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Adding and Subtracting Signed Numbers

Each real number (except 0) is either positive or negative. We refer to
positive and negative numbers as signed numbers because each can be
written with either a positive sign, +, or a negative sign, -.

Letâ€™s review addition and subtraction of signed numbers:

To add two signed numbers:

Example

â€¢ If both numbers are positive, ignore the signs and add.
The sum is positive.

31 + 8 = 39

â€¢ If both numbers are negative, ignore the signs and add.
The sum is negative.

-13 + (-4) = -17

â€¢ If the numbers have different signs, ignore the signs and subtract
the smaller number from the larger number. Then attach the sign
of the larger number.

5 + (-14) = -9

To subtract two signed numbers follow these steps:

Step 1 Change the subtraction sign (-) to an addition sign (+) and
change the sign of the number being subtracted.

3 - (-8) = 3 + (+8) = 11

Step 2 Add using the rules for addition of signed numbers.

4 - 9 = 4 + (-9) = -5

Example 1

Find: 8 - 13

Solution

8 - 13

To add 8 and -3

Step 1 Change the subtraction sign (-) to an addition
sign (+) and change the sign of the number being
subtracted.

= 8 + (-13)

â€¢ ignore the signs:

â€¢ subtract 8 from 13:

8, 13

13 - 8 = 5

Step 2 Add using the rules for addition of signed numbers.

= -5

â€¢
attach the sign of the greater number. The sign of 13 is negative so the
result is -5