Inverses

Additive Inverse

Inverses are related to the properties of real numbers.

The additive inverse is the same number with the opposite sign – it is sometimes just called the

opposite.

The additive inverse of + 5 is - 5The opposite of - 3 is + 3.

Additive Inverse

When you add a number and its opposite, your answer will always be zero.

+ 5 – 5 = 0

Zero is the identity element for addition

The Identity Element for Addition

Zero is called the identity element for addition because if you add zero to any number, you get

identically the same number back again.

2 + 0 = 2

Additive Inverse

When you add a number and its additive inverse, your answer will always be the identity element for

addition.

Multiplicative Inverse

Inverses are related to the properties of real numbers.

The multiplicative inverse is the “flipped” version of the number - it is sometimes called the reciprocal.

The multiplicative inverse of 5 is

The reciprocal of is

1

52

3

3

2

Multiplicative Inverse

When you multiply a number and its reciprocal, your answer will always be one.

One is the identity element for multiplication

15 1

52 3

13 2

The Identity Element for Multiplication

One is called the identity element for multiplication because if you multiply any number by 1, you get

identically the same number back again.

2 x 1 = 2

Multiplicative Inverse

When you multiply a number and its multiplicative inverse, your answer will always be the identity

element for multiplication.

The Additive and Multiplicative Inverses

The additive inverse is the “opposite”

The multiplicative inverse is the “reciprocal”.

When you add or multiply a number by its inverse, you get the identity element for that operation.