Properties 0f

Real

NumbersI can’twait until we

learn about fake numbers!

The properties of real numbers help us simplify math expressions

and help us better understand the concepts of algebra.

Properties 0f Real

Numbers

a + b = b + a

Example: 7 + 3 = 3 + 7

Two real numbers can be added in either order to achieve the same sum.

Does this work with subtraction? Why or why not?

Commutative Property of Addition

a x b = b x a

Example: 3 x 7 = 7 x 3

Two real numbers can be multiplied in either order to achieve the same product.

Does this work with division? Why or why not?

Commutative Property of Multiplication

(a + b) + c = a + (b + c)

Example: (29 + 13) + 7 = 29 + (13 + 7)

When three real numbers are added, it makes no difference which are added first.

Notice how adding the 13 + 7 first makes completing the problem easier mentally.

Associative Property of Addition

(a x b) x c = a x (b x c)

Example: (6 x 4) x 5 = 6 x (4 x 5)

When three real numbers are multiplied, it makes no difference which are multiplied first.

Notice how multiplying the 4 and 5 first makes completing the problem easier.

Associative Property of Multiplication

a + 0 = a

Example: 9 + 0 = 9

The sum of zero and a real number equals the number itself.

Memory note: When you add zero to a number, that number will always keep its identity.

Additive Identity Property

a x 1 = a

Example: 8 x 1 = 8

The product of one and a number equals the number itself.

Memory note: When you multiply any number by one, that number will keep its identity.

Multiplicative Identity Property

TIME OUT!!!

What’s wrong?

My brain’sabout to explode

with all of this crazyproperty stuff!

Hang in there, Sparky! We only have a few more.

Properties 0f Real

Numbers

a(b + c) = ab + ac or a(b – c) = ab – ac

Example: 2(3 + 4) = (2 x 3) + (2 x 4)or

2(3 - 4) = (2 x 3) - (2 x 4)

Distributive Property is the sum or difference of two expanded products.

Distributive Property

a + (-a) = 0

Example: 3 + (-3) = 0

The sum of a real number and its opposite is zero.

Additive Inverse Property

 

Multiplicative Inverse

Go forth and use them wisely!

Use them confidently!And use them well, my

friends!

You are now ONE with the properties

of real numbers.

Sparky’s fixin’to become one with a triple decker, chili-

fire bean burrito!My job here is done!