1. Properties of Addition & Multiplication

2. Before We Begin… What is a VARIABLE? A variable is an unknown amount in a number sentence represented as a letter: 5 + n 8x 6(g) t + d = s

3. Before We Begin… What do these symbols mean? ( ) = multiply: 6(a) or group: (6 + a) * = multiply · = multiply ÷ = divide / = divide

4. Commutative Property COMMUTE To COMMUTE something is to change it COMMUTATIVE The COMMUTATIVE property says that the order of numbers in a number sentence can be changed COMMUTATIVE Addition & multiplication have COMMUTATIVE properties

5. Commutative Property Examples: (a + b = b + a) 7 + 5 = 5 + 7 9 x 3 = 3 x 9 Note: subtraction & division DO NOT have commutative properties!

6. Commutative Property Practice: Show the commutative property of each number sentence. 1. 13 + 18 = 2. 42 x 77 = 3. 5 + y = 4. 7(b) =

7. Commutative Property Practice: Show the commutative property of each number sentence. 1. 13 + 18 = 18 + 13 2. 42 x 77 = 77 x 42 3. 5 + y = y + 5 4. 7(b) = b(7) or (b)7

8. Associative Property ASSOCIATE To ASSOCIATE something is join it, partner it, or combine it ASSOCIATIVE The ASSOCIATIVE property says that the way we group numbers in a number sentence can be changed ASSOCIATIVE Addition & multiplication have ASSOCIATIVE properties

9. Associative Property Examples: (a + b) + c = a + (b + c) 2 + (3 + 4) = (2 + 3) + 4 5 x (3 x 7) = (5 x 3) x 7 Note: subtraction & division DO NOT have associative properties!

10. Associative Property Practice: Show the associative property of each number sentence. 1. (7 + 2) + 5 = 2. 4 x (8 x 3) = 3. 5 + (y + 2) = 4. 7(b x 4) =

11. Associative Property Practice: Show the associative property of each number sentence. 1. (7 + 2) + 5 = 7 + (2 + 5) 2. 4 x (8 x 3) = (4 x 8) x 3 3. 5 + (y + 2) = (5 + y) + 2 4. 7(b x 4) = (7b) x 4 or (7 x b)4

12. Identity Properties IDENTITY An IDENTITY is the state of being one’s self or staying the same IDENTITY The IDENTITY properties says that with certain operations, a number can stay the same ASSOCIATIVE Addition & multiplication have ASSOCIATIVE properties

13. Identity Properties Examples: a + 0 = a b x 1 = b Additive Identity: 7 + 0 = 7 (when you add 0 to a number, it stays the same) Multiplicative Identity: 7 x 1 = 7 (when you multiply a number by 1, it stays the same)

14. Identity Properties Practice: Show the ADDITIVE and MULTIPLICATIVE identity properties of each number. 1. 9 = 2. 17 = 3. 8m = 4. 5 + (6 x 9) =

15. Identity Properties Practice: Show the ADDITIVE and MULTIPLICATIVE identity properties of each number. 1. 9 = 9 + 0 and 9 x 1 2. 17 = 17 + 0 and 17 x 1 3. 8m = 8m + 0 and (8m) x 1 (why parentheses?) 4. 5 + (6 x 9) = 5 + (6 x 9) + 0 and 5 + (6 x 9) x 1

16. Distributive Property DISTRIBUTE To DISTRIBUTE something is give it out or share it. DISTRIBUTIVE The DISTRIBUTIVE property says that we can distribute a multiplier out to each number in a group to make it easier to solve DISTRIBUTIVE MULTIPLICATIONADDITION The DISTRIBUTIVE property uses MULTIPLICATION and ADDITION!

17. Distributive Property Examples: a(b + c) = a(b) + a(c) 2 x (3 + 4) = (2 x 3) + (2 x 4) 5(3 + 7) = 5(3) + 5(7) Note: Do you see that the 2 and the 5 were shared (distributed) with the other numbers in the group?

18. Distributive Property Practice: Show the distributive property of each number sentence. 1. 8 x (5 + 6) = 2. 4(8 + 3) = 3. 5 x (y + 2) = 4. 7(4 + b) =

19. Distributive Property Practice: Show the distributive property of each number sentence. 1. 8 x (5 + 6) = (8 x 5) + (8 x 6) 2. 4(8 + 3) = 4(8) + 4(3) 3. 5 x (y + 2) = (5y) + (5 x 2) 4. 7(4 + b) = 7(4) + 7b

20. Zero Property MULTIPLICATION ZERO Only MULTIPLICATION has a ZERO property. ZERO ZERO ZERO The ZERO property of multiplication says that when we multiply any number by ZERO, the answer is always ZERO.

21. Zero Property Examples: a(0) = 0 2 x 0 = 0 5(3 + 7) x 0 = 0

22. Zero Property Practice: Show the zero property of multiplication for each number or number sentence. 1. 5 2. 4k 3. 9 + (d + 6)

23. Zero Property Practice: Show the zero property of multiplication for each number or number sentence. 1. 5: 5 x 0 = 0 2. 4k: 4k (0) = 0 3. 9 + (d + 6): 9 + (d + 6) x 0 = 0

24. POP QUIZ! Tell which property each sentence represents: 1. 5 + 0 = 5 2. 9 x 8 = 8 x 9 3. (7c + 1) x 0 = 0 4. (8 + 4) + 7 = 8 + (4 + 7) 5. 9a + (5 x 4) x 1 = 9a + (5 x 4) 6. 3(4 + 5) = 3(4) + 3(5)

25. POP QUIZ ANSWERS! Tell which property each sentence represents: 1. 5 + 0 = 5 (add. identity) 2. 9 x 8 = 8 x 9 (commutative) 3. (7c + 1) x 0 = 0 (zero) 4. (8 + 4) + 7 = 8 + (4 + 7) (associative) 5. 9a + (5 x 4) x 1 = 9a + (5 x 4) (mult. identity) 6. 3(4 + 5) = 3(4) + 3(5) (distributive)