Class 5 Maths Chapter 2 Fractions NCERT Solutions – Stepwise Guide

NCERT Textbook Pages 17-18

Playing with a Grid

• Shade $$\frac{1}{8}$$ of Grid A in red.

• Shade $$\frac{1}{6}$$ of Grid B in red.

• Shade $$\frac{1}{12}$$ of Grid C in red.

Do you see $$\frac{1}{3}$$ in any for the grids? Mark it.

Answer:
Yes,

The shaded region represents $$\frac{1}{3}$$ of the grid.

Is $$\frac{1}{3}$$ equal to $$\frac{2}{6}$$ ? Let us find out.

Look at the picture and identify the fractions.

Are there two different ways to write the fraction represented by the shaded part? __________

Answer:

Yes.

The picture shows a bar divided into six equal parts, with two parts shaded. The shaded portion represents the fraction  $$\frac{2}{6}$$.

Now, the same bar is divided into three equal parts, and one part is shaded. The shaded portion represents the fraction $$\frac{1}{3}$$​.

Hence, we can say that $$\frac{1}{3}$$ ​ is equivalent to $$\frac{2}{6}$$​.

NCERT Textbook Page 18

Fun with Fraction Kit

Gurpreet is playing with his fraction kit (a kit is given at the end of the textbook). Do you 

remember how to make a whole with pieces of the same size? How many $$\frac{1}{5}$$ pieces will you need to make a whole?

He makes a whole using two different fraction pieces. The whole looks like the following.

One piece of $$\frac{1}{2}$$ and two pieces of $$\frac{1}{4}$$ make a whole.

What is the relation between $$\frac{1}{2}$$ and $$\frac{1}{4}$$ ? Discuss in class.

$$\frac{1}{2}=\frac{2}{4}$$ ( 12 is equivalent to 24 ).

When a $$\frac{1}{2}$$ piece is broken into 2 equal parts, each part is a $$\frac{1}{4}$$ piece.

2 pieces of $$\frac{1}{4}$$ are equal to 12 .

What else is equivalent to $$\frac{1}{2}$$?

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

Answer: 12=24=36=48=510 $$\frac{1}{2}$$ = $$\frac{2}{4}$$ = $$\frac{3}{6}$$ = $$\frac{4}{8}$$ = $$\frac{5}{10}$$ 21​=42​=63​=84​=105​

These fractions are all equivalent to $12\frac{1}{2}21$​ because the numerator and denominator are multiplied by the same number each time.

NCERT Textbook Pages 19-20

Let Us Do

Question 1.
In groups of 3 or 4, find different ways of making a whole with different fraction pieces from your kit. Write the equivalent fractions for the following that you may find in the process.

(a) $$\frac{1}{3}$$ = = =
(b) $$\frac{1}{4}$$ = = =
(c) $$\frac{1}{5}$$ = = =
(d) $$\frac{1}{6}$$ = = =

Do you see how to generate equivalent fractions for any given fraction? Discuss in class.

Solution:
Students should do it by themselves.

Question 2.
Find the following using your kit. You can also shade and check by shading the following. The first one is partially done for you.

A. How many $$\frac{1}{6}$$ s make $$\frac{1}{3}$$?

Solution:

Two $$\frac{1}{6}$$s make $$\frac{1}{3}$$.

B. How many $$\frac{1}{8}$$ s make $$\frac{1}{4}$$ ?

(a) $$\frac{1}{4}$$

Solution:

Two $$\frac{1}{8}$$s make $$\frac{1}{4}$$.

(b) $$\frac{1}{2}$$?

Solution:

C. How many $$\frac{1}{12}$$ s make?

(a) $$\frac{1}{2}$$?

Solution:

Six $$\frac{1}{12}$$s make $$\frac{1}{2}$$.

(b) $$\frac{1}{3}$$?

Solution:

Four $$\frac{1}{12}$$s make $$\frac{1}{4}$$.

(c) $$\frac{1}{2}$$?

Solution:

Three $$\frac{1}{12}$$s make $$\frac{1}{4}$$.

(d) $$\frac{1}{6}$$?

Solution:

Two $$\frac{1}{12}$$s make $$\frac{1}{6}$$.

Question 3.
Do as instructed using your fraction kit.

• Make a whole using only $$\frac{1}{6}$$ and $$\frac{1}{12}$$ pieces.

• Make a whole using $$\frac{1}{12}$$, $$\frac{1}{4}$$ and $$\frac{1}{2}$$ pieces.

• Make a whole using any five pieces of the same size.

• Make a whole using any seven pieces.

Play in a group with this kit and find other interesting combinations to make a whole. Write or draw your findings.

Solution:
Students shoulddo it by themselves.

NCERT Textbook Pages 20-21

Making Equivalent Fractions

Sameer has shaded one-third of the following figures. He draws horizontal lines to divide the shapes into more equal parts.

He observes an interesting pattern and says that $$\frac{1}{2}$$ and $$\frac{1}{2}$$ show the same shaded region.

$$\frac{2}{6}$$, $$\frac{3}{9}$$ and $$\frac{4}{12}$$ are all equivalent to $$\frac{1}{3}$$. We use the word ‘equivalent’ to indicate the same part of a whole, with different names.

Divide the wholes given below into more equal parts and find fractions equivalent to $$\frac{1}{3}$$. Write them in the boxes below the images.

Solution:

Do you see any pattern in all the equivalent fractions that you found?

