## 1.2 Learn Basic Properties and Operations

This lesson will help you learn the basic properties and rules that govern math problem-solving.

### 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: $$\begin{array}{c}5(12 - 3) = 5(12) - 5(3)\\ \,\,\,\;\;\;\;\;\; = 60 - 15\\ = 45\end{array}$$