1. Properties of
Numbers

2. That long traffic-jammed trip that your parents make to
work is called a commute.
When you think “commute,”
think movement.

3. Commutative Property: In addition and multiplication, numbers may be added or multiplied together in any order.

4. The commutative property of addition:
5 + 2 = 7 so
and
2 + 5 = 7
5 + 2 = 2 + 5
algebraically
a + b = b + a

5. The commutative property of addition:
Notice, the a and b move around. They “commute.”
a + b = b + a

6. The commutative property of multiplication:
3 x 4 = 12 so
and
4 x 3 = 12
3 x 4 = 4 x 3
algebraically
a b = b a

7. The commutative property of multiplication:
a b = b a

8. c a b a c b , & and sometimes b sometimes a associates with b
associates with c
sometimes a
associates with b
are friends
on a couch
they are
associates

9. Associative Property: In addition and multiplication, no matter how the numbers are grouped, the answer will always be the same.

10. The associative property of addition:
(2 + 3) + 4 = 2 + (3 + 4)
9 = 9
5 + 4 = 2 + 7
algebraically
(a + b) + c = a + (b + c)

11. The associative property of addition:
(a + b) + c = a + (b + c)

12. The associative property of multiplication:
(5 x 2) x 6 = 5 x (2 x 6)
60 = 60
10 x 6 = 5 x 12
algebraically
(a b) c = a (b c)

13. The associative property of multiplication:
(a b) c = a (b c)

14. 7
Seven, right?
Seven is its
“identity.”
Can you identify
this number?

15. What number
can we add to
that won’t change
its identity? 7

16. The additive identity property states that zero can be added to any number without changing its identity.
7 + 0 = 7
algebraically
x + 0 = x

17. times that won’t change its identity?
Is there a number
we can multiply
times that won’t change its identity? 7

18. The multiplicative identity property states that multiplying any number times one does not change the number’s identity.
7 x 1 = 7
algebraically
n 1 = n

19. Let’s Summarize: Commutative Properties: numbers move
Associative Properties:
numbers are regrouped
Identity Properties:
numbers stay the same