculate the total sales for these customers. There are two methods you could use to calculate the video game sales. number of each customer' s sales of sales of  customers purchase price bargain games new releases X            8 34.95 814.95   119.60  279.60  399.20

Slide 6: The Distributive Property Eight customers each bought a bargain game and a new release. Calculate the total sales for these customers. There are two methods you could use to calculate the video game sales. number of each customer' s sales of sales of  customers purchase price bargain games new releases X            14.95  34.95 8 34.95 814.95  8 X  8 49.90   119.60  279.60  399.20  399.20

Slide 7: The Distributive Property Eight customers each bought a bargain game and a new release. Calculate the total sales for these customers. There are two methods you could use to calculate the video game sales. number of each customer' s sales of sales of  customers purchase price bargain games new releases X            14.95  34.95 8 34.95 814.95  8 X  8 49.90   119.60  279.60  399.20  399.20 This is an example of the ____________________.

Slide 8: The Distributive Property Eight customers each bought a bargain game and a new release. Calculate the total sales for these customers. There are two methods you could use to calculate the video game sales. number of each customer' s sales of sales of  customers purchase price bargain games new releases X            14.95  34.95 8 34.95 814.95  8 X  8 49.90   119.60  279.60  399.20  399.20 Distributive Property This is an example of the ____________________.

Slide 9: The Distributive Property For any numbers, a, b, and c,

Slide 10: The Distributive Property For any numbers, a, b, and c, a(b+c) =

Slide 11: The Distributive Property For any numbers, a, b, and c, a ( b + c ) = ab + ac

Slide 12: The Distributive Property For any numbers, a, b, and c, a ( b + c ) = ab + ac and (b+c)a =

Slide 13: The Distributive Property For any numbers, a, b, and c, a ( b + c ) = ab + ac and ( b + c ) a = ba + ca

Slide 14: The Distributive Property For any numbers, a, b, and c, a ( b + c ) = ab + ac and ( b + c ) a = ba + ca a(b–c) =

Slide 15: The 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

Slide 16: The 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 =

Slide 17: The 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

Slide 18: The Distributive Property Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.

Slide 19: The Distributive Property Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.  810   8 4 

Slide 20: The Distributive Property Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.  810   8 4   80  32

Slide 21: The Distributive Property Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.  810   8 4   80  32  112

Slide 22: The Distributive Property Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.  810   8 4   80  32  112 Rewrite (12 – 4)6 using the Distributive Property. Then evaluate.

Slide 23: The Distributive Property Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.  810   8 4   80  32  112 Rewrite (12 – 4)6 using the Distributive Property. Then evaluate.  612   6 4 

Slide 24: The Distributive Property Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.  810   8 4   80  32  112 Rewrite (12 – 4)6 using the Distributive Property. Then evaluate.  612   6 4   72  24

Slide 25: The Distributive Property Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.  810   8 4   80  32  112 Rewrite (12 – 4)6 using the Distributive Property. Then evaluate.  612   6 4   72  24  48

Slide 26: The Distributive Property A family owns two cars. In 1995, they drove the first car 18,000 miles and the second car 16,000 miles. Use the graph to find the total cost of operating both cars.

Slide 27: The Distributive Property A family owns two cars. In 1995, they drove the first car 18,000 miles and the second car 16,000 miles. Use the graph to find the total cost of operating both cars. 0.4618,000  16,000 

Slide 28: The Distributive Property A family owns two cars. In 1995, they drove the first car 18,000 miles and the second car 16,000 miles. Use the graph to find the total cost of operating both cars. 0.4618,000  16,000   8280  7360

Slide 29: The Distributive Property A family owns two cars. In 1995, they drove the first car 18,000 miles and the second car 16,000 miles. Use the graph to find the total cost of operating both cars. 0.4618,000  16,000   8280  7360  15,640

Slide 30: The Distributive Property A family owns two cars. In 1995, they drove the first car 18,000 miles and the second car 16,000 miles. Use the graph to find the total cost of operating both cars. 0.4618,000  16,000   8280  7360  15,640 It cost the family $15,640 to operate their two cars.

Slide 31: The Distributive Property Rewrite 4(r – 6) using the Distributive Property. Then simplify.

