Comparing and Ordering Rational Numbers

Comparing and Ordering Rational Numbers

1/15/26

Numbers to the LEFT -> LESS

Numbers to the RIGHT -> MORE

Key Ideas

• Understand decimals as locations on a number line

• Compare positive and negative decimals using position

Learning Goal

MINI-LESSON 1:
Decimals as a Location on a Number Line

Review: Whole Numbers on a Number Line

• Zero is the center of the number line

• Positive numbers are to the right

• Negative numbers are to the left

TOGETHER: Plot 9, 0, -5, 3, -2 and 7 on the number line below.

Decimals Between Whole Numbers

• Decimals show parts between whole numbers

• The space between whole numbers can be divided evenly

• Sometimes we have to approximate (guess) where they go best

Now Add -2.5, 6.5, and -0.5

Zooming In On Negatives

• Between - 1 and -2 there are an INFINTE amount of numbers.

• Plot -1 and -2 on the number line below. Plot -1 on the far right, then count to 10 and plot -2.

Add -1.2, -1.8, and then estimate where -1.65 might go.

Multiple Choice

Which decimal is less than 0.75?

• 0.91

• 0.94

• 0.80

• 0.72

Multiple Choice

Which symbol makes the statement below true?

0.45 ___________ 0.54

• $$>$$

• $$<$$

• $$=$$

Multiple Choice

0.07  ___  0.03
Which symbol correctly compares the two numbers?

• <
• >
• =

Multiple Choice

0.25  ___  0.15
Which symbol correctly compares the two numbers?

• <
• >
• =

Mini Lesson #2:
Converting Fractions & Mixed Numbers to Decimals

• Convert fractions and mixed numbers into decimals

• Prepare numbers so they are easy to compare
  

Negative Fractions as Decimals

• Convert the fraction first

• Attach the negative sign at the end
  

Mixed Numbers

• Convert to an improper fraction

  OR
  

• Separate the whole number and the fraction and just divide the fraction to find the digits for after the decimal
  

Multiple Choice

$$3\frac{4}{5}$$  

• 3.45

• 3.8

• .345

• 0.8

Multiple Choice

 Convert the following mixed number to a decimal:   $$15\ \frac{3}{4}$$  

• 15.25

• 15.5

• 15.75

• 15. 34

Dropdown

$$4\ \frac{5}{8}$$ ​

Select answer

$$4\ \frac{3}{4}$$

Mini Lesson #3:
Comparing Decimals with Different Place Values

• Line Up Decimal Points

• Add zeros as needed (this does not change the numbers value!!
  

​1.9 = 1.90

-0.63 = -0.6333

Comparing Negatives

• Compare digits from left to right

• For negatives, bigger digits mean smaller values

Compare -1.98 and -1.9 on the number line below.

Common Mistake!!

• More digits does NOT mean bigger

• Think about a numbers position on the number line

• Think about converting the number to a fraction using place value

Compare 2.0006 and 2.06 using either the number line or by writing them as fractions.

Multiple Choice

-12.5 ______ 12.5

• <

• >

Multiple Choice

2.07 _____ 2.7

• <

• >

Multiple Choice

-2.07 _____ -2.7

• <

• >

Mini Lesson #4:
Reading Decimals from Number Lines

Learning Goal:

• Convert points on a number line into decimals
  

Counting Equal Parts

• LINES split up the PARTS, do not count lines

• Count how many equal parts are between whole numbers
  

​10 parts = tenths
5 parts = fifths

Multiple Choice

Which number line shows 1/2

• A

• B

• C

• D

Multiple Choice

Label Point C

• 5/6

• -2/6

• -2/3

• -1/2

Multiple Choice

Which decimal is located at point B

• 4.0

• 0.5

• 1.4

• 0.4

Multiple Choice

• -8.2

• 1.3

• -2.2

• -4.5

Multiple Select

Select all that apply: Which number is plotted on the graph?

• -0.67

• 0.67

• $$-\frac{1}{3}$$

• $$-\frac{2}{3}$$

• $$-\frac{1}{2}$$

Mini Lesson #5:
Comparing & Sorting Mixed Representations

Learning Goal:

• Compare and sort numbers shown in different forms
  

Step by Step Strategy

1. Convert everything to decimals

2. Line up decimal points

3. Add zeros

4. Compare digit by digit

5. Check on a number line
   

​

Step by Step Strategy

1. Convert everything to decimals

2. Line up decimal points

3. Add zeros

4. Compare digit by digit

5. Check on a number line
   

​

Multiple Choice

Order from least to greatest.

• 5/6, 0.75, 7/12

• 5/6, 7/12, 0.75

• 7/12, 0.75, 5/6

Multiple Choice

Order from greatest to least.

• 0.9, 0.86, 8/9

• 8/9, 0.9, 0.86

• 0.9, 8/9, 0.86