Adding and subtracting integers
When the signs are the same, add the numbers and keep the sign. When the signs are different, subtract the smaller from the larger and take the sign of the larger. Subtracting a number is the same as adding its opposite: 5 − (−3) = 5 + 3 = 8.
Key idea / Key idea
Same signs → add, keep sign. Different signs → subtract, keep the bigger number's sign. Also a − (−b) = a + b and a + (−b) = a − b.
Multiplying and dividing integers
The sign rule is short: same signs give a positive answer, different signs give a negative answer. This works for both × and ÷.
| (+) × (+) | = + |
| (−) × (−) | = + |
| (+) × (−) | = − |
| (−) × (+) | = − |
Worked example / Worked example
Calculate −4 × 3 + (−12) ÷ 4.
Do × and ÷ first: −4 × 3 = −12 and −12 ÷ 4 = −3.
Then add: −12 + (−3) = −15.
Order of operations
Follow BODMAS: Brackets, then Orders (powers), then Division and Multiplication (left to right), then Addition and Subtraction (left to right). Brackets are always done first, even with negative numbers inside. When a line has only additions and subtractions, work steadily from left to right so the signs stay correct.
Remember / Remember
- A minus times a minus gives a plus.
- Dividing by 0 is undefined.
- Always finish × and ÷ before + and −.