# Identity property of multiplication

The identity property of multiplication states that the product of 1 and any number is that number. Generally,

1 × a = a × 1 = a

where a is any number or expression.

Examples

1. 379 × 1 = 1 × 379 = 379

2. 0.0007 × 1 = 1 × 0.0007 = 0.0007

3. 146739 × 1 = 1 × 146739 = 146739

Regardless how small or large the number being multiplied by 1, the result is still the number. The identity property applies to algebraic expressions too:

4. (x + 1) × 1 = 1 × (x + 1) = (x + 1)

If we set the problems up in terms of repeated addition, we can see how the identity property works. Think of 1 × a as there being 1 group of a. No matter how large or small a is, there is 1 group of a, so multiplying a objects by 1 will always result in there being a total of a objects.

Example

Draw 1 group of 3 objects, 1 group of 7 objects, and 1 group of 10 objects:

In all 3 cases, the number of circles is equal to the number being multiplied by 1.