Slide 32: The Distributive Property Rewrite 4(r – 6) using the Distributive Property. Then simplify. 4 r  6

Slide 33: The Distributive Property Rewrite 4(r – 6) using the Distributive Property. Then simplify. 4 r  6  4 r   4 6 

Slide 34: The Distributive Property Rewrite 4(r – 6) using the Distributive Property. Then simplify. 4 r  6  4 r   4 6   4r  24

Slide 35: The Distributive Property A term is a ________, a _________, or a ________ or _________ of numbers and variables.

Slide 36: The Distributive Property A term is a ________, a _________, or a ________ or _________ number of numbers and variables.

Slide 37: The Distributive Property A term is a ________, a _________, or a ________ or _________ number variable of numbers and variables.

Slide 38: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable of numbers and variables.

Slide 39: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable quotient of numbers and variables.

Slide 40: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable quotient of numbers and variables. y, 4a, p3 , and 8g2h are all terms. Example:

Slide 41: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable quotient of numbers and variables. y, 4a, p3 , and 8g2h are all terms. Example: Like terms are terms that contain the same _______, with corresponding variables having the same ______.

Slide 42: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable quotient of numbers and variables. y, 4a, p3 , and 8g2h are all terms. Example: Like terms are terms that contain the same variable with corresponding variables _______, having the same ______.

Slide 43: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable quotient of numbers and variables. y, 4a, p3 , and 8g2h are all terms. Example: Like terms are terms that contain the same variable with corresponding variables _______, power having the same ______.

Slide 44: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable quotient of numbers and variables. y, 4a, p3 , and 8g2h are all terms. Example: Like terms are terms that contain the same variable with corresponding variables _______, power having the same ______. 2x2  6x  5

Slide 45: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable quotient of numbers and variables. y, 4a, p3 , and 8g2h are all terms. Example: Like terms are terms that contain the same variable with corresponding variables _______, power having the same ______. 2x2  6x  5 three terms

Slide 46: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable quotient of numbers and variables. y, 4a, p3 , and 8g2h are all terms. Example: Like terms are terms that contain the same variable with corresponding variables _______, power having the same ______. 3y2  6 y2  5 y 2x2  6x  5 three terms

Slide 47: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable quotient of numbers and variables. y, 4a, p3 , and 8g2h are all terms. Example: Like terms are terms that contain the same variable with corresponding variables _______, power having the same ______. 3y2  6 y2  5 y 2x2  6x  5 like terms three terms

Slide 48: The Distributive Property A term is a ________, a _________, or a ________ or _________ product number variable quotient of numbers and variables. y, 4a, p3 , and 8g2h are all terms. Example: Like terms are terms that contain the same variable with corresponding variables _______, power having the same ______. 3y2  6 y2  5 y 2x2  6x  5 like terms unlike terms three terms

Slide 49: The Distributive Property The Distributive Property and the properties of equality can be used to show that 5n + 7n = 12n 5n 7n and are __________.

Slide 50: The Distributive Property The Distributive Property and the properties of equality can be used to show that 5n + 7n = 12n 5n 7n like terms and are __________.

Slide 51: The Distributive Property The Distributive Property and the properties of equality can be used to show that 5n + 7n = 12n 5n 7n like terms and are __________. 5n  7 n  (5  7)n

Slide 52: The Distributive Property The Distributive Property and the properties of equality can be used to show that 5n + 7n = 12n 5n 7n like terms and are __________. 5n  7 n  (5  7)n The expressions 5n + 7n and 12n are called ______________________ because they denote the same number.

Slide 53: The Distributive Property The Distributive Property and the properties of equality can be used to show that 5n + 7n = 12n 5n 7n like terms and are __________. 5n  7 n  (5  7)n The expressions 5n + 7n and 12n equivalent expressions are called ______________________ because they denote the same number.

Slide 54: The Distributive Property The Distributive Property and the properties of equality can be used to show that 5n + 7n = 12n 5n 7n like terms and are __________. 5n  7 n  (5  7)n The expressions 5n + 7n and 12n equivalent expressions are called ______________________ because they denote the same number. An expression is in simplest form when it is replaced by an equivalent expression having no __________ or ____________.

