1. POD 12g + (6 + 4g) 12g + (4g + 6) (12g + 4g) + 6 (16g) + 6 commutative
Simplify each expression. Justify each step.
12g + (6 + 4g)
12g + (4g + 6)
commutative
(12g + 4g) + 6
associative
(16g) + 6

2. POD
Use mental math.
5 × 123
5(100) + 5(20) + 5(3)
615

3. 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

4. 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.

5. I do… You watch
8(-9+4) = 8(-9) + 8(4) =
= -40

6. Use mental math to solve.
I do… You watch
Use mental math to solve.
6 × 15
6(10) + 6(5)
60+ 30 90

7. Whiteboard time
(12 − 8)9
9(12) − 9(8)
108 − 72 36

8. Whiteboard time
4(x + 7)
4(x) + 4(7)
4x + 28

9. Whiteboard time
5(-3x + 7y)
5(-3x) + 5(7y)
-15x + 35y

10. Use mental math to solve.
Whiteboard time
Use mental math to solve.
5 × 35
5(30) + 5(5)
175

11. Use mental math to solve.
Whiteboard time
Use mental math to solve.
3 × 124
3(100) + 3(20) + 3(4)
372

12. Whiteboard time
-5( -2 – 18)
-5(-2) − (-5)(18)
10 − (-90)
100

13. Whiteboard time
3( )
3(-4) + 3(12) 24

14. Whiteboard time
12( 2x + 3)
12(2x) + 12(3)
24x +36

15. Whiteboard time
-2g( 4y + 2)
-2g(4y) + -2g(2)
-8gy + -4g

16. Use mental math to solve.
Whiteboard time
Use mental math to solve.
7 × 14
7(10) + 7(4)
70+ 28 98

17. Use mental math to solve.
Whiteboard time
Use mental math to solve.
9 × 22
9(20) + 9(2)
198

18. Rename $19.95 as $20.00−$0.05 9(20 − 0.05) 9(20) − 9(0.05)
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