Properties of Numbers

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

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

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

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

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

The commutative property of multiplication: a b = b a

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

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

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

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

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)

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

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

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

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

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

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

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