Ordering and Comparing Rational Numbers

Here you will find a range of worksheets to help you to compare and order rational numbers and position them on a number line.

Ordering a set of rational numbers can bring together many different skills, from using absolute value to comparing decimals or fractions and understanding negative numbers.

The sheets have been put in order of difficulty, with the easiest first.

Each problem sheet comes complete with an answer sheet.

We have split our sheets into 3 different sections:

• Comparing Rational Numbers
• Ordering Rational Numbers
• Positioning Rational Numbers

Using these sheets will help you to practice these skills:

• compare rational numbers using > , < and =
• order a set of 4 to 5 rational numbers
• position rational numbers on a number line
• convert improper fractions into mixed numbers

A rational number is a number that can be made by dividing one integer by another (non-zero) integer.

All rational numbers can be written in the form a/b , where a and b are both integers and b is not equal to zero.

All integers, fractions, repeating decimals and terminating decimals (which do not go on forever) are rational numbers.

These numbers are rational and can all be written in the form a/b:

• 2.7 (it can be written as 27/10)
• 160 (it can be written as 160/1)
• 0.361 (it can be written as 361/1000)
• 0.121212... = 0.12 (it can be written as 12/99)
• 4.8888888... = 4.8 (it can be written as 44/9)
• -3.25 (it can be written as -13/4)

These numbers are not rational and cannot be written in the form a/b:

• \[ \sqrt{2}, \; \pi, \; \sqrt{11}, \; \sin (12^{\circ}), \; \cos (127^{\circ}), \; { 2\pi \over 3} \]

There are a few different skills you need to be able to do to order a set of rational numbers:

You need to be able to:

• Order a set of negative numbers including decimals
• Understand absolute value
• Convert an improper fraction into a mixed number
• Order a set of fractions

Once you have these skills, you are ready to order your rational numbers!

Example 1) Put the following rational numbers in order, smallest first:

\[ 3.25, \; -2, \; |-1 {1 \over 2} |, \; {3 \over 4}, \; -{7 \over 2} \]

Step 1) Convert any improper fractions into mixed numbers.

\[ {7 \over 2} = 3 {1 \over 2} \]

So \[ -{7 \over 2} = -3 {1 \over 2} \]

Step 2) Sort the numbers into 2 groups: negative and positive:

Negative numbers are:

• \[ -2, \; -3 {1 \over 2} \]

Positive numbers are:

• \[ 3.25, \; |-1 {1 \over 2}|, \; {3 \over 4} \]

Step 3) Order the negative numbers from least to greatest.

The number which is the most negative has the lowest value.

\[ Least \; to \; Greatest: \; -3 {1 \over 2}, \; -2 \]

Step 4) Put the positive numbers in order from least to greatest.

\[ |-1 {1 \over 2}| = 1 {1 \over 2} \]

\[ Least \; to \; Greatest: \; {3 \over 4}, \; |-1 {1 \over 2}|, \; 3.25 \]

Step 5) Put the two lists together:

\[ -3 {1 \over 2}, \; -2, \; {3 \over 4}, \; |-1 {1 \over 2}|, \; 3.25 \]

\[ The \; order \; is \; - {7 \over 2}, \; -2, \; {3 \over 4}, \; |-1 {1 \over 2}|, \; 3.25 \]

Example 2) Put the following rational numbers in order, smallest first:

\[ |-4|, \; {7 \over 4}, \; -0.5, \; |-1.8|, \; -1 {2 \over 3} \]

Step 1) Convert any improper fractions into mixed numbers.

\[ {7 \over 4} = 1 {3 \over 4} \]

Step 2) Sort the numbers into 2 groups: negative and positive:

Negative numbers are:

• \[-0.5, \; -1 {2 \over 3} \]

Positive numbers are:

• \[ |-4|, \; 1 {3 \over 4}, \; |-1.8| \]

Step 3) Order the negative numbers from least to greatest.

The number which is the most negative has the lowest value.

\[ Least \; to \; Greatest: \; -1 {2 \over 3}, \; -0.5 \]

Step 4) Put the positive numbers in order from least to greatest.

\[ 1 {3 \over 4} = 1.75 \; which \; is \; less \; than \; 1.8 \]

\[ Least \; to \; Greatest: \; 1 {3 \over 4}, \; |-1.8|, \; |-4| \]

Step 5) Put the two lists together:

\[ -1 {2 \over 3}, \; -0.5, \; 1 {3 \over 4}, \; |-1.8|, \; |-4| \]

\[ The \; order \; is \; -1 {2 \over 3}, \; -0.5, \; {7 \over 4}, \; |-1.8|, \; |-4| \]

These sheets are put in order of difficulty with the easiest sheet first.

The sheets have been split into 3 sections:

• Comparing Rational Numbers Worksheets
• Ordering Rational Numbers Worksheets
• Positioning Rational Numbers Worksheets

The sheets on this page have been specially designed for 6th graders and are a great introduction to expressions and equations.

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.