Adding Signed Numbers

Subtraction on the number line means counting to the left. A negative number stands for a subtraction that hasn't been carried out yet, so adding a negative number means carrying out that subtraction.

To add a negative number -n to a given number, begin at the given number and count n spaces to the left.

For example, to add -8 to 24, start at 24 and count 8 spaces left, landing on 16: +24 + (-8) = +16 And to add -6 to -4, start at -4 and count 6 spaces left: -4 + (-6) = -10

Absolute value

The numerical or absolute value of a number is its value without regard to sign. The absolute values of -3, -5, and +7 are 3, 5, and 7. Notice that two different numbers, like +6 and -6, can have the same absolute value.

Three working rules

Counting on the line gets slow with big numbers. These rules give the same answers:

1. Two or more positive numbers: add their absolute values and put a plus sign in front.
2. Two or more negative numbers: add their absolute values and put a minus sign in front.
3. A positive and a negative number: find the difference of their absolute values and give it the sign of the one with the greater absolute value.

The result is called the algebraic sum. It's often different from the sum of the absolute values: the algebraic sum of +9 and -5 is +4, while the sum of their absolute values is 14. From now on, add means find the algebraic sum.