Slide 55: The Distributive Property The Distributive Property and the properties of equality can be used to show that 5n + 7n = 12n 5n 7n like terms and are __________. 5n  7 n  (5  7)n The expressions 5n + 7n and 12n equivalent expressions are called ______________________ because they denote the same number. An expression is in simplest form when it is replaced by an equivalent expression having no __________ or ____________. like terms

Slide 56: The Distributive Property The Distributive Property and the properties of equality can be used to show that 5n + 7n = 12n 5n 7n like terms and are __________. 5n  7 n  (5  7)n The expressions 5n + 7n and 12n equivalent expressions are called ______________________ because they denote the same number. An expression is in simplest form when it is replaced by an equivalent expression parentheses having no __________ or ____________. like terms

Slide 57: The Distributive Property Simplify each expression. 7 x  11x a)

Slide 58: The Distributive Property Simplify each expression. 7 x  11x a)  18 x

Slide 59: The Distributive Property Simplify each expression. 7 x  11x a)  18 x 9n  13n 2  4n 2 b)

Slide 60: The Distributive Property Simplify each expression. 7 x  11x a)  18 x 9n  13n 2  4n 2 b)  9n  17 n 2

Slide 61: The Distributive Property Simplify each expression. 1 1 y y c) 7 x  11x a) 6 3  18 x 9n  13n 2  4n 2 b)  9n  17 n 2

Slide 62: The Distributive Property Simplify each expression. 1 1 y y c) 7 x  11x a) 6 3  18 x 1 2  y y 6 6 9n  13n 2  4n 2 b)  9n  17 n 2

Slide 63: The Distributive Property Simplify each expression. 1 1 y y c) 7 x  11x a) 6 3  18 x 1 2  y y 6 6 9n  13n 2  4n 2 b) 3 y  9n  17 n 2 6

Slide 64: The Distributive Property Simplify each expression. 1 1 y y c) 7 x  11x a) 6 3  18 x 1 2  y y 6 6 9n  13n 2  4n 2 b) 3 y  9n  17 n 2 6 1 y 2

Slide 65: The Distributive Property Study Tip! Like terms may be defined as terms that are the same or vary only by the coefficient.

Slide 66: The Distributive Property Study Tip! Like terms may be defined as terms that are the same or vary only by the coefficient. The coefficient of a term is the _______________.

Slide 67: The Distributive Property Study Tip! Like terms may be defined as terms that are the same or vary only by the coefficient. numerical factor The coefficient of a term is the _______________.

Slide 68: The Distributive Property Study Tip! Like terms may be defined as terms that are the same or vary only by the coefficient. numerical factor The coefficient of a term is the _______________. 17xy, Example: in the term the coefficient is ____.

Slide 69: The Distributive Property Study Tip! Like terms may be defined as terms that are the same or vary only by the coefficient. numerical factor The coefficient of a term is the _______________. 17xy, Example: in the term the coefficient is ____. 17

Slide 70: The Distributive Property Study Tip! Like terms may be defined as terms that are the same or vary only by the coefficient. numerical factor The coefficient of a term is the _______________. 17xy, Example: in the term the coefficient is ____. 17 3x 2 in the term the coefficient is 4

Slide 71: The Distributive Property Study Tip! Like terms may be defined as terms that are the same or vary only by the coefficient. numerical factor The coefficient of a term is the _______________. 17xy, Example: in the term the coefficient is ____. 17 3x 2 3 in the term the coefficient is 4 4

Slide 72: The Distributive Property Find the perimeter of the rectangle.

Slide 73: The Distributive Property Find the perimeter of the rectangle. P  2 5in  9in 

Slide 74: The Distributive Property Find the perimeter of the rectangle. P  2 5in  9in   214in 

Slide 75: The Distributive Property Find the perimeter of the rectangle. P  2 5in  9in   214in   28in

Slide 76: The Distributive Property Find the perimeter of the rectangle. P  2 5in   2 9in  P  2 5in  9in   214in   28in

Slide 77: The Distributive Property Find the perimeter of the rectangle. P  2 5in   2 9in  P  2 5in  9in   10in   18in   214in   28in

Slide 78: The Distributive Property Find the perimeter of the rectangle. P  2 5in   2 9in  P  2 5in  9in   10in   18in   214in   28in  28in

Slide 79: The Distributive Property Find the perimeter of the rectangle. P  2 5in   2 9in  P  2 5in  9in   10in   18in   214in   28in  28in The perimeter of the rectangle is 28 inches.

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