Order of operations

The idea

Brackets first, then powers, then $\times$ and $\div$ from left to right, then $+$ and $-$ from left to right. The reciprocal of a number is $1$ divided by it, so the reciprocal of $\tfrac{2}{5}$ is $\tfrac{5}{2}$.

1. Work out anything in brackets.
2. Do powers and roots, then multiply and divide, then add and subtract.
3. $3 + 4 \times 2^2 = 3 + 4 \times 4 = 19$.

Watch out $\times$ and $\div$ have equal rank, as do $+$ and $-$: work them left to right, not multiplication first.