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Order of Operations: Using Parentheses
(4 + 6 + 4 + 23 + 28) ÷ 5 is an example of a numerical expression. Numerical expressions have numbers and operations.
- Consider the expression 3 + 7 2.
- What do you get if you add first and then multiply?
- What do you get if you multiply first and then add?
To avoid confusion, you can use parentheses. Parentheses mean that the calculations inside should be done first.
Examples:
Here the parentheses mean to multiply first: 3 + (7 2) = 3 + 14 = 17
Here the parentheses mean to add first: (3 + 7) 2 = 10 2 = 20
- Find the values of the following expressions:
- (6 2) + 5
- 6 (2 + 5)
- (8 ÷ 4) − 2
- 8 ÷ (4 − 2)
- (16 ÷ 4) 2
- 16 ÷ (4 2)
- (3 6) + (2 5) + (1 2)
In expressions such as (3 6) + (2 5) + (1 2) in the last problem, parentheses clarify the order in which operations should be done. Mathematicians have agreed on rules about the order in which operations should be done so that you do not always need to write parentheses.
Order of Operations
- Do calculations in parentheses first.
- Do all multiplications and divisions in order from left to right.
- Then do all additions and subtractions in order from left to right.