Integers are the whole numbers together with their negatives: … −3, −2, −1, 0, 1, 2, 3 … On the number line, positive integers sit to the right of 0 and negative integers to the left. Thinking of the number line — right means bigger, left means smaller — is the single best way to keep integer questions clear.
Adding integers
- ✓ Same signs: add the numbers and keep the sign. e.g. (−4) + (−3) = −7.
- ✓ Different signs: subtract the smaller from the larger, and keep the sign of the larger. e.g. (−7) + 3 = −4.
Subtracting integers
To subtract, add the opposite. Change the subtraction to addition and flip the sign of the number being subtracted. For example, 5 − (−2) becomes 5 + 2 = 7, and (−6) − 4 becomes (−6) + (−4) = −10.
Multiplying and dividing integers
The sign rule is the same for both, and worth memorising:
- ✓ Same signs → positive answer: (+)(+) = + and (−)(−) = +. e.g. (−5) × (−3) = 15.
- ✓ Different signs → negative answer: (+)(−) = − and (−)(+) = −. e.g. (−5) × 3 = −15.
Division follows exactly the same sign rule: (−12) ÷ 4 = −3, while (−12) ÷ (−4) = 3.
Properties to remember
Integers are closed under addition, subtraction and multiplication (the answer is always an integer). Addition and multiplication are commutative (order doesn't matter) and associative (grouping doesn't matter). 0 is the additive identity (adding 0 changes nothing) and 1 is the multiplicative identity (multiplying by 1 changes nothing).
Want this taught aloud in your language?
The sign rules stick much better when a child sees them on a number line with real examples. Upload this NCERT chapter to Tutorfic and it will teach it aloud in your child's language, then quiz them on the sign rules with the reasoning behind each answer. It's one of all the Class 7 subjects Tutorfic teaches.