Subtract integers

Subtracting integers means finding the difference between positive and negative whole numbers, including zero, by interpreting $a-b$ as adding the additive inverse of $b$ . A number line represents this as moving in the direction opposite to the subtracted number, clarifying why subtracting a negative increases a value and preventing the misconception that subtraction always makes a number smaller; this structure supports simplifying algebraic expressions.

Detailed Explanation: Subtract integers

To subtract integers, rewrite subtraction as adding the opposite:

a-b=a+(-b)

Then add the integers.

Example: Find $(5-(-3))$

Start with the expression:

5-(-3)

The opposite of $(-3)$ is $(+3)$ . Rewrite the subtraction:

5+3

Add:

5+3=8

Therefore,

\boxed{5-(-3)=8}

On a number line, start at $5$ . Because you are subtracting $(-3)$ , move in the opposite direction of negative, which is $3$ spaces to the right. You land on $8$ .

Subtracting a negative increases the value because it is the same as adding a positive.

Learn by doing: Subtract integers

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Negative Integer Subtraction

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