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GRADE 6 · MATHEMATICS

Comparing and Ordering Fractions

Learn how to decide which fraction is greater, which is smaller, and how to arrange several fractions in order. Start with visual models, then use common denominators and helpful benchmarks.

Learning time: approximately 25–30 minutes · Beginner level

What You Will Learn

1. What Does It Mean to Compare Fractions?

Comparing fractions means deciding which fraction represents the greater amount. The symbols help us show the result:

One half is less than three quarters:

12<34

The bars show the same-sized whole divided into equal parts.

Important: You can only compare the shaded parts fairly when the wholes are the same size.

2. Fractions with the Same Denominator

When two fractions have the same denominator, their parts are the same size. Compare the numerators: the fraction with the larger numerator is greater.

Example: Compare 3/8 and 5/8. Both fractions are divided into eighths. Since 5 is greater than 3, 5/8 > 3/8.

Try another: 2/7 and 6/7. The denominator is the same, and 6 is greater than 2, so 2/7 < 6/7.

3. Fractions with the Same Numerator

When two positive fractions have the same numerator, the fraction with the smaller denominator is greater. A whole divided into fewer equal pieces gives larger pieces.

Example: Compare 3/4 and 3/8. Three quarters uses larger pieces than three eighths, so 3/4 > 3/8.
Remember: This rule works for positive fractions with the same numerator. Do not assume a larger denominator always makes a fraction larger.

4. Compare Different Denominators Using Equivalent Fractions

For fractions with different denominators, rewrite them as equivalent fractions with a common denominator. Then compare the numerators.

Worked example: Compare 2/3 and 3/4

  1. Find a common denominator for 3 and 4. The lowest common denominator is 12.
  2. Convert 2/3 into twelfths: multiply the top and bottom by 4, giving 8/12.
  3. Convert 3/4 into twelfths: multiply the top and bottom by 3, giving 9/12.
  4. Compare 8/12 and 9/12. Since 8 is less than 9, 2/3 < 3/4.
23=812<912=34

Both fractions are now expressed in twelfths, so their numerators can be compared directly.

Another example: Compare 5/6 and 7/9

  1. A common denominator for 6 and 9 is 18.
  2. 5/6 = 15/18 and 7/9 = 14/18.
  3. 15/18 is greater than 14/18, so 5/6 > 7/9.

5. Use Benchmarks to Compare Quickly

A benchmark is a familiar value that helps you estimate where a fraction belongs. Useful benchmarks include 0, 1/2 and 1.

Example: Compare 3/8 and 5/9. The fraction 3/8 is less than 1/2 because 3 is less than half of 8 (4). The fraction 5/9 is greater than 1/2 because 5 is greater than half of 9 (4.5). Therefore, 3/8 < 5/9.

Benchmarks are useful for quick comparisons. If the result is not clear, use a common denominator to check it exactly.

6. Put Fractions in Order

To order fractions, compare them carefully and place them from smallest to largest or largest to smallest.

Worked example: Order 1/2, 2/3 and 3/4 from least to greatest

  1. Choose a common denominator: 12 works for 2, 3 and 4.
  2. Convert: 1/2 = 6/12, 2/3 = 8/12 and 3/4 = 9/12.
  3. Order the numerators: 6, 8, 9.
  4. Write the original fractions in that order: 1/2, 2/3, 3/4.
Tip: When ordering several fractions, find one common denominator for all of them. Keep each converted fraction beside its original fraction so you do not mix them up.

7. Common Mistakes to Avoid

Comparing denominators only: A bigger denominator does not automatically mean a bigger fraction. Compare equivalent fractions or use a suitable rule.
Changing only the denominator: To make an equivalent fraction, multiply or divide the numerator and denominator by the same non-zero number.
Comparing different-sized wholes: Fraction comparisons assume the wholes are the same size.
Reversing the order: When a question asks for least to greatest, start with the smallest value.

8. Practice Exercises

Try these questions before revealing the answers.

  1. Use >, < or =: 4/9 ___ 7/9.
  2. Use >, < or =: 3/5 ___ 3/8.
  3. Compare 1/2 and 4/7 using a common denominator.
  4. Compare 5/6 and 7/9 using a common denominator.
  5. Arrange 1/3, 3/4 and 1/2 from least to greatest.
  6. Arrange 5/8, 2/3 and 3/4 from greatest to least.
Show practice answers and explanations
  1. 4/9 < 7/9 because the denominators match and 4 is less than 7.
  2. 3/5 > 3/8 because the numerators match and fifths are larger than eighths.
  3. 1/2 = 7/14 and 4/7 = 8/14, so 1/2 < 4/7.
  4. 5/6 = 15/18 and 7/9 = 14/18, so 5/6 > 7/9.
  5. 1/3, 1/2, 3/4.
  6. 3/4, 2/3, 5/8.

9. Test Your Understanding

Select one answer for each question, then choose Check Answers. Each question is worth one point.

1. Which fraction is greater: 3/8 or 5/8?
2. Which is greater: 2/5 or 2/7?
3. Which fraction is equivalent to 3/4 with denominator 12?
4. Which statement is correct?
5. Which list is in order from least to greatest?

10. Free Printable Worksheet

Print this worksheet or save it as a PDF for extra practice.

Learnora — Grade 6 Mathematics

Comparing and Ordering Fractions Worksheet

Name: __________________________ Date: _______________

Instructions: Show your working. Use equivalent fractions where needed.

  1. Write >, < or =: 2/9 ___ 7/9.
  2. Write >, < or =: 4/5 ___ 4/7.
  3. Compare 3/4 and 5/6. Show equivalent fractions.
  4. Compare 2/3 and 5/8. Show your working.
  5. Order 1/4, 2/3 and 1/2 from least to greatest.
  6. Order 7/8, 3/4 and 5/6 from greatest to least.
  7. Explain why 3/5 is greater than 3/8.

Keep practising — you are making progress!

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key
  1. 2/9 < 7/9.
  2. 4/5 > 4/7.
  3. 3/4 = 9/12 and 5/6 = 10/12, so 3/4 < 5/6.
  4. 2/3 = 16/24 and 5/8 = 15/24, so 2/3 > 5/8.
  5. 1/4, 1/2, 2/3.
  6. 7/8, 5/6, 3/4.
  7. Both fractions have the same numerator. Fifths are larger parts than eighths, so three fifths is greater than three eighths.

11. Lesson Summary

Next learning goal: Build on fraction comparisons by practising addition and subtraction of fractions.

Educational note: This is a curriculum-neutral Grade 6 lesson. Teachers and parents can adapt examples and practice to their local curriculum.