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Solutions

Overview

Step-by-step NCERT solutions for Fractions (Chapter 7, NCERT Class 6 Mathematics) — every question and answer worked out in full, not just the final result. You can also read the Fractions textbook chapter.

Solved

What these solutions cover

All 47 questions in Fractions are solved in the PDF. Here's what's inside, exercise by exercise:

Fractional Units and Equal Shares

  1. Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh ____ kg.
  2. A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ___ kg.
  3. Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank ____ glass of sugarcane juice.
  4. The big fish weighs 1/2 kg. The small one weighs 1/4 kg. Together they weigh ____ kg.
  5. Arrange these fraction words in order of size from the smallest to the biggest: One and a half, three quarters, one and a quarter, half, quarter, two and a half.

Fractional Units as Parts of a Whole

  1. The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? (a) through (h)

Measuring Using Fractional Units

  1. Continue this table of 1/2 for 2 more steps.
  2. Can you create a similar table for 1/4?
  3. Make 1/3 using a paper strip. Can you use this to also make 1/6?
  4. Draw a picture and write an addition statement to show:
    • (a) 5 times 1/4 of a roti,
    • (b) 9 times 1/4 of a roti.
  5. Match each fractional unit with the correct picture: 1/3, 1/5, 1/8, 1/6 (four circles each divided differently).

Marking Fraction Lengths on the Number Line

  1. On a number line, draw lines of lengths 1/10, 3/10, and 4/5.
  2. How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.
  3. What is the length of the black line shown on the number line? The unit (0 to 1) is divided into two equal parts, and the blue line has length 1/2. Write the fraction for the black line.
  4. Write the fraction that gives the lengths of the black lines on the number line where the unit is divided into 5 equal parts. Marks shown: 1/5, 2/5, 3/5, 4/5, 1 — the four black lines extend beyond 1.

Mixed Fractions

  1. How many whole units are there in 7/2?
  2. How many whole units are there in 4/3 and in 7/3?

Mixed Fractions — Writing improper fractions as mixed numbers

  1. Figure out the number of whole units in each of the following fractions:
    • (a) 8/3,
    • (b) 11/5,
    • (c) 9/4.
  2. Can all fractions greater than 1 be written as mixed numbers?
  3. Write the following fractions as mixed fractions:
    • (a) 9/2,
    • (b) 9/5,
    • (c) 21/19,
    • (d) 47/9,
    • (e) 12/11,
    • (f) 19/6.

Mixed Fractions — Writing mixed numbers as fractions

  1. Write the following mixed numbers as fractions:
    • (a) 3 1/4,
    • (b) 7 2/3,
    • (c) 9 4/9,
    • (d) 3 1/6,
    • (e) 2 3/11,
    • (f) 3 9/10.

Equivalent Fractions — Fraction wall

  1. Looking at the fraction wall: Are the lengths 1/2 and 3/6 equal?
  2. Are 2/3 and 4/6 equivalent fractions? Why?
  3. How many pieces of length 1/6 will make a length of 1/2?
  4. How many pieces of length 1/6 will make a length of 1/3?

Equivalent Fractions — Fraction wall (extended)

  1. Are 3/6, 4/8, and 5/10 equivalent fractions? Why?
  2. Write two equivalent fractions for 2/6.
  3. 4/6 = __ = __ = __ = … (Write as many equivalent fractions as you can.)

Equivalent Fractions — Equal shares (missing numbers)

  1. Find the missing numbers:
    • (a) 5 glasses of juice shared equally among 4 friends is the same as ____ glasses of juice shared equally among 8 friends. So 5/4 = __/8.
    • (b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kg of potatoes divided equally in ___ bags. So 4/3 = 12/___.
    • (c) 7 rotis divided among 5 children is the same as ____ rotis divided among _____ children. So 7/5 = ___/___.
  2. Three rotis are shared equally by four children. Write a fraction for how much each child gets, and write the corresponding division, addition, and multiplication facts.
  3. Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Write the division, addition, and multiplication facts.
  4. Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?

Equivalent Fractions — Finding equivalent fractions with same denominator

  1. Find equivalent fractions for the given pairs of fractions such that the fractional units (denominators) are the same:
    • (a) 7/2 and 3/5,
    • (b) 8/3 and 5/6,
    • (c) 3/4 and 3/5,
    • (d) 6/7 and 8/5,
    • (e) 9/4 and 5/2,
    • (f) 1/10 and 2/9,
    • (g) 8/3 and 11/4,
    • (h) 13/6 and 1/9.

