Skill: Subtract integers symbolically

To subtract an integer, add its additive inverse:

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

The additive inverse is the number that is the same distance from zero but on the opposite side. For example, the additive inverse of $-5$ is $5$.

Example:

$$-3-(-5)$$

Step 1: Rewrite subtraction as addition.
Change the subtraction sign to addition and find the opposite of the number being subtracted:

$$-3-(-5)=-3+5$$

Step 2: Add the integers.
Starting at $-3$ on a number line, move $5$ units to the right because you are adding $5$:

$$-3+5=2$$

Therefore,

$$\boxed{-3-(-5)=2}$$

Subtracting does not always make a number smaller. Subtracting a negative means adding a positive, so the result can become greater.