To add integers, think about their signs (positive or negative) and then either add or subtract their sizes (absolute values).

Core rules (the “quick scoop”)

  • Two positives: add and keep positive.
    • Example: 3+5=83+5=83+5=8.
  • Two negatives: add their absolute values and keep negative.
    • Example: −3+(−5)=−(3+5)=−8-3+(-5)=-(3+5)=-8−3+(−5)=−(3+5)=−8.
  • One positive, one negative: subtract the smaller absolute value from the larger, keep the sign of the larger.
    • Example: 7+(−4)7+(-4)7+(−4): 7−4=37-4=37−4=3, answer +3+3+3.
* Example: −9+5-9+5−9+5: 9−5=49-5=49−5=4, answer −4-4−4.
  • Adding zero: the number stays the same.
    • Example: 6+0=66+0=66+0=6, −8+0=−8-8+0=-8−8+0=−8.

Tiny story to remember it

Imagine a number line as a street.

  • Positive integers are steps to the right, negative integers are steps to the left.
  • Adding a positive integer means walking right; adding a negative means walking left.

So, −2+7-2+7−2+7 is “start at −2-2−2, walk 7 steps right,” and you land on 5.

Number line view

  • Start at the first integer on the number line.
  • If the second integer is positive, move right that many spaces.
  • If the second integer is negative, move left that many spaces.

Example: 5+(−10)5+(-10)5+(−10)

  • Start at 5, move 10 steps left, land at −5-5−5.

Mini table of sign rules (HTML)

Here’s a simple HTML table capturing the sign rules.

html

<table>
  <thead>
    <tr>
      <th>First integer</th>
      <th>Second integer</th>
      <th>Operation on sizes</th>
      <th>Sign of result</th>
      <th>Example</th>
    </tr>
  </thead>
  <tbody>
    <tr>
      <td>Positive</td>
      <td>Positive</td>
      <td>Add</td>
      <td>Positive</td>
      <td>2 + 5 = 7</td>
    </tr>
    <tr>
      <td>Negative</td>
      <td>Negative</td>
      <td>Add absolute values</td>
      <td>Negative</td>
      <td>(-2) + (-5) = -7</td>
    </tr>
    <tr>
      <td>Positive</td>
      <td>Negative</td>
      <td>Subtract absolute values</td>
      <td>Sign of larger absolute value</td>
      <td>2 + (-5) = -3</td>
    </tr>
    <tr>
      <td>Any integer</td>
      <td>Zero</td>
      <td>No change</td>
      <td>Same as first integer</td>
      <td>0 + 5 = 5; 0 + (-5) = -5</td>
    </tr>
  </tbody>
</table>

A few practice examples

  1. 4+(−6)+134+(-6)+134+(−6)+13
    • 4+13=174+13=174+13=17 (both positive).
 * 17+(−6)17+(-6)17+(−6): subtract 17−6=1117-6=1117−6=11, keep positive → 111111.
  1. −2+(−9)-2+(-9)−2+(−9)
    • Same sign, both negative.
    • 2+9=112+9=112+9=11, keep negative → −11-11−11.
  1. −5+7-5+7−5+7
    • Different signs.
    • 7−5=27-5=27−5=2, larger absolute value is 7 (positive) → +2+2+2.

TL;DR:

  • Same sign → add and keep that sign.
  • Different signs → subtract absolute values, keep the sign of the larger absolute value.
  • Adding zero changes nothing.

Information gathered from public forums or data available on the internet and portrayed here.