A.1 Order of Operations

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When performing a series of mathematical operations, begin with those inside parentheses or brackets. Next, calculate any exponents or square roots. This is followed by multiplication and division, and finally, addition and subtraction.

  1. Parentheses
  2. Exponents & Square Roots
  3. Multiplication and Division
  4. Addition and Subtraction

Example A.1

Simplify: $(5+\dfrac{9}{3})^{2}$

Answer
\begin{align} (5+\frac{9}{3})^{2} &=(5+3)^{2} &&\text{(Parentheses first, 9/3)}\\ &=8^{2}&&\text{(Add inside parentheses)}\\ &=64 &&\text{(Square 8)}\\
\end{align}

Example A.2

Simplify: $\dfrac{5+6+7}{3}$

Answer
\begin{align} \frac{5+6+7}{3} &=\frac{18}{3}  &&\text{(Simplify the numerator)}\\ &=6 &&\text{(Divide)}\\
\end{align}

Example A.3

Simplify: $\dfrac{2^{2}+3^{2}+4^{2}}{3-1}$

Answer
\begin{align} \frac{2^{2}+3^{2}+4^{2}}{3-1} &=\frac{4+9+16}{2} &&\text{(Exponents in the numerator)}\\ &=\frac{29}{2} &&\text{(Simplify the numerator)}\\ &=14.5 &&\text{(Divide)}\\\end{align}