Subtract integers using models

Subtraction of integers is understood as adding the additive inverse: in $a-b$ , the second integer is replaced by its opposite, so subtracting a positive moves left on a number line and subtracting a negative moves right. Integer-chip and number-line models connect this meaning to zero pairs and directed distance, while correcting the misconception that subtraction always makes a quantity smaller; the focus remains on signed whole numbers, not fractions or more abstract number systems.

Detailed Explanation: Subtract integers using models

To subtract integers, keep the first integer and add the opposite of the second integer:

a-b=a+(-b)

On a number line:

Subtracting a positive number means moving left.
Subtracting a negative number means moving right.

Example: $\,-2-(-3)$

Start at $-2$ .
The number being subtracted is $-3$ . Its opposite is $+3$ .
Rewrite the subtraction as addition:

-2-(-3)=-2+3

On the number line, start at $-2$ and move $3$ spaces right:

-2\longrightarrow -1\longrightarrow 0\longrightarrow 1

Therefore,

\boxed{-2-(-3)=1}

With integer chips, subtracting $3$ negative chips means removing three negative chips. If there are not enough negative chips, add zero pairs—one positive and one negative chip—without changing the value. After removing the three negative chips, one positive chip remains, giving $1$ .

Notice that subtracting a negative made the number greater. Subtraction does not always make a quantity smaller.

Learn by doing: Subtract integers using models

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Negative Integer Subtraction

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