Integers

Integers

• Consist of positive and negative whole numbers

The Number Line……

• A number line consists of positive numbers (right of 0) and negative numbers (left of 0).

• A real life example of a number line is a temperature thermometer.

Negative Positive0

For example…..

• -5 would represent 5 degrees below zero.

• +4 would represent 4 degrees above zero.

Make the Comparison……

• 7 degrees below 0 is (warmer/colder) than 4 degrees above 0.

• 7 degrees below 0 is a (lower/higher) temperature than 4 degrees above 0.

Coordinates on a Graph….

• Find the best estimate of the point.

a. -2 b. 2 c. -1.75 d. -1.5

0 1 212

Sets and Subsets……

• A set is a group of numbers.

Example: Set A = {1,2,3,4,5}

• A subset is a group of numbers in which every member is in another set.

Example: Set B = {1,2,3}

• So, B is a subset of A.

Which of the following would represent a subset of integers?

• States Sales Tax Rate

• Amount of Gas in a Car

• Number of Students in Class

• A Dinner Receipt

You Try…Which of the following would represent a subset of integers?

• Costs of a TV

• # of miles on the odometer of a car

• A person’s weight

• Number of residents in South Carolina

Inequalities…..

• We use inequalities to compare numbers.

• The following are inequalities:

Examples…….

• “4 is less than 7” -

• “9 is greater than or equal to 5” -

74

59

You Try……Insert the appropriate inequality sign.

1. -5 -2

2. -7 2

3. 4 -12

We have the Yellow Team and the Red Team….

Assign the left side of the room to the red team and right side to the yellow team.

Who is favored & by how much if we have…

So…how can I represent: -7 + 3

Start with:

Add 3: Which Leaves:

Use the counters….

86

Use the counters….

5 2

Use the counters….

3 4

Use the counters….

6 2

Use the counters….

5 8

No Counters!

100 150

No Counters

220 170

So…How do I add signed numbers?

How close were you?

• Same Signs• Add the numbers• Take their sign

• Different Signs• Subtract the numbers• Take the sign of the number with largest absolute

value

Opposites:

• The opposite of 5 is -5.

• What is –(-2)?

Use the counters….

3 2( )

Use the counters….

12 20( )

Do the following:

• 9 – 8 =

• -6 – (-9)=

• -14 + 3 =

• 10 – 19 =

Do the following:

• 29 - 32 =

• -82 – 12 =

• -45 + 78 =

• 16- (-27) =

What’s 4 x -3?

=

Let’s Multiply:

52

Let’s Multiply:

3 2

So…How do I explain -3 x -4?

• I like to think of this as – (3 x -4) and think of it as the opposite of (3 x -4).

• Can you develop a rule for Multiplication?

Let’s Multiply:

3 2

So…what’s the rule for multiplying integers?

Division: 8 2

Divide: 6 3

So..what’s the rule for Dividing integers

Multiplying & Dividing:

• Like signs – positive

• Unlike signs - Negative

Homework

• Worksheet