This presentation about Math Law, how we learn about commutative, associative and distributive law with easy way.

1. Math Properties
Commutative, Associative,
Distributive, Identity, and Zero
Properties
𝐴 ∗ 𝐵 = 𝐵 ∗ 𝐴

2. What are properties?
Math Properties are rules in math.
Properties are always true for every
number.
**Once you go beyond the set of Real numbers the properties may no longer hold.

3. Commute
• To commute means to travel from one place
to another.
• For example, you commute to school in the
morning.

4. Commutative Property
• Just like you commute from home to school, a
number may commute from one spot to
another.
• A + B = B + A (The numbers change places.)
• This is called the commutative property of
addition.
• Ex) 2 + 3 = 3 + 2
• Both 2 + 3 and 3 + 2 equal 5.

5. The commutative property may be used with
addition as seen previously and also with
multiplication.
• A * B = B * A
• Ex) 3 * 5 = 5 * 3
• Both 3 * 5 and 5 * 3 equal 15.
• This is called the commutative property of
multiplication.

6. Associate
• An associate is a friend or someone
you work with.
• For example, the head cheerleader is
an associate of the school mascot.

7. Now imagine the football team played a late game
and the cheerleader and mascot forgot to study for
the math test.
Suddenly the cheerleader associates
with someone else.

8. Associative Property
The associative property is when a number
associates with a different number.
A + (B + C)
(A + B) + C
A + + C
B

9. Associative Property
• (A + B) + C = A + (B + C) is called the
associative property of addition.
• Ex) (2 + 3) + 4 = 2 + (3 + 4)
• The order in which you add does not change
your answer.
• A * (B * C) = (A * B) * C is called the
associative property of multiplication.

10. Identity
• Your identity is who you are.
• Changing your clothes or getting a new haircut
does not change your identity.
• Your identity remains the same.

11. Identity Property of Addition
• A number also has an identity
• The identity of a number is the value of the
number
• The additive identity is the number that when
added to another number does not change
the identity of the original number
• 3 + __ = 3 (What goes in the blank?)
0

12. Zero
• The additive identity is zero.
• We can add zero to any number
and the answer is the original
number.

13. Identity Property of Multiplication
• We also have a multiplicative identity
• 3 * __ = 3 (What goes in this blank?)
• We can multiply any number by one and the
answer will be the original number.
1

14. Identity Properties
Identity Property of Addition
A + 0 = A
Identity Property of Multiplication
A * 1 = A

15. Zero Property
• The zero property sounds just like what it is, a
property about zero.
• A * 0 = 0
• The zero property tells us that any number
multiplied by zero equals zero.

16. Summary
Property Name Rule
Commutative Property of Addition A + B = B + A
Commutative Property of Multiplication A * B = B * A
Associative Property of Addition A + (B + C) = (A + B) + C
Associative Property of Multiplication A * (B * C) = (A * B) * C
Identity Property of Addition A + 0 = A
Identity Property of Multiplication A * 1 = A
Zero Property A * 0 = 0

17. Distribute
• Distribute means to deliver or pass out
• If we distribute food to three boxes, we put
food in each of the three boxes

18. Distributive Property
• A(B + C) = A*B + A*C
• The A is the food and the boxes are B and C.
• We pass out A to each of B and C.
• In this case that means that we multiply A by
both B and C separately and then add the
resulting products.

19. Ex) 4(X + 3)
4
X 3
4X 12
=4X + 12

20. Now you try these examples.
1) 5(X + 3) =
2) 7(X + 4) =
3) 2(Z -3) =
5X + 15
7X + 28
2Z - 6

21. Summary
Property Name Rule
Commutative Property of Addition A + B = B + A
Commutative Property of Multiplication A * B = B * A
Associative Property of Addition A + (B + C) = (A + B) + C
Associative Property of Multiplication A * (B * C) = (A * B) * C
Identity Property of Addition A + 0 = A
Identity Property of Multiplication A * 1 = A
Zero Property A * 0 = 0
Distributive Property A(B + C) = A*B + A*C