#### 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.

**You Should Also Read:**

Integers - Multiplication and Division

Integers - Positive and Negative Numbers

Pre-Algebra - Kiss My Math - Review

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