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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, -.

Let’s review addition and subtraction of signed numbers:

To add two signed numbers: Example
• If both numbers are positive, ignore the signs and add. The sum is positive. 31 + 8 = 39
• If both numbers are negative, ignore the signs and add. The sum is negative. -13 + (-4) = -17
• 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) • ignore the signs:

• subtract 8 from 13:

8, 13

13 - 8 = 5

Step 2 Add using the rules for addition of signed numbers. = -5 • attach the sign of the greater number. The sign of 13 is negative so the result is -5

So, 8 - 13 = -5.

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