Lesson 3: Subtracting Integers

Property

Subtraction Property
$a - b = a + (-b)$

Subtracting a number is the same as adding its opposite.

Examples

• To solve $10 - 18$, change it to adding the opposite: $10 + (-18)$. The result is $-8$.
• To solve $-5 - (-12)$, change it to adding the opposite: $-5 + 12$. The result is $7$.
• Simplify $20 - (-5 - 2) - 10$. First solve inside the parentheses: $20 - (-7) - 10$. Then change to addition: $20 + 7 + (-10) = 17$.

Property

Apply the rule that subtraction of integers is equivalent to adding the opposite: $a - b = a + (-b)$. This allows any integer subtraction problem to be solved using addition rules, including cases with negative integers where $a - (-b) = a + b$.

Examples