A.1 Order of Operations
A.1 Order of OperationsWhen 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.
- Parentheses
- Exponents & Square Roots
- Multiplication and Division
- 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}
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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}
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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}