Algebra

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# Properties of Multiplication

## The Four Properties of Multiplication with Examples

**Associative Property:** The order that multiplied numbers are grouped does not affect the product.

Example: (a×b)×c = b×(c×a)

**Commutative Property: **Changing the order of multiplied numbers does not affect the product.

Example: a×b = b×a

**Distributive Property:** Multiplying the sum of a quantity by a number is equivalent to multiplying that number by each of the numbers within the quantity, then summing them.

Example: a(b + c + d) = a×b + a×c + a×d

**Identity Property:** The product of any number and 1 is equal to the number.

Example: 1×a = a

### Lesson Summary

*These four properties are fundamental to algebra and all other math, science, and engineering topics that use algebra.* Although some of the properties may seem obvious, that are the foundation of being able to solve equations. You use these properties already, even if you never thought about their name or the property itself while using it.