Order of Operations
When performing arithmetic operations there is exactly one correct answer. To avoid confusion, mathematicians have devised a standard order of operations for calculations involving more than one arithmetic operation.
1st: Perform any calculations inside parentheses, doing the innermost first.
2nd: Simplify any exponential expressions.
3rd: Work all multiplications and divisions, from left to right, as they appear.
4th: Work all additions and subtractions, from left to right, as they appear.
So you do not get confused remember PEMDAS which stands for Parentheses, Exponents, Multiplication-Division, Addition-Subtraction.
In California, we say Powerful Earthquakes May Deliver After-Shocks.
Example 1:
Simplify. 2 + 3 × 4
Multiplication must be done before addition.
= 2 + 12
= 14
Example 2:
Simplify. 1 + 3 × 42
Exponential expressions are simplified before multiplication or addition.
= 1 + 3 × 16
Multiplication is done before addition.
= 1 + 48
= 49
Example 3:
Simplify. 3 + 2(5 – 7)
Do parentheses first.
= 3 + 2(–2)
Multiply and then add.
= 3 + (–4)
= –1
Be especially careful with problems like the following.
(3 × 4)2 = 122 = 144 because parentheses come before exponents, BUT 3 × 42 = 48 because exponents come before multiplication.
(–4)2 = (–4)(–4) = 16 BUT –42 = – 4 × 4 = –16
3 + 4(5 + 6) ≠ 7(5 + 6) because multiplication gets done before addition.
So, 3 + 4(5 + 6) = 3 + 4(11) = 3 + 44 = 47.
