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Adding and Subtracting Signed Integers

The Number Line

7

-7

- Previously, we learned that numbers to the right

of zero are positive and numbers to the left of

zero are negative. By putting points on the

number line, we can graph values.

- If one were to start at zero and move seven

places to the right, this would represent a value

of positive seven.

- If one were to start at zero and move seven

places to the left, this would represent a value

of negative seven.

Adding Integers - Same Sign

We can show addition using a number line.

What is 5 4?

Start at five (5 units to the right from zero).

Move four units to the right.

The final point is at 9 on the number line.

Therefore, 5 4 9.

Adding Integers - Same Sign

Now add two negative numbers on a number line.

What is -5 (-4)?

Start at 5 (5 units to the left from zero).

Move four units to the left. Go left since we

are adding a negative number.

The final point is at -9 on the number line.

Therefore, -5 (-4) -9.

Adding Integers - Same Sign

We can also show how to do this by using algebra

tiles. Each dark tile is a positive 1, each light

tile is a negative 1

What is 5 7?

5

7

12

What is 5 7?

-12

-7

-5

Adding Integers - Same Sign

RULE To add integers with the same sign, add

the absolute values of the integers. Give the

answer the same sign as the integers.

Solution

Examples

Additive Inverse

What is (-7) 7?

To show this, start at the value -7 (seven units

left of zero).

Now, move seven units to the right (adding

positive seven).

Notice, we are back at zero (0).

For every positive integer on the number line,

there is a corresponding negative integer. These

integer pairs are opposites or additive inverses.

Additive Inverse Property For every number a, a

(-a) 0.

Additive Inverse

When using algebra tiles, the additive inverses

make what is called a zero pair. For example, the

following is a zero pair, the two tiles cancel

each other out.

1 (-1) 0.

This also represents a zero pair.

x (-x) 0

Adding Integers - Different Signs

Add the following integers (-4) 7.

Start at the value -4 (four units to the left of

zero).

Move seven units to the right (because we are

adding a positive number.

The final position is at 3. Therefore, (-4) 7

3.

Adding Integers - Different Signs

Add (-9) 3

Start at the value -9 (nine places to the left of

zero).

Move three places to the right (adding a positive

number).

The final position is at negative six,

(-6). Therefore, (-9) 3 -6.

Adding Integers - Different Signs

Add 7 (-3)

Start at the value 7 (seven places to the right

of zero).

Move three places to the left (adding a negative

number).

The final position is at positive four,

(4). Therefore, 7 (-3) 4.

Adding Integers - Different Signs

Each dark tile is a positive 1, each light tile

is a negative 1. One 1 and one - 1 make a zero

pair, they cancel each other.

What is (- 4) 7?

-4

7

3

What is 4 (-7)?

-3

-7

4

Adding Integers - Different Signs

RULE To add integers with different signs

determine the absolute value of the two numbers.

Subtract the smaller absolute value from the

larger absolute value. The solution will have

the same sign as the number with the larger

absolute value.

Solution

Example

Subtract

Subtracting Integers

Subtraction is defined as addition a - b a

(-b). To perform subtraction, remember this

rule

Keep-Change-Change.

3

-9

Subtracting Integers

Keep-Change-Change doesnt mean the 2nd number

always ends up being negative

7

-2

You Try It!

Find each sum or difference.

1. -24 11 2. 18 (-40) 3.

-9 9 4. -16 (-14) 5.

13 35 6. -29 65

Simplify each expression.

7. 18r 27r 8. 9c (-12c)

9. -7x 45x 10. -3y (-7y)

Solutions

-24 (-11) -35

1. -24 11 2. 18 (-40) 3.

-9 9 4. -16 (-14) 5. 13

35 6. -29 65

-22

0

-16 (14) -2

13 (-35) -22

36

Solutions

7. 18r 27r 8. 9c (-12c) 9.

-7x 45x 10. -3y (-7y)

18r (-27r) -9r

9c (12c) 21c

38x

-10y

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