Equivalent Fractions — Lowest terms

  1. Express the following fractions in lowest terms:
    • (a) 17/51,
    • (b) 64/144,
    • (c) 126/147,
    • (d) 525/112.

Comparing Fractions

  1. Compare the following fractions and justify your answers:
    • (a) 8/3 and 5/2,
    • (b) 4/9 and 3/7,
    • (c) 7/10 and 9/14,
    • (d) 12/5 and 8/5,
    • (e) 9/4 and 5/2.
  2. Write the following fractions in ascending order:
    • (a) 7/10, 11/15, 2/5;
    • (b) 19/24, 5/6, 7/12.
  3. Write the following fractions in descending order:
    • (a) 25/16, 7/8, 13/4, 17/32;
    • (b) 3/4, 12/5, 7/12, 5/4.

Addition and Subtraction of Fractions — Same denominator

  1. 5/8 − 3/8 = ?
  2. 7/9 − 5/9 = ?
  3. 10/27 − 1/27 = ?

Addition and Subtraction of Fractions — Brahmagupta's method (addition)

  1. Add the following fractions using Brahmagupta's method:
    • (a) 2/7 + 5/7 + 6/7,
    • (b) 3/4 + 1/3,
    • (c) 2/3 + 5/6,
    • (d) 2/3 + 2/7,
    • (e) 3/4 + 1/3 + 1/5,
    • (f) 2/3 + 4/5,
    • (g) 4/5 + 2/3,
    • (h) 3/5 + 5/8,
    • (i) 9/2 + 5/4,
    • (j) 8/3 + 2/7,
    • (k) 3/4 + 1/3 + 1/5,
    • (l) 2/3 + 4/5 + 3/7,
    • (m) 9/2 + 5/4 + 7/6.
  2. Rahim mixes 2/3 litres of yellow paint with 3/4 litres of blue paint to make green paint. What is the volume of green paint he has made?
  3. Geeta bought 2/5 metre of lace and Shamim bought 3/4 metre of lace to put a complete border on a table cloth whose perimeter is 1 metre. Find the total length of lace they bought. Will it be sufficient to cover the whole border?

Addition and Subtraction of Fractions — Brahmagupta's method (subtraction)

  1. Carry out the following subtractions using Brahmagupta's method:
    • (a) 8/15 − 3/15,
    • (b) 2/5 − 4/15,
    • (c) 5/6 − 4/9,
    • (d) 2/3 − 1/2.
  2. Subtract as indicated:
    • (a) 13/4 from 10/3,
    • (b) 18/5 from 23/3,
    • (c) 29/7 from 45/7.
  3. Jaya's school is 7/10 km from her home. She takes an auto for 1/2 km from her home, then walks the remaining distance. How much does she walk daily to reach school?
  4. Jeevika takes 10/3 minutes to complete a round of the park and her friend Namit takes 13/4 minutes. Who takes less time and by how much?
Sample

Worked examples

3 questions from Fractions, solved step by step.

Fractional Units and Equal Shares

Arrange these fraction words in order of size from the smallest to the biggest: One and a half, three quarters, one and a quarter, half, quarter, two and a half.

Convert each to a fraction:

Quarter = 1/4, Half = 1/2, Three quarters = 3/4,

One and a quarter = 1 + 1/4 = 5/4,

One and a half = 1 + 1/2 = 3/2,

Two and a half = 2 + 1/2 = 5/2.

Ordering: 1/4 < 1/2 < 3/4 < 5/4 < 3/2 < 5/2.

Answer: Quarter, half, three quarters, one and a quarter, one and a half, two and a half

Measuring Using Fractional Units

Make 1/3 using a paper strip. Can you use this to also make 1/6?

Fold a paper strip into 3 equal parts — each part is 1/3.

Now fold each 1/3 part in half: each piece becomes 1/6.

So yes, by halving each 1/3 piece we get 1/6.

Answer: Yes; fold the 1/3 piece in half to obtain 1/6

Marking Fraction Lengths on the Number Line

How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.

Between 0 and 1, we can place fractions with any denominator n (n ≥ 2): 1/n, 2/n, …, (n-1)/n.

As n can be any whole number, there is no limit.

Therefore, infinitely many (uncountably many) fractions lie between 0 and 1.

Answer: Infinitely many fractions lie between 0 and 1

All 47 questions in Fractions are solved step by step in the Solutions PDF above.

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More NCERT Solutions for Class 6

Read the Fractions textbook chapter / PDF, or browse all NCERT Class 6 Mathematics solutions.

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