1.1 Positive and Negative Numbers

1.2 Addition with Negative Numbers

1.3 Subtraction with Negative Numbers

1.1- Definition

Positive number – a number greater than zero.

0 1 2 3 4 5 6

Definition

Negative number – a number less than zero.

0 1 2 3 4 5 6-1-2-3-4-5-6

Definition

Opposite Numbers – numbers that are the same distance from zero in the opposite direction

0 1 2 3 4 5 6-1-2-3-4-5-6

Definition

Integers – Integers are all the whole numbers and all of their opposites on the negative number line including zero.

7 opposite -7

Definition

Absolute Value – The size of a number with or without the negative sign.

The absolute value of 9 or of –9 is 9.

Negative Numbers Are Used to Measure Temperature

Negative Numbers Are Used to Measure Under Sea Level

0102030

-10-20-30-40-50

Negative Numbers Are Used to Show Debt

Let’s say you bought a car but had to get a loan from the bank for $5,000.When counting all your money you would add in -$5,000 to show you still owe the bank $5,000.

Hint

If you don’t see a negative or positive sign in front of a number it is positive.

9+

Pg 93 #28, 30, 32, 34

28) -4 -40

Place either < or > between each of the following pairs of numbers so that the statement is true.

30) |8| -233) |-2| |-7|34) |-3| |-1|

<

>

>

>

Pg 93 #40, 46, 50, 64, 68Find each of the following absolute

values.

40) |-9|

46) |-350|

50) |457|Simplify each of the following.

64) -(-5)

68) -|-5|

9350457

5

-5

1.2 -Integer Addition RulesRule #1 – If the signs are the

same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer.

9 + 5 = 14-9 + (-5) = -14

Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer.

Rule #2 – If the signs are different pretend the signs aren’t there.

Subtract the smaller from the larger one

put the sign of the one with the larger absolute value in front of your answer.

Integer Addition Rules

Rule #2 – If the signs are different pretend the signs aren’t there.

Subtract the smaller from the larger one

put the sign of the one with the larger absolute value in front of your answer.

-14+ 7 =14 - 7 = 7Larger abs. value

Answer = - 7

One Way to Add Integers Is With a Number Line• When the number is positive, count to

the right.• When the number is negative, count to

the left.

+-0 1 2 3 4 5 6-1-2-3-4-5-6

One Way to Add Integers Is With a Number Line

+

-

+3 + (-5) = -2

0 1 2 3 4 5 6-1-2-3-4-5-6

One Way to Add Integers Is With a Number Line

+

-

+6 + (-4) = +2

0 1 2 3 4 5 6-1-2-3-4-5-6

+

-

+3 + (-7) = -4

0 1 2 3 4 5 6-1-2-3-4-5-6

One Way to Add Integers Is With a Number Line

One Way to Add Integers Is With a Number Line

-

+

-3 + 7 = 4

0 1 2 3 4 5 6-1-2-3-4-5-6

Solve the Problems

Pg 101-10233, 44, 58, 68, 72

Pg 101-10233, 44, 58, 68, 72, 7933) -375 + 409

44) -27 + (-56) + (-89)

58) (-11 + 5) + (-3 + 2)

72)What number do you add to -5 to get -8?

Rule #2: 409 – 375 = 34

Rule #1: 27 + 56 + 89 =172

= -172

Rule #2: (11 – 5) = 6 = -6Rule #2: (3 - 2) = 1 = -1Order of operations: Rule #1: -6 + (-1) = -7

n + (-5) = -8 n = -3 -3 + (-5) = -8

1.3 Integer Subtraction RuleSubtracting a negative number is the same as adding a positive. Change the signs and add.

2 – (-7) is the same as

2 + (+7)2 + 7 = 9!

1.3 Integer Subtraction RuleIf a and b represent any two numbers, then it is always true that

a – b = a + (-b) (Change the signs and add)

2 – 7 is the same as

2 + (-7)Rule #2: 7 – 2 = 5

= -5

Table in Example 3

Here are some more examples.

12 – (-8)

12 + (+8)

12 + 8 = 20

-67 – (-17)

-67 + (+17)

-67 + 17 = -50

Solve the Problems

Pg 109-11024, 27, 41, 44, 46, 61, 62

Pg 109-110 #24, 27, 41, 44, 4624) -86 – 31

27) -35 – (-14)

41) -900 + 400 – (-100)

44) Subtract 8 from -2.

45) Find the difference of -5 and -1.

(-86) + (-31) = -117

(-35) + 14 = -21

-900 + 400 + 100 = -900 + 500 = -400

-2 – 8 = -2 + (-8) = -10

-5 – (-1) = -5 + 1 = -4

Pg 110 #61, 6261) On Monday, the temperature reached a high of 28

degrees above 0. That night it dropped to 16 degrees below 0. What is the difference between the high and the low temperature for Monday?

62) A gambler loses $35 playing poker one night and then loses another $25 the next night. Express the situation with numbers. How much did the gambler lose?

28 – (-16) = 28 + 16 = 44 deg.

-35 – 25 = -35 + (-25) = -60