# Subtracting Integers

If you already know how to add integers, subtracting them should be simple. The first step in subtracting integers is to turn the subtraction problem into an addition one, and then follow the rules for addition.

So I highly recommend that you review the rules of adding integers.

RULE: To subtract integers, change the operation from subtraction to addition then switch the sign of the following number. Finally, apply the addition rules for integers.

**Example 1: **\(\left( { + 7} \right) – \left( { – 3} \right)\)

Let’s transform this into an addition problem by changing the operation from subtraction (\(-\)) to addition (\(+\)) and then switching the sign of the following number (subtrahend) from negative to positive, meaning \( -3 \) becomes \( +3 \).

We have just converted the subtraction to an addition problem. From this point forward, we are going to apply the addition rules of integers.

\(\left( { + 7} \right) + \left( { + 3} \right)\)

Since the signs of the two numbers are the same, we are going to add their absolute values.

The absolute value of \(+7\) is \(7\).

The absolute value of \(+3\) is \(3\).

Adding their absolute values, \(7+3=10\).

The sign will be determined by the common sign which in this case is also positive.

\(\left( { + 7} \right) + \left( { + 3} \right) = 10\)

Therefore, \(\left( { + 7} \right) – \left( { – 3} \right) = \left( { + 7} \right) + \left( { + 3} \right) = 10\).

**Example 2:** \(\left( { – 14} \right) – \left( { – 9} \right)\)

We convert the problem from subtraction to addition. We can do that by changing the operation from subtraction to addition then switching the sign of the following number.

\(\left( { – 14} \right) + \left( { + 9} \right)\)

Since they have different signs, we will have to subtract their absolute values.

The absolute value of \(-14\) is \(14\).

The absolute value of \(+9\) is \(9\).

\(14\, – \,9 = 5\)

The number \(-14\) has the bigger absolute value so we will adopt its sign.

Therefore, \(\left( { – 14} \right) + \left( { + 9} \right) = – 5\).