In math, what is the definition of order of operations?
A math equation can look intimidating — until you use the order of operations to work it out bit by bit. If multiplication, division, powers, addition, parentheses, and so on, are all contained in one problem, you work them out in a particular order (thus, the order of operations).
- To begin, work within parentheses ( ), then brackets [ ], and then braces { } from innermost and work outward. For example: 2{1 + [4(2+1) + 3]} = 32
- Simplify exponents and roots working from left to right.
- Do multiplication and division, whichever comes first left to right.
- Do addition and subtraction, whichever comes first left to right.
An easy way to remember the order is Please Excuse (My Dear) (Aunt Sally), or PEMDAS
Parentheses (followed by brackets and then braces)
Exponents (and roots)
Multiplication
Division
Addition
Subtraction
Give it a try! Simplify 10 - 3 x 6 + 102 + (6 + 1) x 4
First, parentheses,
10 - 3 x 6 + 102 + (6 + 1) x 4 = 10 - 3 x 6 + 102 + (7) x 4
Then, exponents,
102 = 10 x 10 = 100, so
10 - 3 x 6 + 102 + (7) x 4 = 10 - 3 x 6 + 100 + (7) x 4
Then, multiplication,
10 - 3 x 6 + 100 + (7) x 4 = 10 - 18 + 100 + 28
There's no division involved, so move on to addition and subtraction (left to right),
10 - 18 + 100 + 28 = -8 + 100 + 28
= 92 + 28
= 120