Integers: are positive and negative whole numbersExamples:

…-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5…

Numbers placed in a line make a scale. Scales can include regular (positive) numbers as well as zero and negative numbers. When we put numbers in a line we make a scale. The distance between the numbers is always the same.

If you want to know the temperature in your room, you use a thermometer. We can easily read the temperature by looking at the numbers next to the tube.

A Cold Night As the temperature falls in a green house on a

cold winter night, Mr. Leumer’s plants might be damaged. The Celsius (°C) scale on the thermometer includes zero. Although, you cannon count zero things, a temperature of zero is real enough.

Zero °C is temperature at which ice forms. If the night is cold enough, the temperature could go on falling. What could be below zero? The answer is written down using negative numbers.

If the temperature continued to fall in equal steps, we would count down like this: negative one, negative two, negative three, and so on.

Negative numbers are written using the “ – “ symbol, which is also used for subtraction. Thus, “negative 3” is also written as “ –3”. In mathematical symbols this would be written:

–5 < –3

The number line can be divided into positive and negative numbers much like the thermometer. Numbers that are opposite additive inverses are the same distance away from zero but on opposite sides of 0 on a number line.

The opposite of a number. Additive Inverses have a sum

of zero.Example: 5 and -5

- 7 and 7

-34 and 34

0 and 0

Absolute Value: is the distance away from zero on a number line.Example: |5| = 5

|-7| = 7

|5 – 8| = 3

|-6 + 9| = 3

On the first plays in the football game, Gannon’s team, starting on the 20 yard line, lost 5 yards and then gained 5 yards. On the next two downs the team rushed for 3 yards and then 4 more yards. What yard line is Gannon’s team on?

20 – 5 + 5 = 20 20 + 3+ 4 = 27 27 yard line

To ADD integers with the same sign, just add and keep the sign.Example:

7 + 2 = 9

-7 + -2 = -9

-15 + -3 = -18

To ADD integers with different signs, subtract and take the sign of the larger number (absolute value)Example:

-2 + 9 = 7

2 + -9 = -7

4 + -18 = -14

To SUBTRACT : Keep-change-change(rewrite as an addition problem)

Then follow the addition rules.Example: (Keep-change-change)

-2 – 3 → -2 + (-3) = -5-2 – (-3) → -2 + (+3) = 1

5 – 6 → 5 + (-6) = -1

To MULTIPLY or DIVIDE, multiply or divide as usual.If they have the same signs, the answer is positive.

Example: -3 (-6) = 18

3 • 6 = 18-10 ÷ -5 = 2

10 ÷ 5 = 2

If they have different signs, the answer is negative.

Example:

-2 (-3) = 6 2 (-3) = -6

-10 ÷ 5 = -210 ÷ -5 = -2