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Order of operations

What is the value of this expression? $$$ (4-2)^3 - 5\div (2 + 3) $$$

When there are several operations in an expression, we must do them in a specific order.

The rule is BIDMAS: Brackets first; then indices; division and multiplication next; addition and subtraction last.

$$\Torange{5 \times 3} - 2 = \Tred{15 -2} = 13$$ : multiplication then subtraction.

\begin{align*} \Torange{(3+4)}^2 &+ 3 \times 7 \\ &= \Tred{7^2} + 3\times 7= 49 + \Tgreen{3\times 7} = \Tblue{49 + 21} = 70.\\ \Torange{(4-2)}^3 &- 5\div \Torange{(2 + 3)}\\ & = \Tred{2^3} - 5\div 5 = 8 - \Tgreen{5\div 5} = \Tblue{8 - 1} = 7. \end{align*}

When we work through addition and subtraction, we work from left to right. For example, we work out $$2-3+5$$ as $$$\Tred{2-3} +5 = \Tred{-1} + 5 = 4,$$$ not as $$2 - (\Tred{3+5}) = 2 - \Tred{8} = -6$$.

The same applies to multiplication and division.