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Comparing and ordering fractions: Class 6 practice

To compare fractions with different denominators, rewrite them with a common denominator (or cross-multiply two at a time). Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Equivalent fractions
  • LCM

The idea behind comparing and ordering fractions

To compare fractions with different denominators, rewrite them with a common denominator (or cross-multiply two at a time). With equal numerators, the fraction with the smaller denominator is bigger.

Step-by-step method

  1. Find the LCM of the denominators.
  2. Convert each fraction.
  3. Compare numerators and order them.

Worked example 1 (Basic)

Arrange in ascending order: 3/5, 4/5.

  1. Common denominator 5: 3/5 = 3/5, 4/5 = 4/5
  2. Order the numerators
  3. Answer: 3/5 < 4/5

Worked example 2 (Standard)

Arrange in ascending order: 1/12, 2/4, 4/9.

  1. Common denominator 36: 1/12 = 3/36, 2/4 = 18/36, 4/9 = 16/36
  2. Order the numerators
  3. Answer: 1/12 < 4/9 < 2/4

Worked example 3 (Challenge)

Arrange in descending order: 3/5, 1/5, 7/12.

  1. Common denominator 60: 3/5 = 36/60, 1/5 = 12/60, 7/12 = 35/60
  2. Order the numerators
  3. Answer: 3/5 > 7/12 > 1/5

Common mistakes and misconceptions

  • Thinking a bigger denominator gives a bigger fraction
  • Comparing only the numerators

Practice questions

  1. (Basic) Arrange in ascending order: 6/12, 4/9.
  2. (Basic) Arrange in ascending order: 1/4, 2/5.
  3. (Standard) Arrange in ascending order: 1/4, 3/4, 3/9.
  4. (Standard) Arrange in ascending order: 3/4, 7/12, 7/8.
  5. (Challenge) Arrange in descending order: 8/10, 3/6, 2/3.
  6. (Challenge) Arrange in descending order: 2/5, 5/10, 1/3.

Answer key with full working

  • Q1: Common denominator 36: 6/12 = 18/36, 4/9 = 16/36 → Order the numerators → Answer: 4/9 < 6/12
  • Q2: Common denominator 20: 1/4 = 5/20, 2/5 = 8/20 → Order the numerators → Answer: 1/4 < 2/5
  • Q3: Common denominator 36: 1/4 = 9/36, 3/4 = 27/36, 3/9 = 12/36 → Order the numerators → Answer: 1/4 < 3/9 < 3/4
  • Q4: Common denominator 24: 3/4 = 18/24, 7/12 = 14/24, 7/8 = 21/24 → Order the numerators → Answer: 7/12 < 3/4 < 7/8
  • Q5: Common denominator 30: 8/10 = 24/30, 3/6 = 15/30, 2/3 = 20/30 → Order the numerators → Answer: 8/10 > 2/3 > 3/6
  • Q6: Common denominator 30: 2/5 = 12/30, 5/10 = 15/30, 1/3 = 10/30 → Order the numerators → Answer: 5/10 > 2/5 > 1/3

Syllabus note

This skill is listed under "Fractions" for Class 6 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

Frequently asked questions

Which chapter is comparing and ordering fractions in?

"Fractions", Class 6 Maths (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

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