Chapter 7 of 10

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Updated 6 August 2026

NCERT Solutions

Fractions

CBSE · Class 6 · Mathematics

NCERT Solutions for Fractions — CBSE Class 6 Mathematics.

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Figure it Out — Section 7.1 (Fractional Units and Equal Shares)

1Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh ___ kg.Show solution

Given: 3 guavas together weigh 1 kg and all are of the same size.

Concept: When 1 whole unit is divided equally among 3 parts, each part =

\frac{1}{3}

of the whole.

\text{Weight of each guava} = 1 \div 3 = \frac{1}{3} \text{ kg}

Answer: Each guava will roughly weigh

\dfrac{1}{3}

kg.

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2A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ___ kg.Show solution

Given: 1 kg of rice packed equally into 4 packets.

Concept: When 1 whole unit is divided equally into 4 parts, each part =

\frac{1}{4}

\text{Weight of each packet} = 1 \div 4 = \frac{1}{4} \text{ kg}

Answer: The weight of each packet is

\dfrac{1}{4}

kg.

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3Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank ___ glass of sugarcane juice.Show solution

Given: 3 glasses shared equally among 4 friends.

Concept: Equal sharing gives a fraction =

\frac{\text{number of glasses}}{\text{number of friends}}

\text{Each friend's share} = 3 \div 4 = \frac{3}{4} \text{ glass}

Answer: Each one drank

\dfrac{3}{4}

glass of sugarcane juice.

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4The big fish weighs

\frac{1}{2}

kg. The small one weighs

\frac{1}{4}

kg. Together they weigh ___ kg.Show solution

Given: Big fish =

\dfrac{1}{2}

kg, Small fish =

\dfrac{1}{4}

kg.

Concept: To add fractions, convert to the same denominator.

\frac{1}{2} = \frac{2}{4}

\text{Total weight} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \text{ kg}

Answer: Together they weigh

\dfrac{3}{4}

kg.

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5Arrange 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.Show solution

First, convert each fraction word to a number:
- Quarter

= \dfrac{1}{4} = 0.25

- Half

= \dfrac{1}{2} = 0.5

- Three quarters

= \dfrac{3}{4} = 0.75

- One and a quarter

= 1\dfrac{1}{4} = 1.25

- One and a half

= 1\dfrac{1}{2} = 1.5

- Two and a half

= 2\dfrac{1}{2} = 2.5

Arranging from smallest to biggest:

\frac{1}{4} < \frac{1}{2} < \frac{3}{4} < 1\frac{1}{4} < 1\frac{1}{2} < 2\frac{1}{2}

Answer: Quarter, Half, Three quarters, One and a quarter, One and a half, Two and a half.

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Figure it Out — Fractional Units of a Chikki

aThe figure shows a piece of chikki. How much of a whole chikki is each piece? (The chikki is broken into 2 equal pieces.)Show solution

Given: The whole chikki is broken into 2 equal pieces.

Concept: Each equal part of a whole divided into

n

parts

= \dfrac{1}{n}

\text{Each piece} = \frac{1}{2} \text{ of the whole chikki}

Answer: Each piece is

\dfrac{1}{2}

of the whole chikki.

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bThe figure shows a piece of chikki. How much of a whole chikki is each piece? (The chikki is broken into 4 equal pieces.)Show solution

Given: The whole chikki is broken into 4 equal pieces.

\text{Each piece} = \frac{1}{4} \text{ of the whole chikki}

Answer: Each piece is

\dfrac{1}{4}

of the whole chikki.

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cThe figure shows a piece of chikki. How much of a whole chikki is each piece? (The chikki is broken into 3 equal pieces.)Show solution

Given: The whole chikki is broken into 3 equal pieces.

\text{Each piece} = \frac{1}{3} \text{ of the whole chikki}

Answer: Each piece is

\dfrac{1}{3}

of the whole chikki.

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dThe figure shows a piece of chikki. How much of a whole chikki is each piece? (The chikki is broken into 5 equal pieces.)Show solution

Given: The whole chikki is broken into 5 equal pieces.

