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P O D. Simplify each expression. Justify each step. 12g + (6 + 4g). 12g + (4g + 6). commutative. (12g + 4g) + 6. associative. (16g) + 6. P O D. Use mental math. 5 × 123. 5(100) + 5(20) + 5(3). 500 + 100 + 15. 615.

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P O D

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P o d

POD

Simplify each expression. Justify each step.

12g + (6 + 4g)

12g + (4g + 6)

commutative

(12g + 4g) + 6

associative

(16g) + 6


P o d

POD

Use mental math.

5 × 123

5(100) + 5(20) + 5(3)

500 + 100 + 15

615


P o d

The Distributive Property states that to multiply a sum or difference by a number, multiply each term inside the parenthesis by the number outside the parenthesis.

a( b + c ) = ab + ac

a( b – c ) = ab − ac


P o d

2 ( y + 2) = 2(y) +2(2)

= 2y + 4

The expressions 2(y+2) and 2y+4 are equivalent expressions. No matter what y is, these expressions have the same value.


P o d

8(-9+4) = 8(-9) + 8(4)

= -72 + 32

= -40


P o d

Whiteboard time

5(-9 + 11)

5(-9) + 5(11)

-45 + 55

10


P o d

Whiteboard time

7(10 − 5)

7(10) − 7(5)

70 − 35

35


P o d

Whiteboard time

(12 − 8)9

9(12) − 9(8)

108 − 72

36


P o d

Whiteboard time

4(x + 7)

4(x) +4(7)

4x + 28


P o d

Whiteboard time

5(-3x + 7y)

5(-3x) + 5(7y)

-15x + 35y


P o d

Whiteboard time

Use mental math to solve.

6 × 15

6(10) + 6(5)

60+ 30

90


P o d

Whiteboard time

Use mental math to solve.

5 × 35

5(30) + 5(5)

150+ 25

175


P o d

Whiteboard time

Use mental math to solve.

3 × 124

3(100) + 3(20) + 3(4)

300 + 60 + 12

372


P o d

Whiteboard time

-5( -2 – 18)

-5(-2) − (-5)(18)

10 − (-90)

100


P o d

Whiteboard time

3(-4 + 12)

3(-4) + 3(12)

-12 + 36

24


P o d

Whiteboard time

12( 2x + 3)

12(2x) + 12(3)

24x +36


P o d

Whiteboard time

-2g( 4y + 2)

-2g(4y) + -2g(2)

-8gy + -4g


P o d

Whiteboard time

Use mental math to solve.

7 × 14

7(10) + 7(4)

70+28

98


P o d

Whiteboard time

Use mental math to solve.

9 × 22

9(20) + 9(2)

180+ 18

198


P o d

Mr. Ito needs to buy batting helmets for the baseball team. The helmets he plans to buy are $19.95 each. Find the total cost if Mr. Ito needs to buy 9 batting helmets for the team.

Rename $19.95 as $20.00−$0.05

9(20 − 0.05)

9(20) − 9(0.05)

$180 − $0.45

$179.55


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