1. POD 7 12g + (6 + 4g) − 10 + (-2g) 12g + (6 + 4g) +(-10) + (-2g)
Simplify the expression.
12g + (6 + 4g) − 10 + (-2g)
12g + (6 + 4g) +(-10) + (-2g)
12g + 4g + (-2g) (-10)
14g+ (-4)

2. Let’s take a look back at what we’ve learned so far in this unit…

3. Properties of Operations
Commutative: order
Associative: grouping
Distributive: sharing

4. terms
-4x x
constant
coefficient
like terms

5. An algebraic expression is in simplest form if it has no like terms and no parenthesis.
Follow these steps to simplify:
Change subtraction to adding the opposite
Look for like terms that can be moved closer to each other (commutative property)
Combine like terms and constants

6. Let’s take a closer look at the distributive property and how we can use it to simplify equations and do mental math:

7. 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
8( ) = 8(2) + 8(7) =
= 72

8. Example: 1
2 ( y + 2)
Share the number outside the parentheses with both terms inside
= 2(y) +2(2)
= 2y + 4

9. 5(-3x + 7y) 5(-3x) + 5(7y) -15x + 35y Example 2:
You are allowed to multiply these
5(-3x) + 5(7y)
-15x + 35y

10. Use mental math to solve.
Example 3:
Use mental math to solve.
6 × 15
6(10) + 6(5)
60+ 30 90

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

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

13. Whiteboard time
12( 2x − 3)
12(2x) − 12(3)
24x − 36

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

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

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

17. Let’s keep practicing:
Pg worksheet

19. POD #8 basic advanced 12m + 12 + 3m − (-6) 5(3v + 2) + 2(-2v + 6v)

20. Take out last nights HW:
Pg worksheet

21. (12 − 8)9 9(12) − 9(8) 108 − 72 36 Whiteboard time
This is just like all the other problems. The only difference is that the 9 is on the other side.
(12 − 8)9
9(12) − 9(8)
108 − 72 36

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

23. Whiteboard time
10x(4x − 2)
10x(4x) − 10x(2)
40x2 − 20x

24. Whiteboard time
1 2 (10g + 28)
1 2 (10g) (28)
5g + 14

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

26. 5 × 123 5(100) + 5(20) + 5(3) 500 + 100 + 15 615 Whiteboard time
Use mental math.
5 × 123
5(100) + 5(20) + 5(3)
615

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

28. How can the distributive property help us solve complicated problems?

29. 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

30. Let’s keep practicing:
BIM pg #2-26 evens

31. POD basic advanced 8 × 34 7 × 231 8(30) + 8(4) 7(200) + 7(30) + 7(1)
Use mental math to solve:
basic
advanced
8 × 34
7 × 231
8(30) + 8(4)
7(200) + 7(30) + 7(1)
272
1617