Subtracting Integers

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.

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.

Related lessons

• Basic Math