SIGNED NUMBERS ADDITION

Concept: Signed numbers are whole numbers, their negatives, and zero. To show the complete set of numbers called signed numbers, we extend the positive number line to the left of zero to include the negative numbers. See the graph after the Absolute value definition.

Absolute value: These are numbers, whether they are positive or negative, that are between two of the following symbols “|“. It is a way of telling how far a number is away from zero.

Example "5" is 5 away from zero, but "-5" is also 5 away from zero.
So, the absolute value of 5 is 5 and the absolute value of -5 is also 5.
The symbol "|" is placed on both sides of a number to mean "Absolute Value", so we can write: |-5| = 5.

Rules for Addition

Rule 1 | If the numbers have like signs, | ( – 2 ) + ( – 6 ) =
| add the numbers | 2 + 6 = 8
| and give the answer the same sign as the numbers being added. | ( – 2 ) + ( – 6 ) = – 8
Rule 2 | If the numbers have unlike signs, | ( –20) + (+13) =
| subtract the smaller number from the larger number | 20 – 13 = 7
| and give the answer the sign of the larger number. | ( –20) + (+13) = –7
Rule 3 | If any number is between two absolute value symbols, | ( – 5 ) + ( |– 8| ) =
| make that number a positive number and then follow either Rule 1 or Rule 2. | ( – 5 ) + ( + 8 ) =

To add more than two numbers find the sum of the positive numbers and the sum of the negative numbers. Then use Rule 2 to find the total.

Example: ( + 30 ) + ( - 8 ) + ( - 15 ) + ( + 3 ) + ( - 20 ) = ?

Step 1 | Add the positive numbers. (Rule 1) | (+30) + (+3) = +33
| Add the negative numbers. (Rule 1) | (– 8) + (–15) + (–20) = –43
Step 2 | Add the unlike sums. (Rule 2) | (+33) + (–43) = 43 – 33 = 10 (+33) + (–43) = – 10