1. Unit 1, Lesson 6: The Number Properties
Objective: To learn the number properties.

2. The Number Properties
You use operations such as addition, subtraction, multiplication, and division to solve expressions.
These operations follow certain properties that are always true.

3. What rule can you make about adding zero?
The Number Properties
Tell if it is true or false.
a) = 8
b) = 0
c) 8 = 0 + 8
d) a + 0 = a
e) 0 + a = 0
What rule can you make about adding zero?

4. Identity Property of Addition
The Number Properties
Identity Property of Addition
- adding zero does not change the value of a number
x + 0 = x

5. The Number Properties 2. Tell if it is true or false. a) 5 ● 1 = 1
c) 1 ● 5 = 15
d) a ● 1 = a
e) 1 ● a = 1
What rule can you make about multiplying by one?

6. 2) Identity Property of Multiplication
The Number Properties
2) Identity Property of Multiplication
- Multiplying by 1 does not change the value of a number
x ● 1 = x

7. What rule can you make about the order of numbers?
The Number Properties
3. Tell if it is true or false.
a) = 1 + 5
b) 5 – 1 = 1 – 5
c) =
d) a + b = b + a
e) 10 – 8 = 8 – 10
f) 4 ● 1 = 1 ● 4
g) 4 ÷ 2 = 2 ÷ 4
What rule can you make about the order of numbers?

8. 3) The Commutative Property (addition & multiplication)
The Number Properties
3) The Commutative Property
(addition & multiplication)
-The order of numbers does not matter!
a + b = b + a
ab = ba

9. What rule can you make about the grouping of numbers?
The Number Properties
4. Tell if it is true or false.
a) (5 + 1) + 2 = 5 + (1 + 2)
b) 9 + (3 + 2) =(9 + 3) + 2
c) (8 – 2) – 1 = 8 – (2 – 1)
d) 4 ● (1 ● 2) = (4 ● 1) ● 2
e) 4 ÷ (2 ÷ 1)= (4 ÷ 2) ÷ 1
What rule can you make about the grouping of numbers?

10. 3) The Associative Property (addition & multiplication)
The Number Properties
3) The Associative Property
(addition & multiplication)
-You can regroup numbers!
(a + b) + c = a + (b + c)
(a ● b) ● c = a ● (b ● c)

11. Practice Identify the property below: 5 + 14 = 14 + 5 0 + 11 = 11
8 ● (4 ● 7) = (8 ● 4) ● 7
6 = 1 ● 6
Write an example for the property
5) The Associative Property of Addition
6) The Commutative Property of Multiplication