Read the two signs separately
In 4 − (−3), the middle minus is the operation “subtract.” The minus inside the brackets belongs to the number −3. Keeping brackets around a negative value makes these roles easier to see.
Subtract integers
Give the subtraction sign and the negative sign different jobs.
Understand it
Make the idea make sense.
Keep the first value. Add the opposite of the second.
The identity a − b = a + (−b) works for every integer. To rewrite −4 − (−7), keep −4, change subtraction to addition, and replace −7 with +7. Now solve −4 + 7.
Why does subtracting a negative increase the value?
Imagine a balance made from positive and negative counters. Removing a negative unit increases the total by one. On a number line, subtracting −3 has the same effect as adding +3: move three units right.
Subtraction also finds a signed change
To find the change from a starting value to an ending value, calculate ending − starting. From −6 °C to 2 °C, the change is 2 − (−6) = +8 °C. A signed change can be negative; a distance is never negative.
Words worth knowing
- Subtraction
- Finding a difference; subtracting a value is equivalent to adding its opposite.
- Subtrahend
- The number being subtracted.
- Difference
- The result of subtraction.
Remove counters. Preserve the value.
Predict before showing the steps. If the counters to remove are missing, add zero pairs first. Adding a zero pair changes the representation, not its value.
Choose values and predict the result.
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)
- Keep the first value, −4.
- Subtracting −7 is equivalent to adding its opposite, +7: −4 + 7.
- Starting at −4, move 7 units right. The result is 3.
−6 − 5
- Rewrite as −6 + (−5).
- Start at −6 and move 5 units left.
- −6 − 5 = −11.
3 − 8
- Rewrite as 3 + (−8).
- Eight negative units outweigh three positive units by five.
- 3 − 8 = −5.
Try together
A little support. Your thinking.
Rewrite and solve −4 − (−7).
Nicely reasoned. Try a fresh question below, or revisit any step.
Your turn
Practice with purpose.
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Connections
In the real world
All Class Notes →An elevator moves from level 4 to level −3. Its change is −3 − 4 = −7 floors: seven floors downward.