The big picture
Read the operation sign (+, −, × or ÷) first. It decides most of the answers below.
| Idea | Remember | Example |
|---|---|---|
| Add, same side | Add the sizes. Keep the side. | (−3) + (−4) = −7 |
| Add, mixed sides | The bigger size wins the side. | (−7) + 3 = −4 |
| Take away | a − b is a + (−b). One rule, not two. | 8 − 3 = 8 + (−3) |
| Two dashes | Take away below zero. The walk turns right. | 5 − (−3) = 8 |
| In your head | Rewrite as an add, compare sizes, then pick the side. | (−6) − (−9) = 3 |
| Multiply | One move, repeated. | (−3) × 4 = −12 |
| Multiply, both below | Not zero: same signs give more than zero. | (−3) × (−4) = 12 |
| Share | Same sign rule as multiply. | (−12) ÷ 4 = −3 |
| Zero | Times zero is zero. ÷ 0 has no answer. | 5 ÷ 0: no answer |
| A change | Later reading take away earlier reading. | 6 − (−4) = 10, up |
| Zero pairs | A zero pair is one positive and one negative token. To take away tokens you lack, add zero pairs first. | 5 − 9: add 4 pairs, left −4 |
| Additive inverse | Adding a number to its additive inverse gives 0. For a, that partner is written −a. Multiplying by −1 finds the partner. | 8 + (−8) = 0 |
| Many factors | No zero among the factors? Count the negative ones. An even count gives a product more than zero. An odd count gives a product less than zero. A zero factor makes the product 0. | (−2) × 3 × (−1) × (−4) = −24 |
| A bracket | Multiply the number by each part of the bracket, then add. The answer matches adding the bracket first. It still holds when a number is below zero. | 4 × (5 + (−3)) = 8 |
Now open Part II, Chapter 2, Operations with Integers. Look for these ideas in it.