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Class 6 Maths: Fractions, 8 practice questions with answers

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These are 8 practice questions on Chapter 7, Fractions, of the new NCERT Class 6 Maths textbook, Ganita Prakash. Each has a worked answer and the textbook page it comes from. They cover comparing fractions by their units, a mistake with mixed numbers, an equal fraction with a given total, the odd one out among equal fractions, which fraction is closer to 1/2, a missing fraction in a sum, a mistake in adding fractions, and writing a fraction as a sum of two different fractional units. For a walk-through of the chapter itself, see our Class 6 Maths Chapter 7 explainer. Try each question on paper before you open the answer.

These questions are our own, drafted with AI help. Every answer was re-computed by a test script in exact fractions, and none of the chapter's own examples is reused or turned round. No practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Prakash, Grade 6, Chapter 7, printed pages 151 to 186):

Units and mixed numbers

Question 1. Decide which is bigger without changing to a common denominator, and say why: (a) 4/9 or 4/11; (b) 6/7 or 8/9.

Answer: (a) 4/9; (b) 8/9. (a) Both are 4 copies of a fractional unit. A whole cut into 9 equal parts has bigger parts than one cut into 11, so 1/9 is bigger than 1/11, and 4 ninths are more than 4 elevenths: 4/9 is bigger. (b) Each one is a whole with one unit missing: 6/7 is 1 − 1/7 and 8/9 is 1 − 1/9. Since 1/9 is smaller than 1/7, 8/9 is missing less, so 8/9 is bigger. (Fractional units, pages 151 and 152.)

Question 2. (a) Kabir wrote 3 2/5 = 3 × 2/5 = 6/5. What went wrong? Write 3 2/5 correctly as a fraction. (b) Kabir has a rope 3 2/5 m long and cuts it into pieces each 1/5 m long. How many pieces does he get?

Answer: (a) 3 2/5 means 3 + 2/5, not 3 × 2/5; it is 17/5. (b) 17 pieces. (a) A mixed number is a whole part plus a fractional part. Kabir multiplied instead of adding: his 6/5 is only a little more than 1, but 3 2/5 is more than 3. Each whole is 5 fifths, so 3 wholes are 15 fifths, and with 2 more fifths that makes 17/5. (b) Each piece is one fifth of a metre, so the number of pieces is the number of fifths in the rope. Each metre gives 5 pieces, so 3 metres give 15, and the 2/5 m left gives 2 more: 15 + 2 = 17 pieces, the same 17 as in 17/5. (Mixed fractions, pages 161 to 163.)

Question 3. Find a fraction equal to 5/8 whose numerator and denominator add up to 52. Explain your answer using equal shares.

Answer: 20/32. In 5/8 the numerator and denominator add up to 5 + 8 = 13. Multiplying both by the same number keeps the fraction equal and multiplies their sum by that number too, and 52 = 4 × 13, so multiply both by 4: 5 × 4 = 20 and 8 × 4 = 32, giving 20/32. Check: 20 + 32 = 52, and 20/32 = 5/8 because dividing 20 and 32 by 4 gives 5 and 8. With equal shares: 5 melons shared among 8 people gives each person 5/8 of a melon. Put 4 such groups together, 20 melons among 32 people, and everyone still gets the same share, 20/32 = 5/8. (Equivalent fractions as equal shares, pages 166 to 168.)

Question 4. Which one of these is NOT equal to 2/5: 18/45, 14/35, 22/55, 21/49? Show how you know, and write the odd one out in lowest terms.

Answer: 21/49, which is 3/7. Write each in lowest terms by dividing the numerator and denominator by their highest common factor: 18/45 ÷ 9 gives 2/5; 14/35 ÷ 7 gives 2/5; 22/55 ÷ 11 gives 2/5; but 21/49 ÷ 7 gives 3/7. Another check: a fraction equals 2/5 when 5 times its numerator equals 2 times its denominator. 5 × 18 = 90 = 2 × 45, 5 × 14 = 70 = 2 × 35 and 5 × 22 = 110 = 2 × 55, but 5 × 21 = 105 while 2 × 49 = 98, so 21/49 is the odd one out. (Equivalent fractions and lowest terms, pages 166 to 168 and 172 to 173.)

Comparing, adding and subtracting

Question 5. Which is closer to 1/2: 5/9 or 3/8? By how much is each one away from 1/2?

Answer: 5/9 is closer; 5/9 is 1/18 more than 1/2, and 3/8 is 1/8 less. Compare each with 1/2 using a common denominator. 1/2 = 9/18 and 5/9 = 10/18, so 5/9 is 1/18 above 1/2. 1/2 = 4/8 and 3/8 is 1/8 below it. Since 1/18 is a smaller fractional unit than 1/8, 5/9 is closer to 1/2. (Comparing fractions, pages 173 and 174.)

Question 6. Find the missing fraction: 2/9 + ___ = 7/12. Write it in lowest terms.

Answer: 13/36. The missing fraction is 7/12 − 2/9. A common multiple of 12 and 9 is 36: 7/12 = 21/36 and 2/9 = 8/36. Subtracting the numerators: 21 − 8 = 13, so the missing fraction is 13/36, already in lowest terms because 13 and 36 have no common factor except 1. Check: 8/36 + 13/36 = 21/36 = 7/12. (Subtracting fractions with different denominators, page 181.)

Question 7. Ravi wrote 2/3 + 1/4 = 3/7, adding the tops and adding the bottoms. (a) Show, without working out the right answer, that 3/7 cannot be correct. (b) Find the right sum.

Answer: (a) 3/7 is less than 2/3 alone; (b) 11/12. (a) Adding 1/4 to 2/3 must give more than 2/3. But 3/7 is less than 2/3: with denominator 21, 3/7 = 9/21 and 2/3 = 14/21. So 3/7 is wrong. (b) Fractions are added by first writing them in the same fractional unit. A common multiple of 3 and 4 is 12: 2/3 = 8/12 and 1/4 = 3/12, so the sum is 8/12 + 3/12 = 11/12. (Brahmagupta's method for adding fractions, pages 177 to 179.)

Question 8. Write each of these as the sum of two different fractional units (fractions with numerator 1), and find both ways for each: (a) 3/10, (b) 5/12, (c) 2/9. (d) Why does 1/9 + 1/9 not count for (c)?

Answer: (a) 1/5 + 1/10 or 1/4 + 1/20; (b) 1/3 + 1/12 or 1/4 + 1/6; (c) 1/6 + 1/18 or 1/5 + 1/45; (d) the two units must be different. (a) 1/5 + 1/10 = 2/10 + 1/10 = 3/10, and 1/4 + 1/20 = 5/20 + 1/20 = 6/20 = 3/10. (b) 1/3 + 1/12 = 4/12 + 1/12 = 5/12, and 1/4 + 1/6 = 3/12 + 2/12 = 5/12. (c) 1/6 + 1/18 = 3/18 + 1/18 = 4/18 = 2/9, and 1/5 + 1/45 = 9/45 + 1/45 = 10/45 = 2/9. A search over all pairs confirms these are the only two ways for each. (d) 1/9 + 1/9 does make 2/9, but it uses the same unit twice, and the question asks for different fractional units, as in the chapter's puzzle. (Adding fractional units, pages 178 and 183 to 185.)

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Sources

All opened and read on 1 November 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 150 for this chapter.

The rules are from the textbook pages above. The questions, worked answers and checks are our own, and every answer was re-computed by script. This guide is general information; follow your teacher and the textbook.

Practise with the worksheet: Add, Subtract, Compare Fractions, Class 6. Printable, in English, Hindi and Marathi, with an answer key.