Integers:Integers:Comparing and Comparing and

OrderingOrdering

EQEQ• How do we compare and order

rational numbers?

Rational NumbersRational Numbers

Rational Numbers

Integers Fractions/Decimals

Whole Numbers(Positive Integers)

Negative Integers

Rational numbersRational numbers

•Numbers that can be written as a fraction.

Example: 2 = 2 = 2 ÷ 1 = 2

1

Whole NumbersWhole Numbers• Positive numbers that are not

fractions or decimals.

1 2 3 4 5 6

IntegersIntegers• The set of whole numbers and their

opposites.

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

Positive IntegersPositive Integers• Integers greater than zero.

0 1 2 3 4 5 6

Negative IntegersNegative Integers• Integers less than zero.

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

Comparing IntegersComparing Integers• The further a number is to the right

on the number line, the greater it’s value.

Ex: -3 ___ -1

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

-1 is on the right of -3, so it is the greatest.

..

<

Comparing IntegersComparing Integers• The farther a number is to the right

on the number line, the greater it’s value.

Ex: 2 ___ -5

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

2 is on the right of -5, so it is the greatest.

..

>

Comparing IntegersComparing Integers• The farther a number is to the right

on the number line, the greater it’s value.

Ex: 0 ___ -2

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

0 is on the right of -2, so it is the greatest.

..

>

Ordering IntegersOrdering IntegersWhen ordering integers from least to

greatest follow the order on the number line from left to right.

Ex: 4, -5, 0, 2

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

Least to greatest: -5, 0, 2, 4

.. . .

Ordering IntegersOrdering IntegersWhen ordering integers from greatest

to least follow the order on the number line from right to left.

Ex: -4, 3, 0, -1

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

Greatest to least: 3, 0, -1, -4

.. . .

Try This:Try This:a. -13 ___ 4

b. -4 ___ -7

c. -156 ___ 32

<

<

<d. Order from least to greatest:15, -9, -3, 5 _______________

e. Order from greatest to least:-16, -7, -8, 2 _______________

-9, -3, 5, 15

2, -7, -8, -16

EQEQ• How do we find the absolute value of

a number?

Absolute ValueAbsolute Value• The distance a number is from zero

on the number line.

Symbols: |2| = the absolute value of 2

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

It takes two jumps from 0 to 2.

Start at 0, count the jumps to 2.

|2| = 2

Absolute ValueAbsolute Value• The distance a number is from zero

on the number line.

Ex: |-4| =

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

It takes four jumps from 0 to -4.

Start at 0, count the jumps to -4.

|-4| = 4

Solving Problems with Solving Problems with Absolute ValueAbsolute Value

When there is an operation inside the absolute value symbols; solve the problem first, then take the absolute value of the answer.

Ex: |3+4| = |7| = 7

Ex: |3|- 2 = 3-2 = 1

Hint: They are kind of like parentheses – do them first!

Try This:Try This:a. |15| = _____

b. |-12| = _____

c. |-9| + 4 = _____

d. |13 - 5| = _____

15

12

13

8