# 1.2 Learn Basic Properties and Operations

## Properties

The **distributive property** can be used when a number is multiplied by a sum or a difference. Instead of adding or subtracting first, we can multiply each number inside the parentheses by the number outside the parentheses. Then add or subtract.

Distributive property | $$a(b + c) = ab + ac$$ | $$a(b - c) = ab - ac$$ |

### Example

What does $$2(7 + 9)$$ equal?

One way to solve the problem is to add first and then multiply by 2. | $$2(7 + 9) = 2(16) = 32$$ |

Another way is to use the distributive property. Multiply each term inside the parentheses by 2 and then add. | $$\begin{array}{c}2(7 + 9) = 2(7) + 2(9)\\\,\,\,\,\,\,\,\,\,\,\, \,\,=14 + 18\\ = 32\end{array}$$ |

### Example

What does $$5(12 - 3)$$ equal?

Without the distributive property: | $$\,5(12 - 3) = 5(9) = 45$$ |

With the distributive property: | $$\begin{array}{c}5(12 - 3) = 5(12) - 5(3)\\ \,\,\,\;\;\;\;\;\; = 60 - 15\\ = 45\end{array}$$ |