2.4Combined Operations (BODMAS)

Brackets
Orders: powers and roots
Division and Multiplication, left to right
Addition and Subtraction, left to right

When negatives are present, the most common error is ignoring BODMAS and calculating left to right. Always apply BODMAS first, then handle the signs.

BODMAS with negatives

Evaluate $\displaystyle (-3)^2 - 4 \times (-5) + [8 - (\sqrt{49} + 1)]$ .

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(-3)^2 = 9

and

\sqrt{49} = 7

(-3)^2 - 4 \times (-5) + [8 - (\sqrt{49} + 1)]

= 9 - 4 \times (-5) + [8 - (7 + 1)] \quad \scriptsize\textit{B and O}

= 9 - 4 \times (-5) + 0 \quad \scriptsize\textit{brackets}

= 9 - (-20) + 0 \quad \scriptsize\textit{D and M}

= 9 + 20 + 0 \quad \scriptsize\textit{A and S}

= 29

Now you try

Evaluate $7 \times (-8) + 5$ .

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7 \times (-8) + 5

= -56 + 5 \quad \scriptsize\textit{multiply first}

= -51

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