# Identity property of multiplication

The identity property of multiplication, also called the multiplication property of one says that a number does not change when that number is multiplied by 1.

To help students get the point, I usually pick a number very big such as 25 billion and tell them to times this number by 1

If they get the point, they will say 25 billion and it proves that the size of the number does not matter.

Believe it or not, some students were confused and gave me a different answer. I hope you got the point!

Other examples

3 × 1 = 3

10 × 1 = 10

6 × 1 = 6

68 × 1 = 68

1 × 4 = 4

1 × -9 = - 9

x × 1 = x

(a + b) × 1 = a + b

Multiplicative inverse property

If you multiply two numbers and the product is 1, we call the two numbers multiplicative inverses or reciprocals of each other

For example, 4 is the multiplicative inverse of 1/4 because 4 × 1/4 = 1

1/4 is also the multiplicative inverse of 4 because 1/4 × 4 = 1

Notice that the multiplicative inverse of 1 is 1. In fact, 1 and -1 are the only two numbers that can be their own multiplicative inverse

Notice also that any number divided by 1 return the same number

We call this the identity property of division

Examples

2 ÷ 1 = 2

50 ÷ 1 = 50

-5 ÷ 1 = -5

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