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Subtracting integers

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Subtracting Integers

Subtracting integers means subtraction with positive or negative numbers. The key rule is that subtracting a number equals adding its opposite: a minus b equals a plus negative b. Learn to apply it, picture it on a number line, and work through examples with every combination of signs.

What subtracting integers means

Subtracting integers is subtraction where the numbers can be positive or negative. The key idea makes every case simple: subtracting a number is the same as adding its opposite. In symbols, a − b = a + (−b). Once you rewrite a subtraction as an addition, you only need the rules for adding integers.

Subtracting integers on a number line A number line from minus 2 to 8. Starting at 3, subtracting negative 4 is the same as adding 4, so you move four units right and land on 7. The rule shown is a minus b equals a plus the opposite of b. -2-1012345678 +4 (add the opposite) start: 3 3 − (−4) = 7 a − b = a + (−b)
Subtracting a negative means adding: 3 − (−4) = 7 on the number line.

To subtract, change the subtraction to addition and flip the sign of the number being subtracted. For example, 3 − (−4) becomes 3 + 4 = 7, and −5 − 2 becomes −5 + (−2) = −7. This one move handles every combination of signs, building on the introduction to integer subtraction.

A number line makes the idea visual. Subtracting a positive moves you left; subtracting a negative moves you right. Starting at 3 and subtracting −4, you move four units to the right and land on 7 — the same answer the rule gives.

  • 7 − 10 = 7 + (−10) = −3
  • −4 − 6 = −4 + (−6) = −10
  • −8 − (−3) = −8 + 3 = −5

The same reasoning shows up whenever you work through an application of integer operations, such as temperature drops or money owed.

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