\text{Each piece} = \frac{1}{5} \text{ of the whole chikki}

Answer: Each piece is

\dfrac{1}{5}

of the whole chikki.

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eThe figure shows a piece of chikki. How much of a whole chikki is each piece? (The chikki is broken into 6 equal pieces.)Show solution

Given: The whole chikki is broken into 6 equal pieces.

\text{Each piece} = \frac{1}{6} \text{ of the whole chikki}

Answer: Each piece is

\dfrac{1}{6}

of the whole chikki.

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fThe figure shows a piece of chikki. How much of a whole chikki is each piece? (The chikki is broken into 8 equal pieces.)Show solution

Given: The whole chikki is broken into 8 equal pieces.

\text{Each piece} = \frac{1}{8} \text{ of the whole chikki}

Answer: Each piece is

\dfrac{1}{8}

of the whole chikki.

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gThe figure shows a piece of chikki. How much of a whole chikki is each piece? (The chikki is broken into 9 equal pieces.)Show solution

Given: The whole chikki is broken into 9 equal pieces.

\text{Each piece} = \frac{1}{9} \text{ of the whole chikki}

Answer: Each piece is

\dfrac{1}{9}

of the whole chikki.

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hThe figure shows a piece of chikki. How much of a whole chikki is each piece? (The chikki is broken into 10 equal pieces.)Show solution

Given: The whole chikki is broken into 10 equal pieces.

\text{Each piece} = \frac{1}{10} \text{ of the whole chikki}

Answer: Each piece is

\dfrac{1}{10}

of the whole chikki.

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Figure it Out — Tables and Paper Strips

1Continue this table of

\frac{1}{2}

for 2 more steps.Show solution

The table of

\dfrac{1}{2}

is built by repeatedly adding

\dfrac{1}{2}

1 \times \frac{1}{2} = \frac{1}{2}

2 \times \frac{1}{2} = \frac{2}{2} = 1

3 \times \frac{1}{2} = \frac{3}{2}

4 \times \frac{1}{2} = \frac{4}{2} = 2

Continuing 2 more steps:

5 \times \frac{1}{2} = \frac{5}{2} = 2\frac{1}{2}

6 \times \frac{1}{2} = \frac{6}{2} = 3

Answer: The next two steps are

\dfrac{5}{2}

(or

2\dfrac{1}{2}

) and

3

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2Can you create a similar table for

\frac{1}{4}

?Show solution

Yes. The table of

\dfrac{1}{4}

is built by repeatedly adding

\dfrac{1}{4}

1 \times \frac{1}{4} = \frac{1}{4}

2 \times \frac{1}{4} = \frac{2}{4} = \frac{1}{2}

3 \times \frac{1}{4} = \frac{3}{4}

4 \times \frac{1}{4} = \frac{4}{4} = 1

5 \times \frac{1}{4} = \frac{5}{4} = 1\frac{1}{4}

6 \times \frac{1}{4} = \frac{6}{4} = 1\frac{1}{2}

7 \times \frac{1}{4} = \frac{7}{4} = 1\frac{3}{4}

8 \times \frac{1}{4} = \frac{8}{4} = 2

Answer: Yes, the table for

\dfrac{1}{4}

can be made as shown above.

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3Make

\frac{1}{3}

using a paper strip. Can you use this to also make

\frac{1}{6}

?Show solution

**Making

\dfrac{1}{3}

:** Take a paper strip and fold it into 3 equal parts. Each part represents

\dfrac{1}{3}

of the strip.

**Making

\dfrac{1}{6}

:** Now take the

\dfrac{1}{3}

piece and fold it into 2 equal parts. Each of these smaller parts is

\dfrac{1}{2}

\dfrac{1}{3}

\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}

Answer: Yes, by folding the

\dfrac{1}{3}

strip in half, we get

\dfrac{1}{6}

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4aDraw a picture and write an addition statement to show: 5 times

\frac{1}{4}

of a roti.Show solution

Picture: Draw 5 pieces, each being

\dfrac{1}{4}

of a roti (i.e., a circle divided into 4 equal parts, with one part shaded, repeated 5 times).

