1. Properties of Addition & Multiplication

2. Why do we need rules or properties in math?
Lets see what can happen if we didn’t have rules.

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

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

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

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

8. As you can see, when you have two lengthsb
As you can see, when you have two lengths
a and b, you get the same length whether you put
a first or b first. b a

9. b a a b
The commutative property of multiplication says that you may multiply quantities in any order and you will get the same result. When computing the area of a rectangle it doesn’t matter which side you consider the width, you will get the same area either way.

10. Commutative Property
Practice: Show the commutative property of each number sentence. =
42 x 77 =
5 + y =
7(b) =

11. Commutative Property
Practice: Show the commutative property of each number sentence. =
42 x 77 = 77 x 42
5 + y = y + 5
7(b) = b(7) or (b)7

12. + + to   to And the result will not change You can change
Keep in mind the  and  do not have to be numbers.
They can be expressions that evaluate to a number.

13. 17 17 Example: (2 * 7) + (8 – 5) (8 - 5) + (2 * 7) + _ * 8 5 2 7 + _ * 17 17

14. Lets see why subtraction and division are NOT commutative.

15. The commutative property: a + b = b + a and a * b = b * a
10 = = 21
Try this subtraction: – 4 = 4 – ÷ 4 = 4 ÷ 8
and division
≠ ≠ 0.5

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

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

18. 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?

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

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

21. Ella sold 37 necklaces for $20. 00 each at the craft fair
Ella sold 37 necklaces for $20.00 each at the craft fair. She is going to donate half the money she earned to charity. Use the Commutative Property to mentally find how much money she will donate. Explain the steps you used.
Math Connects Plus 6 Pg #22

22. Use the Associative Property to write two equivalent expressions for the perimeter of the triangle
Math Connects Plus 6
Pg #19

23. Six Friends are going to the state fair
Six Friends are going to the state fair. The cost of one admission is $9.50, and the cost for one ride on the Ferris wheel is $ Write two equivalent expressions and then find the total cost.
Math Connects Plus6
Pg #4