This document discusses properties of addition and multiplication. It explains the commutative, associative, identity, and distributive properties and provides examples of how each applies to addition and multiplication. Practice problems are included for students to identify which properties are being used and to solve expressions using the properties.

1. C O L E G I O M Y R A N G 5 T H G R A D E
M R S . S H I A R A A G O S T O
Properties of Addition and
Multiplication

2. Properties of Addition and Multiplication
 There are 4 main properties, 3 of which are used
both in Addition and Multiplication.
 Associative (+) (×)
 Commutative (+) (×)
 Identity (+) (×)
 Distributive

3. Properties of Addition
 Commutative Property of Addition
 If you change the order of addends the sum stays the same.
 12 + 24 = 24 + 12
 Associative Property of Addition
 If you change the grouping of addends the sum stays the same.
 15 + (52 + 6) = (15 + 52) + 6
 Identity Property of Addition
 The sum of any number and zero is the same number.
 28 + 0 = 28

4. Properties of Multiplication
 Commutative Property of Multiplication
 If you change the order of factors the product stays the same.
 12 x 24 = 24 x 12
 Associative Property of Multiplication
 If you change the grouping of factors the product stays the
same.
 15 x (52 x 6) = (15 x 52) x 6
 Identity Property of Multiplication
 The product of any number and one is the same number.
 28 x 1 = 28

5. Distributive Property
 The Distributive Property states that multiplying a
sum by a number is the same as multiplying each
addend by the number and then adding the
products.
 5 x (17 + 8) = (5 x 17) + (5 x 8)
 It can also be used with subtraction:
 2 x (10 – 8) = (2 x 10) – (2 x 8)

6. Properties Practice
 Identify the properties that are used in each exercise.
 52 + 85 = 85 + 52
 65 x 3 = 3 x 65
 12 x (6 + 8) = (12 x 6) + (12 x 8)
 5 + 0 = 5

7. Properties Practice
 Identify the properties that are used in each exercise.
 52 + 85 = 85 + 52
 Commutative Property of Addition
 65 x 3 = 3 x 65
 Commutative Property of Multiplication
 12 x (6 + 8) = (12 x 6) + (12 x 8)
 Distributive Property
 5 + 0 = 5
 Identity Property of Addition

8. Solve Using Properties
 What property(ies) can you use to solve the following
exercises?
 (24 x 5) – (24 x 1)

9. Solve Using Properties
 What property(ies) can you use to solve the following
exercises?
 (24 x 5) – (24 x 1)
 We can use the Distributive Property.
 24 x (5 – 1)
 24 x 4
 = 96

10. Solve Using Properties
 9 + 65 + 1

11. Solve Using Properties
 9 + 65 + 1
 Using the Commutative Property
 9 + 1 +65
 10 + 65
 = 75
 Using the Associative Property
 9 + (65 +1)
 9 + 66
 = 75

12. Solve Using Properties
 12 x ___ = 12
 49 + 56 = ___+ 49
 60 + (52 + ___)= (60+ 52) + 39
 8 x 298
 8 x (300 - ___ )
 (8 x 300) – (8 x ___)
 _____ – ____
 =

13. Solve Using Properties
 12 x ___ = 12
 Identity Property of Multiplication
 49 + 56 = ___+ 49
 Commutative Property of Addition
 60 + (52 + ___)= (60+ 52) + 39
 Associative Property of Multiplication
 8 x 298
 8 x (300 - ___ )
 (8 x 300) – (8 x ___)
 _____ – ____
 =
56
39
1
1
1
2,400 8
2,392
 Distributive Property