🍕 Class 6 · Number system

Fractions for Class 6: notes, worked examples and practice

A fraction is a part of a whole. Once you can simplify, compare and add fractions with different denominators, the rest of fractions, decimals and ratios becomes much easier.

Updated 21 October 2026. Every worked example and answer on this page is checked by automated tests.

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Notes

Fractions: what you need to know

Chapter names and order differ by board and textbook edition, so follow your own textbook for the order.

What a fraction means

A fraction names equal parts of a whole. In 3/4 the denominator (4) says how many equal parts the whole is cut into, and the numerator (3) says how many parts you have.

Proper, improper and mixed fractions

A proper fraction like 3/5 is less than 1. An improper fraction like 7/4 is 1 or more. A mixed number such as 1 3/4 shows a whole number and a fraction. To convert 7/4, divide 7 by 4: the quotient 1 is the whole part and the remainder 3 is the new numerator.

Equivalent fractions

Multiply or divide the numerator and the denominator by the same number and the value does not change: 2/3 = 4/6 = 6/9. Dividing both by their highest common factor gives the simplest form.

Comparing fractions

If the denominators are equal, the bigger numerator is the bigger fraction. If not, make the denominators equal using the LCM, or cross-multiply: a/b is greater than c/d when a × d is greater than b × c.

Adding and subtracting

Make the denominators equal first, then add or subtract only the numerators and keep the denominator. Simplify at the end.

Formulas and rules to remember

a/b + c/b = (a + c)/b
a/b + c/d = (a × d + b × c)/(b × d), or use the LCM of b and d
a/b × c/d = (a × c)/(b × d)
a/b ÷ c/d = a/b × d/c

Solved examples

Example 1

Add 2/3 and 1/6.

The LCM of 3 and 6 is 6.
2/3 = 4/6.
4/6 + 1/6 = 5/6.

Answer: 5/6

Example 2

Simplify 18/24.

The HCF of 18 and 24 is 6.
18 ÷ 6 = 3 and 24 ÷ 6 = 4.

Answer: 3/4

Example 3

Convert 17/5 into a mixed number.

17 ÷ 5 = 3 with remainder 2.
So 17/5 = 3 and 2/5.

Answer: 3 2/5

Example 4

Which is greater, 3/4 or 5/7?

Cross-multiply: 3 × 7 = 21 and 5 × 4 = 20.
21 is greater than 20, so 3/4 is greater.

Answer: 3/4 is greater

Avoid these

Common mistakes

Adding the denominators

1/2 + 1/3 is not 2/5. The parts must be the same size before you add, so write 3/6 + 2/6 = 5/6.

Stopping before the simplest form

6/12 is not finished. Divide by the HCF (6) to get 1/2.

Thinking a bigger denominator means a bigger fraction

1/8 is smaller than 1/4 because the whole is cut into more, smaller parts.

10 practice questions with answers

Try each question on paper first, then tap it to check your answer. The questions are generated by code and each answer is checked.

Simplify 4/16:
Answer: 1/4
Simplify 21/35:
Answer: 3/5
Simplify 12/28:
Answer: 3/7
2/4 = 1/___
Answer: 2
8/16 = 1/___
Answer: 2
3/8 + 1/3 =
Answer: 17/24
4/12 + 2/4 =
Answer: 5/6
3/5 + 1/4 =
Answer: 17/20
5/7 × 2/3 =
Answer: 10/21
4/5 × 2/4 =
Answer: 2/5

More practice

Printable worksheets (PDF with answers)

Simplifying fractions (Grade 6)
Equivalent fractions (Grade 4)
Adding fractions with different denominators (Grade 5)

Games and lessons

Maths dictionary

Fraction calculator

Add, subtract, multiply and divide fractions and mixed numbers, with the answer simplified and the working shown step by step.

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FAQ

Fractions Class 6: questions students ask

How do I add fractions with different denominators?

Find the LCM of the denominators, rewrite each fraction with that denominator, add the numerators and simplify.

How do I compare fractions quickly?

Cross-multiply. For 3/4 and 5/7 compare 3 × 7 with 5 × 4. The side with the larger product is the larger fraction.

What is the difference between proper and improper fractions?

A proper fraction has a numerator smaller than its denominator, like 2/5. An improper fraction has a numerator equal to or larger than the denominator, like 9/4.

Is a whole number a fraction?

Yes. Every whole number can be written as a fraction with denominator 1, so 5 = 5/1.

Which board is this fractions page for?

It covers the ideas taught in CBSE, ICSE and state-board maths. Chapter names and order differ by board and textbook edition, so follow your own textbook for the exact order.

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