# Ordering and Comparing Rational Numbers

Welcome to our Ordering and Comparing Rational Numbers page.

Here you will find our range of 6th Grade worksheets and support which will help you learn to order and compare negative numbers, fractions and decimals.

Want to test yourself to see how well you have understood this skill?.

• Try our NEW quick quiz at the bottom of this page.

## Ordering and Comparing Rational Numbers

### Ordering Rational Numbers Examples

#### 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:

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

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

### More Recommended Math Worksheets

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### Ordering Rational Numbers Online Quiz

Our quizzes have been created using Google Forms.

At the end of the quiz, you will get the chance to see your results by clicking 'See Score'.

This will take you to a new webpage where your results will be shown. You can print a copy of your results from this page, either as a pdf or as a paper copy.

For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

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We also collect the results from the quizzes which we use to help us to develop our resources and give us insight into future resources to create.

This quiz tests your skill and apply your knowledge of ordering rational numbers here.

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