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Order of Operations Solutions

Use the acronym PEMDAS to help you remember the order to simplify expressions.
PEMDAS stands for P arentheses, E xponents, M ultiplication/ D ivision, and A ddition/ S ubtraction.
Parentheses means any grouping symbol including absolute value bars.
Exponents include any square roots since exponents and square roots are related.
Multiplication/division are simplified from left to right across the expression.
Addition/subtraction are simplified from left to right across the expression .
The addition/subtraction symbols are natural breaks in the expression. You can simplify a large expression into a few smaller ones by adding grouping symbols where you find addition and subtraction symbols.

Example 1

Evaluate.

$3^{3} + 4 \div {(\frac{1}{2})}^{2} - 4 {(1 - 3)}^{2} + |- 5 + 3| + \sqrt{25}$

Implement

$3^{3} + 4 \div {(\frac{1}{2})}^{2} - 4 {(- 2)}^{2} + |- 2| + \sqrt{25} 27 + 4 \div \frac{1}{4} - 4 (4) + 2 + 5 27 + 4 \cdot 4 - 16 + 2 + 5 27 + 16 - 16 + 2 + 5 34$

Explain

Group the expression using the addition and subtraction symbols
P: parentheses
E: exponents
M/D: multiply or divide from left to right
A/S: add or subtract from left to right

Example 2

Evaluate.

$- 4 |- 3 - 2| + 2^{3} - {(5 + 1)}^{2} \div 12$

Implement

$- 4 | - 5 | + 2^{3} - {(6)}^{2} \div 12 - 4 (5) + 8 - 36 \div 12 - 20 + 8 - 3 - 15$

Explain

Group the expression using the addition and subtraction symbols