Distributive Property Chapter 5 Lesson 2 C Pages

Distributive Property Chapter 5, Lesson 2 C Pages 296 -299

You have already evaluated numerical expressions using addition and multiplication. • Use the Distributive Property to write equivalent numerical expressions • Use the Distributive Property to write equivalent algebraic expressions.

Equivalent Expressions Writing a problem in a different way so it has the same end value Examples?

Distributive Property

Why use Distributive Property ? ü You can use the distributive property to break-up a number to individual parts and solve easier… ü Example: 2 x 13 2(10 + 3) = 2(10) + 2(3)

Distributive Property ü Let's say I have to quickly multiply: 4 x 53 4(50 + 3) = 4(50) + 4(3)

Distributive Property ü One more! 6 x 27 6(20 + 7) = 6(20) + 6(7)

Distributive Property ü Use the distributive property to rewrite each expression 1. 4 (x + 3) 2. 7 (x + 9) 3. (x + 13) 2

Evaluate Numerical Expressions A. Use the Distributive Property to write 4(5 + 8) as an equivalent expression. Then evaluate the expression. 4(5 + 8) = 4 ● 5 + 4 ● 8 = 20 + 32 = 52 Answer: Add. 52

Evaluate Numerical Expressions B. Use the Distributive Property to write (6 – 9)2 as an equivalent expression. Then evaluate the expression. (6 – 9)2 = 6 ● 2 – 9 ● 2 = 12 – 18 = – 6 Answer: – 6 Subtract.

Distributive Property ü Solve using the distributive property: ü Rewrite first a( b + c) = ab + bc 1. 7(20 + 6) 2. 2(8 + ½) 3. 4 (3 + ¼)

A. Use the Distributive Property to write 3(9 + 2) as an equivalent expression. Then evaluate the expression. A. 3 ● 9 + 3 ● 2; 30 B. 3 ● 9 + 3 ● 2; 33 C. (3 + 9)(3 + 2); 60 D. (3 + 9)(3 + 2); 72

B. Use the Distributive Property to write (8 – 10)3 as an equivalent expression. Then evaluate the expression. A. 8 • 3 – 10 • 3; – 6 B. 8 • 3 – 10 • 3; 6 C. 8 • 3 – 10; 14 D. 8 • 3 + 10 • 3; 54

Use the Distributive Property RECREATION A community center offers a canoeing day trip. The canoeing fee is $80 person. The cost of food is an additional $39 person. Find the total cost for a family of four. Understand You know the cost of the fee person and the cost of food person. You need to find the total cost for a family of four. Plan You can use the Distributive Property and mental math to find the total cost for the family of four. To find the cost mentally, find 4($80 + $39) or 4($80) + 4($39).

Use the Distributive Property Solve 4($80 + $39) = 4($80) + 4($39) Distributive Property = $320 + $156 Multiply. = $476 Add. Answer: The total cost is $476.

MOVIES The cost of a movie ticket is $7 and the cost of a box of popcorn is $2. Write two equivalent expressions to find the total cost for a family of five to go to the movies if each member of the family gets a box of popcorn. Then find the total cost. A. 5($7) + 5($2); 5($7 ● $2); $40 B. 5($7) + 5($2); 5($7 + $2); $45 C. $7 + 5($2); $7 + $10; $17 D. $7 + 5($2); 5($7 + $2); $70

Simplify Algebraic Expressions A. Use the Distributive Property to write 2(x + 4) as an equivalent algebraic expression. 2(x + 4) = 2 x + 2 ● 4 = 2 x + 8 Answer: 2 x + 8 Simplify.

Simplify Algebraic Expressions B. Use the Distributive Property to write (y + 3)6 as an equivalent algebraic expression. (y + 3)6 = y ● 6 + 3 ● 6 = 6 y + 18 Answer: 6 y + 18 Simplify.

A. Use the Distributive Property to write 4(m + 7) as an equivalent algebraic expression - SIMPLIFIED. A. m + 28 B. 4 m + 11 C. (4 m)(28) D. 4 m + 28

B. Use the Distributive Property to write (p + 3)5 as an equivalent algebraic expression. A. 5 p + 8 B. 5 p + 15 C. p + 15 D. (5 p)(15)

Simplify Expressions with Subtraction A. Use the Distributive Property to write 4(x – 2) as an equivalent algebraic expression. 4(x – 2) = = 4 x + 4(– 2) Distributive Property = 4 x + (– 8) Simplify. Answer: 4 x – 8

Simplify Expressions with Subtraction B. Use the Distributive Property to write – 2(n – 3) as an equivalent algebraic expression – SIMPLIFY!. – 2(n – 3) = Answer: = – 2 n + (– 2)(– 3) Distributive Property = – 2 n + 6 Simplify. – 2 n + 6

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