Order of Operations with Integers

When a calculation mixes operations, everyone must agree on the order — otherwise the same sum gives different answers. The order is BODMAS:

1. Brackets
2. Of / Division and Multiplication (left to right)
3. Addition and Subtraction (left to right)

This holds for integers too, signs included.

Worked example 1. $-5 + 2 \times 4$. Multiply first: $2 \times 4 = 8$, then $-5 + 8 = 3$.

Worked example 2. $(6 - 10)\times 3$. Brackets first: $6 - 10 = -4$, then $-4 \times 3 = -12$.

Worked example 3. $-20 \div (2 - 6)$. Brackets: $2 - 6 = -4$, then $-20 \div (-4) = 5$.

Exam checkpoint

A long integer calculation is not read strictly left to right. Work inside brackets first, then powers, then multiplication or division, then addition or subtraction. Keep negative numbers in brackets when they are bases of powers, so $(-3)^2$ is clearly different from $-3^2$.

Short worked example. $18-3(4-7)=18-3(-3)=18-(-9)=27$. The bracket creates a negative, and subtracting that negative increases the total.