Unit 1, Lesson 6:
The Number Properties
Objective: To learn the number
properties.
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.
The Number Properties
1. Tell if it is true or false.
a) 8 + 0 = 8
b) 0 + 8 = 0
c) 8 = 0 + 8
d) a + 0 = a
e) 0 + a = 0
What rule can you make about adding zero?
The Number Properties
1) Identity Property of Addition
- adding zero does not change the
value of a number
x+0=x
The Number Properties
2. Tell if it is true or false.
a) 5 ● 1 = 1
b) 1 ● 5 = 5
c) 1 ● 5 = 15
d) a ● 1 = a
e) 1 ● a = 1
What rule can you make about multiplying by one?
The Number Properties
2) Identity Property of Multiplication
- Multiplying by 1 does not change
the value of a number
x●1=x
The Number Properties
3. Tell if it is true or false.
a) 5 + 1 = 1 + 5
b) 5 – 1 = 1 – 5
c) 9 + 3 + 2 = 2 + 3 + 9
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?
The Number Properties
3) The Commutative Property
(addition & multiplication)
-The order of numbers does not
matter!
a+b=b+a
ab = ba
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?
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)
Practice
• Identify the property below:
1) 5 + 14 = 14 + 5
2) 0 + 11 = 11
3) 8 ● (4 ● 7) = (8 ● 4) ● 7
4) 6 = 1 ● 6
• Write an example for the property
5) The Associative Property of Addition
6) The Commutative Property of Multiplication