Addition combines signed changes
On a number line, start at the first addend. Adding a positive number moves right; adding a negative number moves left. The distance moved is the absolute value of the second addend.
Add integers
Connect addition to direction, distance and zero pairs.
Understand it
Make the idea make sense.
Same signs: combine the distances
−4 + (−3) combines 4 negative units and 3 negative units. The result is 7 negative units: −7. Positive addends work the same way in the positive direction.
Different signs: cancel zero pairs
For −4 + 7, four positive units cancel four negative units. Three positive units remain, so the sum is 3. Equivalently, subtract the smaller absolute value from the larger and use the sign of the addend with the larger absolute value.
Equal distances can cancel completely
−6 + 6 = 0. Neither sign wins when the absolute values are equal. Adding zero leaves a value unchanged, and changing the order of the addends leaves the sum unchanged.
Words worth knowing
- Addend
- A number being added.
- Sum
- The result of addition.
- Zero pair
- A positive unit and a negative unit together have a value of zero.
Make it visible
See what zero pairs do.
A positive unit and a negative unit make a zero pair. Cancel pairs to see what remains.
Khan Academy
Pause before the next calculation. Predict the sign and explain the model, then compare the reasoning.
See the thinking
One step at a time.
Predict each next step, then reveal the explanation.
−4 + 7
- Start with 4 negative units and 7 positive units.
- Cancel four zero pairs. Three positive units remain.
- −4 + 7 = 3.
−9 + 4
- The addends have different signs. Compare their absolute values: 9 and 4.
- 9 − 4 = 5. The negative addend has the larger absolute value.
- −9 + 4 = −5.
−5 + (−6)
- Both addends are negative, so combine the negative units.
- 5 + 6 = 11 negative units.
- −5 + (−6) = −11.
Try together
A little support. Your thinking.
Work through −6 + 10.
Nicely reasoned. Try a fresh question below, or revisit any step.
Your turn
Practice with purpose.
New questions, useful feedback and hints that build on your thinking.
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Connections
In the real world
All Class Notes →It is −8 °C and warms by 11 °C. The change is positive: −8 + 11 = 3 °C.