Lesson 5-3: Subtract Integers and Rational Numbers

Property

To model the subtraction problem $a - b$ on a number line, start at the point representing the first integer, $a$. Then, move a distance of $|b|$ units. Move to the left if $b$ is positive, and move to the right if $b$ is negative.

Examples

• To find $3 - 5$: Start at $3$ and move $5$ units to the left. You land on $-2$. So, $3 - 5 = -2$.
• To find $-2 - 4$: Start at $-2$ and move $4$ units to the left. You land on $-6$. So, $-2 - 4 = -6$.
• To find $1 - (-4)$: Start at $1$ and move $4$ units to the right. You land on $5$. So, $1 - (-4) = 5$.

Explanation

A number line provides a visual way to understand integer subtraction. You always begin at the first number in the expression. Subtracting a positive integer is like a decrease, so you move to the left. Subtracting a negative integer is equivalent to adding its positive opposite, so you move to the right. The final position on the number line represents the answer to the subtraction problem.

Property

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

Subtracting a number is the same as adding its opposite.

Examples

• The expression $14 - 8$ can be rewritten as adding the opposite: $14 + (-8)$, which both equal $6$.

Property

When subtracting a negative number, the result equals adding the positive version of that number:

Examples