Integers are the whole numbers extended in both directions, so the line runs on for ever to the left as well as to the right.
Minus 5 degrees, level minus 2 in a car park, a bank balance of minus 3000 rupees. The minus sign is not saying something is wrong; it says which side of zero you are on.
Comparing integers
Further right always means larger. So minus 2 is larger than minus 7. This feels wrong at first, but a debt of 7 rupees is worse than a debt of 2.
Among negative numbers, the larger the digits, the further left it sits and the smaller it is. Picture the line, or ask which is colder.
Adding and subtracting
| What you do | Which way you move | Example |
|---|---|---|
| Add a positive | Move RIGHT | −3 + 5 = 2 |
| Subtract a positive | Move LEFT | 2 − 5 = −3 |
| Add a negative | Move LEFT | 2 + (−5) = −3 |
| Subtract a negative | Move RIGHT | 2 − (−5) = 7 |
Taking away a debt makes you richer. If someone owes 500 rupees and that debt is cancelled, they are 500 rupees better off. So removing a negative moves you upwards.
Multiplying and dividing
Two signs the same give a positive answer; two signs different give a negative one. So minus 3 times minus 4 is 12, while minus 3 times 4 is minus 12.
Minus 3 times 3 is minus 9, then minus 6, then minus 3, then 0. Each answer goes up by 3. Carrying that on, minus 3 times minus 1 must be 3. The rule is the only continuation that keeps the pattern working.
Minus 3 plus minus 4 is minus 7, not 7, because adding two debts makes a bigger debt. But minus 3 times minus 4 is 12. Before touching the signs, look at which operation you are doing.
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