In mathematics, calculations have to be performed in the correct order—called the order of operations. Multiplication and division are computed before addition and subtraction, and exponents are computed first of all. If you want to change the order of operations, parentheses are the tool you need to use. What’s inside a pair of parentheses has to be calculated before the rest of the expression.

Example 1

Find $2 + 3 \times 6$ and $(2 + 3) \times 6$

For $2 + 3 \times 6$ , you must find $3 \times 6$ first, because multiplication is computed before addition:

2 + \underset{18}{\underset{⏟}{3 \times 6}} = 2 + 18 = 20

For $(2 + 3) \times 6$ , you must find $2 + 3$ first, because that part is inside parentheses:

\underset{5}{\underset{⏟}{(2 + 3)}} \times 6 = 5 \times 6 = 30

In this case, one of the expressions is equal to 20, and the other is equal to 30, so you can see how important parentheses can be! It’s important to perform the operations in the correct order to avoid getting the wrong answer!