Understanding Rational Numbers

Focus Question

Reason about rational numbers using a number line

Learn: Rational Numbers

A rational number is any number that can be written in the form
a/b where a and b are integers, and b ≠ 0.

Recall that natural numbers are from the set {1, 2, 3, 4, . . .}
where . . . means continues without end.

An integer is any number from the set {..., -3, -2, -1, 0, 1,2,3,...},
where “...” means continues on and on.

Learn: Rational Numbers

Multiple Choice

Which of the following is an integer?

• $$\frac{1}{2}$$  

• 0.53

• -9

• -1.6

Multiple Select

Check all that apply.

The number 7.10 is a(n) _______________________.

• Whole Number

• Integer

• Rational Number

Multiple Select

Check all that apply.

The number 75% is a(n) _______________________.

• Whole Number

• Integer

• Rational Number

Multiple Choice

Numbers like -3, -2, -1, 0, 1, 2, 3 are called

• whole numbers

• integers

• rational numbers

• natural numbers

Multiple Choice

The numbers 0, 1, 2, 3, ... are called

• whole numbers

• integers

• rational numbers

• natural numbers

Multiple Choice

-10 is a whole number

• True

• False

Multiple Choice

0.8 is a rational number

• True

• False

Multiple Choice

0 is a whole number

• True

• False

Multiple Choice

-9 is an integer

• True

• False

Multiple Choice

How would 5/9 be classified?

• rational 

• whole and integer

• whole

• rational and integer

Multiple Choice

How would 0.333333 be classified?

• rational 

• rational and whole

• only integer 

• only whole

Learn: Graph Rational Numbers on Number Line

Learn: Graph Rational Numbers on Number Line

Multiple Choice

What rational number is represented by the point A?

• -1.75

• -0.5

• -0.25

• 0.75

Multiple Choice

What rational number is represented by the point B?

• -1.75

• -0.5

• -0.25

• 0.75

Multiple Choice

What rational number is represented by the point A?

• -1 3/4

• -1/2

• -1/4

• 3/4

Multiple Choice

What rational number is represented by the point A?

• -1.75

• -0.5

• -0.25

• 0.75

Multiple Choice

What rational number is represented by the point B?

• -1 3/4

• -1/2

• -1/4

• 3/4

Learn: Absolute Value of Rational Numbers

Learn: Find Absolute Value of Rational Numbers

Multiple Choice

Which rational number has the LEAST value?

Multiple Choice

Which rational number has the GREATEST value?

Multiple Select

Which of these have an absolute value greater than 10?  Select all that apply.

• $$\left|-12.5\right|$$  

• $$\left|-7\right|$$  

• $$\left|15\ \frac{1}{4}\right|$$  

• $$\left|-10.6\right|$$  

Multiple Choice

Fill in the blank with the correct sign:  <, >, or =.
−|4| _____ −(−4)

• <

• >

• =

Multiple Choice

Fill in the blank with the correct sign:  <, >, or =. 
 |-⅓| ____ |⅓|

• <

• >

• =

For different signs: Use the SIGNS to compare

The POSITIVE is always GREATER than negative

Learn: Compare Rational Numbers

Learn: Compare Rational Numbers

For same signs: Use the SIZE to compare on number line

The number further to the RIGHT is always GREATER

Multiple Choice

Use <, >, or = to compare.

• <

• >

• =

Multiple Choice

Use <, >, or = to compare.

• <

• >

• =

Multiple Choice

Use <, >, or = to compare.

• <

• >

• =

Multiple Choice

Use <, >, or = to compare.

• <

• >

• =

Learn: Order Rational Numbers

To order rational numbers, follow these steps:
1. Write each value in the same form.
All numbers as fractions or All numbers as decimals

2. Use the signs of the numbers, place value, or a number line to
compare the numbers.

3. Order the values from least to greatest, or greatest to least,
depending on what you are asked to do.

Learn: Order Rational Numbers

Use the steps to order these rational numbers,

Multiple Choice

Order the rational numbers from least to greatest.

• -1.25, 1.25, -3/2, 1 1/2

• -1.25, -3/2, 1.25, 1 1/12

• -3/2, -1.25, 1.25, 1 1/2

• 1 1/2, 1.25, -1.25, -3/2

Multiple Choice

Order the rational numbers from least to greatest.

• -0.5, 1/2, -0.75, 3/4

• 3/4, 1/2, -0.5, -0.75

• -0.75, -0.5, 3/4, 1/2

• -0.75, -0.5, 1/2, 3/4

Multiple Choice

Given x = -2, what order would these expressions appear on the number line?

• -4, x, |-1.5|, -x, |5|, |-6|

• |-6|, -4, x, |-1.5|, -x, |5|

• |-6|, -4, -x, |-1.5|, x, |5|

Multiple Choice

Which graph correctly shows all the temperatures that are warmer than -2 degrees Celsius?

Complete the Textbook Check Questions in

your Textbook on the correct pages.

Then check your answers on the next slide

and mark your work in your book.

Check Questions (Pg )

Check Answers (Pg )