Adding and Subtracting Integers

Working with positive and negative integers becomes easy once you understand a few simple rules. You can think of positive numbers as having money, and negative numbers as owing money, or you can use a number line to visualize the math.

Adding Integers

When adding integers, look at their signs to decide what to do:

1. Same Signs (Both Positive or Both Negative)

• Rule: Add their absolute values (the numbers without the signs) and keep the original sign.
• Example: $5 + 4 = 9$
• Example: $-3 + (-6) = -9$

2. Different Signs (One Positive, One Negative)

• Rule: Subtract the smaller absolute value from the larger absolute value. Then, keep the sign of the number that had the larger absolute value.
• Example: $-8 + 5$
  • Subtract the absolute values: $8 - 5 = 3$.
  • Since $-8$ has a larger absolute value than $5$, the answer is negative.
  • Answer: $-8 + 5 = -3$
• Example: $6 + (-11)$
  • Subtract: $11 - 6 = 5$.
  • Keep the negative sign from the $-11$.
  • Answer: $6 + (-11) = -5$

Subtracting Integers

Subtracting an integer is the exact same as adding its opposite. The rule is often remembered as "Keep, Change, Change":

1. Keep the first number exactly the same.
2. Change the subtraction sign to an addition sign.
3. Change the sign of the second number to its opposite.

Mathematically, this is written as: $a - b = a + (-b)$

Let's look at an example:

• Problem: $-15 - (-8)$
• Keep, Change, Change: Keep $-15$, change $-$ to $+$, change $-8$ to $8$.
• New Problem: $-15 + 8$
• Apply Addition Rules: Since the signs are different, subtract ($15 - 8 = 7$) and keep the sign of the larger absolute value (negative).
• Answer: $-15 - (-8) = -7$

Using a Number Line

You can also solve these problems using a number line:

• Start at the first number.
• When adding a positive number (or subtracting a negative), move to the right.
• When adding a negative number (or subtracting a positive), move to the left.