Lesson 2: Adding Integers

Property

To add the integers $p$ and $q$: begin at zero and draw the line segment (arrow) to $p$.
Starting at the endpoint $p$, draw the line segment representing $q$. Where it ends is the sum $p + q$.
An arrow pointing right is positive, and a negative arrow points left.
Each arrow is a quantity with both length (magnitude) and direction (sign).

Examples

• To calculate $3 + 4$, start at 0, move 3 units right, and then move 4 more units right. You land at 7. So, $3 + 4 = 7$.
• To find $-6 + 4$, start at 0, move 6 units left to $-6$, then move 4 units right. You land at $-2$. So, $-6 + 4 = -2$.
• To compute $-3 + (-5)$, start at 0, move 3 units left to $-3$, then move 5 more units left. You land at $-8$. So, $-3 + (-5) = -8$.

Explanation

Think of adding on a number line as taking a journey. Positive numbers are steps to the right, and negative numbers are steps to the left. Your final position is the sum of the integers.

Property

To add integers with the same sign, add their absolute values and keep the common sign.

To add integers with different signs, subtract the smaller absolute value from the larger absolute value. The sum has the sign of the number with the larger absolute value.

Examples

• To add $-15 + (-8)$, the signs are the same. Add $15 + 8 = 23$ and keep the negative sign, so the sum is $-23$.
• To add $-10 + 25$, the signs are different. Subtract $25 - 10 = 15$. Since $25$ has the larger absolute value, the result is positive: $15$.
• To add $12 + (-30)$, the signs are different. Subtract $30 - 12 = 18$. Since $-30$ has the larger absolute value, the result is negative: $-18$.