Arithmetic Expressions

An expression is a sum of terms. Brackets and the order of operations decide what to work out first; rearranging terms makes sums easier.

Key ideas

• Work out brackets first, then multiplication and division from left to right, then addition and subtraction from left to right.
• Every expression can be read as a sum of terms: 30 − 8 + 5 has terms 30, −8 and +5.
• Terms can be added in any order and grouped in any way without changing the value.
• A minus sign before a bracket changes the sign of every term inside it.
• Compare two expressions by seeing which terms differ, without working out both.

Remember

Watch out

• Working strictly left to right and ignoring brackets or multiplication.
• Changing the sign of only the first term after a minus bracket.
• Treating subtraction as if the order did not matter: 10 − 3 is not 3 − 10.

Worked example