Understanding and Comparing Integers

1.4

Comparing and Ordering Integers

1) 11 ( 7) – 9 (5 )

2) 5.8(3) + 3(1.1)

3) 7 [2.5 + 3(12 – 7)]

4)  (9.8+ 2.2)/(7 - 5)

Complete on your printed note sheet or Copy the problem and solve in your notebook

Bell Ringer

Evaluate using PEMDAS

• 1)  11 ( 7) – 9 (5 )

• 2)  5.8(3) + 3(1.1)

• 3)  7 [2.5 + 3(12 – 7)]

• 4)   (9.8+ 2.2)/(7 - 5)

Vocabulary

write these in your notes

Integer: any positive or negative whole number including 0

• Negative Integer: integers that are less than 0

• Positive Integer: integers that are MORE than 0

Absolute Value: is a numbers distance from 0 on a number line

• absolute value is ALWAYS a positive number

• example |-10| = 10 and |10| = 10

Opposite: The opposite of a number is the numbers equal distance from 0 on both sides of the number line

• The opposite of 10 is - 10

• The opposite of -6 is 6

Multiple Select

What number is greater?

• 99

• 101

Multiple Select

what number is greater?

• 3.14

• 3.15

Multiple Select

What number is greater

• 2.5

• 2.49

Multiple Choice

What number is greater?

• -1

• 1

-3, -2, -1, 0, 1, 2, 3 are called INTEGERS

• Negative Integers are integers that are LESS than 0; they are found on the left side of 0 on the number line

• Positive Integers are integers that are MORE than 0; they are found on the right side of 0 on the number line

In the space provided create a number line that looks like this: Note, 0 does not have to be the middle if you are graphing more negative integers than positive

inters in the real world - get ready to graph these on a number line

Poll

On your number line, graph the following numbers and choose Which insect has the lowest super cooling point measured in $$\degree C$$  ?

• Arctic Beetle  $$-54\degree C$$  

• Gall beetle  $$-39\degree C$$  

• Goldenrod Gallfly  $$-9\degree C$$  

• Snow Flea  $$-19\degree C$$  

• Wooly Bear Caterpillar  $$-70\degree C$$  

were you right?

-8, 5, -4, 2, 0, 6

graph in your notes

Multiple Choice

Which of the following are NOT integers

• -3

• 1

• 0

• 2.2

|Absolute Value|

Absolute Value - the absolute value on an integer is equal to it's distance from 0. (absolute value is always a positive number)

The integers -4 and 4 both have an absolute value of 4.

|5| and |-5| = 5

|-7| and |7| = 7

|0| = 0

Multiple Choice

Can an absolute value of a number ever be a negative number?

• yes

• no

Multiple Choice

find the absolute value of -24

|-24|

• 24

• -24

Multiple Choice

find the absolute value of 10

|10|

• 10

• -10

copy the problem and answer in your notes

1) |-7| =

2) | 9| =

3) |6| =

4) |-11| =

Opposite Numbers

Opposite numbers are numbers that share the same distance from 0 on a number line.

-4 and 4 are opposite numbers

-4 can be read as "negative 4" or "the opposite of 4"

The opposite of 6 is -6

The opposite of -15 is 15

Multiple Choice

Find the opposite of 9

• 9

• -9

Multiple Choice

Find the opposite of -24

• -24

• 24

Copy and solve for the opposite

1)  3

2)  -1

3)  -12

4)  10

Multiple Choice

how do you say this variable expression 9|x|

• 9 times the absolute value of x

• 9 times x

• 9 divided by x

Multiple Choice

How would you read this variable expression

|y| + 8

• y plus 8

• the absolute value of y plus 8

• the opposite of y plus 8

Multiple Choice

How do you read and solve this variable expression when y = -5

-y

• the opposite of -5 is 5

• y is -5

• negative y is -5

Example 4: Evaluating Variable Expressions

solve when y = -5

1) -y

2) 17- |y|

3) |y| + 9

4) |y| - 1

examples for 1 and 2 on the next slide

This is #1 and 2 of Example 3 in your notes

Open Ended

$$\left|y\right|+9$$  

solve when y = -5

Example 4: Evaluating Variable Expressions

solve when y = -5

1) -y

2) 17- |y|

3) |y| + 9

4) |y| - 1

examples for 1 and 2 on the next slide

Open Ended

$$\left|y\right|-1$$  

solve when y = -5