Integers

Every integer has an opposite integers. A number and its opposite are the same distance from zero.

How many units is 4 from 0?› 4

How many units is -4 from 0? › 4

4 and -4 are called › opposites

2

3

Ordering Integers You can use a number line to list and

order number. The numbers get greater as you

move to the right on the number line.

Write the integers in order from least to greatest:

-2, -6, 4 -3, 7, 2

-6, -2, 4

-3, 2, 7

Absolute Value The absolute value of an integer is its

distance away from 0 on a number line

-5 is 5 units away from 0. The absolute value of -5 is 5 or 5 units.

How many units form 0 is -3?

What is |4|? 4

3

Place the appropriate symbol on the line between the numbers:

7 _______ 10 12 _______ 3

-8 _______ -5 0 _______ -6

-45 ______ 0 2 _______ -100

The balance scale “weighs” positive and negative numbers. Negative numbers go on the left side of the balance and positive numbers go on the right side.

The scale will tip The scale will tip The scale will tip to the to the to the -11 and +8 is -2 and +7 is -1 and -3 is -11 + 8 = -2 + 7 = -1 + (-3) =

to the left -11 and +8 is -3 -11 + 8 =

left

right

left -4

-3

+5

5-3

-4

1. Find 3 + (-9) _____ 2. Find -5 + (-8) _____

3. 7 + (-3) = 4. -2 + (-3) = 5. -5+4 =

6. -3 + (-1) = 7. -7 + 9 = 8. 4 + (-9)

-6

-1-54

-13

-52-4

Starting at zero, the addition is shown on the number line. Write the sum.

9. 2 + (-3) = _____ 10. -3 + (-4) = _____

-1 -7

Example 12 “minus” 3 or 2 “take away” 3

2 - 3 = -1

Example 2How to “take away” a negative number?

2 – (-3) The negative sign means “do the opposite”

Subtracting a negative means to add

This makes 2 – (-3) and 2 + 3 the same process!!

2 – (-3) 2 + 3 = 5

Example 3

-2 - 3 = -5

The product of two integers with the same sign is positive

The product of two integers with the different signs is negative

( + ) ( – ) = _____ ( – ) ( + ) = _____

( + ) ( + ) = _____ ( – ) ( – ) = _____

The quotient of two integers with the same sign is positive

( + ) ( + ) = _____ ( – ) ( – ) = _____

The quotient of two integers with the different signs is negative

( + ) ( – ) = _____ ( – ) ( + ) = _____

-20

-5 4

-181-16

4

-30

-6

81

-4

-3

32-21

-9

3