Addition statement:

\frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} + \frac{1}{4} = \frac{5}{4} = 1\frac{1}{4}

Answer: 5 times

\dfrac{1}{4}

of a roti

= \dfrac{5}{4} = 1\dfrac{1}{4}

rotis.

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4bDraw a picture and write an addition statement to show: 9 times

\frac{1}{4}

of a roti.Show solution

Picture: Draw 9 pieces, each being

\dfrac{1}{4}

of a roti.

Addition statement:

\underbrace{\frac{1}{4} + \frac{1}{4} + \cdots + \frac{1}{4}}_{9 \text{ times}} = \frac{9}{4} = 2\frac{1}{4}

Answer: 9 times

\dfrac{1}{4}

of a roti

= \dfrac{9}{4} = 2\dfrac{1}{4}

rotis.

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5Match each fractional unit with the correct picture:

\frac{1}{3}

\frac{1}{5}

\frac{1}{8}

\frac{1}{6}

.Show solution

Each fractional unit

\dfrac{1}{n}

corresponds to a shape divided into

n

equal parts with 1 part shaded.

-

\dfrac{1}{3}

→ the picture showing a shape divided into 3 equal parts (1 part shaded).
-

\dfrac{1}{5}

→ the picture showing a shape divided into 5 equal parts (1 part shaded).
-

\dfrac{1}{6}

→ the picture showing a shape divided into 6 equal parts (1 part shaded).
-

\dfrac{1}{8}

→ the picture showing a shape divided into 8 equal parts (1 part shaded).

Answer: Match by counting the number of equal parts in each picture —

\dfrac{1}{3}

with 3 parts,

\dfrac{1}{5}

with 5 parts,

\dfrac{1}{6}

with 6 parts,

\dfrac{1}{8}

with 8 parts.

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Figure it Out — Fractions on a Number Line

1On a number line, draw lines of lengths

\frac{1}{10}

\frac{3}{10}

, and

\frac{4}{5}

.Show solution

Concept: On a number line from 0 to 1, divide the segment into 10 equal parts. Each part has length

\dfrac{1}{10}

.

-

\dfrac{1}{10}

: Mark the point 1 division from 0.
-

\dfrac{3}{10}

: Mark the point 3 divisions from 0.
-

\dfrac{4}{5} = \dfrac{8}{10}

: Mark the point 8 divisions from 0.

0 \quad \frac{1}{10} \quad \cdots \quad \frac{3}{10} \quad \cdots \quad \frac{8}{10} \quad \cdots \quad 1

Answer: Draw a number line, divide 0–1 into 10 equal parts, and mark

\dfrac{1}{10}

\dfrac{3}{10}

, and

\dfrac{8}{10}

(which equals

\dfrac{4}{5}

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2Write five more fractions of your choice and mark them on the number line.Show solution

Sample fractions chosen:

\frac{1}{2},\quad \frac{1}{4},\quad \frac{3}{4},\quad \frac{2}{5},\quad \frac{7}{10}

Converting to tenths for easy marking:
-

\dfrac{1}{2} = \dfrac{5}{10}

→ 5th mark
-

\dfrac{1}{4} = \dfrac{2.5}{10}

→ halfway between 2nd and 3rd mark
-

\dfrac{3}{4} = \dfrac{7.5}{10}

→ halfway between 7th and 8th mark
-

\dfrac{2}{5} = \dfrac{4}{10}

→ 4th mark
-

\dfrac{7}{10}

→ 7th mark

Answer: (Students may choose any five fractions and mark them appropriately on the number line.)

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3How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.Show solution

Concept: Between any two numbers on the number line, there are infinitely many fractions.

For example, between 0 and 1 we have:

\dfrac{1}{2}, \dfrac{1}{3}, \dfrac{1}{4}, \dfrac{1}{5}, \ldots

and also

\dfrac{2}{3}, \dfrac{3}{4}, \dfrac{5}{7}, \ldots

— these go on without end.

Answer: There are infinitely many fractions between 0 and 1.

