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Integers - Subtracting Signed Numbers


1. Rewrite as an addition sentence
2. Apply addition rules (details below)


1. Rewrite as an addition sentence
a) Change subtraction operand to an addition operand or a plus sign
b) Change the sign of the following number to its opposite

This process is referred to as "addition of the opposite".


Example 1
5 9 = would become 5 + (-9)

Example 2
-9 - 4 =
-9 + (-4) =
Notice the first number, -9, was not changed.

Example 3
-4 (-8) =
-4 + 8 =

Example 4
7 (-5) =
7 + 5 =

2. Follow the Addition Rules


ADDING TWO ALIKE SIGNS two positive numbers or two negative numbers
First Method:
1. Add absolute values
2. Attach same sign to the answer

Example:
Adding two positives integers
4 + 5 = 9

Adding two negative integers
(-4) + (-5) = (-9)

Second Method: (+) positive (-) negative
Draw (+) and (-) to represent the number sentence.

Note: A pair of (+) and (-) cancels each other or equals zero. (See end of page for more an illustration.)

4 + 5 = 9
+ + + + and + + + + +

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

(-) (-) (-) (-) and
(-) (-) (-) (-) (-)
Parentheses are used for clarity only.
Are there any zero pairs to cancel? No. So, count the signs to get a total.

Memory tip for adding two integers with same signs: Alike Signs Add

ADDING TWO UNLIKE SIGNS
- 6 + 4 = ?
First Method:
1. Subtract absolute values
2. Use the sign of the number with the larger absolute value
| - 6| = 6 | 4 | = 4
Remember to put the larger number first when subtracting two numbers. -- > 6 - 4 = 2
Six is larger. So, the answer will have a negative sign.
- 6 + 4 = - 2

Second Method:
Parentheses are used for clarity only.

(-) (-) (-) (-) (-) (-)
+ + + +
Are there any zero pairs to cancel? Yes. Four pairs cancel each other. So, count the remaining signs to get a total. Two negatives are left. Thus, - 6 + 4 = - 2

Memory tip for adding two integers with unlike signs: Different Signs Find the Difference

Here is proof that a positive and negative cancel each other.
( -3) + 3 = ?

(-) (-) (-)
+ + +
Three negative / positive pairs cancel each other. Thus, the answer is zero.




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Content copyright © 2014 by Beverly Mackie. All rights reserved.
This content was written by Beverly Mackie. If you wish to use this content in any manner, you need written permission. Contact Beverly Mackie for details.

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