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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.

$3^3+4÷{\left(\frac{1}{2}\right)}^2–4{\left(1–3\right)}^2+\left|–5+3\right|+\sqrt{25}$

Implement	Explain
	Group the expression using the addition and subtraction symbols
$3^3+4÷{\left(\frac{1}{2}\right)}^2–4{\left(–2\right)}^2+\left|–2\right|+\sqrt{25}$	P: parentheses E: exponents
$$\begin{gathered} 27+4÷\frac{1}{4}–4\left(4\right)+2+5 \\ 27+4·4–16+2+5 \end{gathered}$$	M/D: multiply or divide from left to right
$$\begin{gathered} 27+16–16+2+5 \\ \overline{)34} \end{gathered}$$	A/S: add or subtract from left to right

Example 2

Evaluate.

$–4\left|–3–2\right|+2^3–{\left(5+1\right)}^2÷12$

Implement	Explain
$$\begin{gathered} –4|‘5|+2^3–{\left(6\right)}^2÷12 \\ ‘4\left(5\right)+8–36÷12 \\ ‘20+8–3 \\ \overline{)‘15} \end{gathered}$$	Group the expression using the addition and subtraction symbols