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4What is the length of the blue line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is

\frac{1}{2}

. So the blue line is

\frac{1}{2}

units long. Write the fraction that gives the length of the black line in the box.Show solution

Given: The segment from 0 to 1 is divided into 2 equal parts, so each part

= \dfrac{1}{2}

.

- Blue line spans 1 part

\Rightarrow

length

= \dfrac{1}{2}

.
- The black line spans both parts (from 0 to 1)

\Rightarrow

length

= \dfrac{2}{2} = 1

.

*(Note: The exact length of the black line depends on the figure. Based on the description, if the black line covers the full unit, its length is 1. If it covers one and a half units, it would be

\dfrac{3}{2}

. Students should read the figure carefully.)*

Answer: The blue line is

\dfrac{1}{2}

units long. The black line's length is written in the box based on how many half-units it spans (e.g., if it spans 3 half-units, the answer is

\dfrac{3}{2}

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5Write the fraction that gives the lengths of the black lines in the respective boxes.

Figure it Out — Whole Units in Fractions

1How many whole units are there in

\frac{7}{2}

2How many whole units are there in

\frac{4}{3}

and in

\frac{7}{3}

Figure it Out — Mixed Fractions

1aFigure out the number of whole units in

\frac{8}{3}

1bFigure out the number of whole units in

\frac{11}{5}

1cFigure out the number of whole units in

\frac{9}{4}

2Can all fractions greater than 1 be written as mixed numbers?

3aWrite

\frac{9}{2}

as a mixed fraction.

3bWrite

\frac{9}{5}

as a mixed fraction.

3cWrite

\frac{21}{19}

as a mixed fraction.

3dWrite

\frac{47}{9}

as a mixed fraction.

3eWrite

\frac{12}{11}

as a mixed fraction.

3fWrite

\frac{19}{6}

as a mixed fraction.

Figure it Out — Equivalent Fractions (Fraction Wall)

1Are

\frac{3}{6}

\frac{4}{8}

\frac{5}{10}

equivalent fractions? Why?

2Write two equivalent fractions for

\frac{2}{6}

\frac{4}{6} = \square = \square = \square = \dots

(Write as many as you can)

Figure it Out — Equal Shares and Division Facts

1Three rotis are shared equally by four children. Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts, and multiplication facts.

2Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.

3Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get? Now, if there are 10 children in my group, how many cakes will I need so that they get the same amount of cake as Anil? What if we put two such groups together?

Figure it Out — Finding Missing Numbers in Equivalent Fractions

a5 glasses of juice shared equally among 4 friends is the same as ___ glasses of juice shared equally among 8 friends. So,

\frac{5}{4} = \frac{\square}{8}

b4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in ___ bags. So,

\frac{4}{3} = \frac{12}{\square}

c7 rotis divided among 5 children is the same as ___ rotis divided among ___ children. So,

\frac{7}{5} = \frac{\square}{\square}

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Frequently Asked Questions

What are the important topics in Fractions for CBSE Class 6 Mathematics?

Fractions covers several key topics that are frequently asked in CBSE Class 6 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.

How to score full marks in Fractions — CBSE Class 6 Mathematics?

Understand the core concepts first, then work through the 124 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

Where can I get free NCERT Solutions for Fractions Class 6 Mathematics?

This page has free step-by-step NCERT Solutions for every exercise question in Fractions (CBSE Class 6 Mathematics) — written the way examiners award marks: given, formula, working, answer.

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Fractions

Studying Fractions? Get the full interactive chapter.

Figure it Out — Section 7.1 (Fractional Units and Equal Shares)

Figure it Out — Fractional Units of a Chikki

Figure it Out — Tables and Paper Strips

Figure it Out — Fractions on a Number Line

Figure it Out — Whole Units in Fractions

Figure it Out — Mixed Fractions

Figure it Out — Equivalent Fractions (Fraction Wall)

Figure it Out — Equal Shares and Division Facts

Figure it Out — Finding Missing Numbers in Equivalent Fractions

Frequently Asked Questions

Sources & Official References

More resources for Fractions

Practice Quiz

Important Questions

Revision Notes

Formula Sheet

Chapter Summary

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Study Plan

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Syllabus

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