Solution:

$$\frac{1}{3}=\frac{2}{6}=\frac{3}{9}=\frac{4}{12}=\frac{5}{15}=\frac{6}{18}=\frac{7}{21}=\frac{8}{24}=\frac{9}{36}$$

How do you know when a fraction is equivalent to another?

Solution: If two fractions represent the same shaded portion of a whole, then they are equivalent fractions.

The below pictures show $$\frac{2}{5}$$ of a whole. Find the different fractions that are equivalent to $$\frac{2}{5}$$ and write your fractions below each image.

Solution:

NCERT Textbook Page 22

Let Us Do

Question 1.
Fill in the blanks with equivalent fractions. There may be more than one answer.

(a) $$\frac{1}{7}$$ = ____
(b) $$\frac{2}{3}$$ = ____
(c) $$\frac{3}{4}$$ = ____
(d) $$\frac{3}{5}$$ = ____

Solution:
To find equivalent fractions multiply both numerator and denominator by the same number.

(a) $$\frac{1}{7}$$ = $$\frac{1 \times 3}{7 \times 3}=\frac{3}{21}$$ (Answer may vary)
(b) $$\frac{2}{3}$$ = $$\frac{2 \times 5}{3 \times 5}=\frac{10}{15}$$ (Answer may vary)
(c) $$\frac{3}{4}$$ = $$\frac{3 \times 3}{4 \times 3}=\frac{9}{12}$$ (Answer may vary)
(d) $$\frac{3}{5}$$ = $$\frac{3 \times 6}{5 \times 6}=\frac{18}{30}$$ (Answer may vary)

Question 2.
Put a tick (✓) against the fractions that are equivalent.

(a) $$\frac{2}{3}$$ and $$\frac{3}{4}$$

Solution:
To check if the fractions are equivalent or not, we need to make the denominators the same.
So, $$\frac{1}{2}$$ and $$\frac{1}{2}$$
Here, denominators are the same but numerators are different. So, $$\frac{2}{3}$$ and $$\frac{3}{4}$$ are not equivalent.

(b) $$\frac{3}{5}$$ and $$\frac{6}{10}$$

Solution:
To check if the fractions are equivalent or not, we need to make the denominators the same.
$$\frac{3}{5}=\frac{3 \times 2}{5 \times 2}=\frac{6}{10}$$, and $$\frac{6}{10}=\frac{6}{10}$$
Here, numerators and denominators of both fractions are the same. So, $$\frac{3}{5}$$ and $$\frac{6}{10}$$ are equivalent.

(c) $$\frac{4}{12}$$ and $$\frac{2}{6}$$

Solution:
To check if fractions are equivalent or not, we need to make denominators the same.
$$\frac{4}{12}=\frac{4}{12}$$ and $$\frac{2}{6}=\frac{2 \times 2}{6 \times 2}=\frac{4}{12}$$

Here, numerators and denominators of both fractions are the same.
So, $$\frac{4}{12}$$ and $$\frac{2}{6}$$ are equivalent.

(d) $$\frac{6}{9}$$ and $$\frac{1}{3}$$

Solution:
To check if the fractions are equivalent or not, we need to make denominators the same.
$$\frac{6}{9}=\frac{6}{9}$$ and $$\frac{1}{3}=\frac{1 \times 3}{3 \times 3}=\frac{3}{9}$$
Here, denominators are the same but numerators are different. So, $$\frac{6}{9}$$ and $$\frac{1}{3}$$ are not equivalent.

Question 3.
Fill in the boxes such that the fractions become equivalent.

Solution:
(a) $$\frac{2}{5}=\frac{2 \times 2}{5 \times 2}=\frac{4}{10}$$
(b) $$\frac{3}{4}=\frac{3 \times 4}{4 \times 4}=\frac{12}{16}$$
(c) $$\frac{4}{7}=\frac{4 \times 2}{7 \times 2}=\frac{8}{14}$$
(d) $$\frac{5}{9}=\frac{5 \times 5}{9 \times 5}=\frac{25}{45}$$

NCERT Textbook Page 23

Let Us Do

Question 1.
Compare the fractions given below using < and > signs.

(a) $$\frac{3}{8}$$ ____ $$\frac{3}{7}$$

Solution:
$$\frac{3}{8}$$ ____ $$\frac{3}{7}$$

Here, $$\frac{1}{8}$$ is smaller than $$\frac{1}{7}$$. So, $$\frac{3}{8}<\frac{3}{7}$$

(b) $$\frac{4}{9}$$ ____ $$\frac{4}{10}$$

Solution:

$$\frac{4}{9}$$ ____ $$\frac{4}{10}$$

Here, $$\frac{1}{9}$$ is bigger than $$\frac{1}{10}$$. So, $$\frac{4}{9}>\frac{4}{10}$$.

(c) $$\frac{2}{7}$$ ____ $$\frac{2}{5}$$

Solution:
$$\frac{2}{7}$$ ____ $$\frac{2}{5}$$

Here, $$\frac{1}{7}$$ is smaller than $$\frac{1}{5}$$. So, $$\frac{2}{7}<\frac{2}{5}$$

(d) $$\frac{5}{7}$$ ____ $$\frac{5}{6}$$

Solution:
$$\frac{5}{7}$$ ____ $$\frac{5}{6}$$

Here, $$\frac{1}{7}$$ is smaller than $$\frac{1}{6}$$. So, $$\frac{5}{7}<\frac{5}{6}$$

(e) $$\frac{6}{9}$$ ____ $$\frac{6}{10}$$

Solution:

$$\frac{6}{9}$$ ____ $$\frac{6}{10}$$

Here, $$\frac{1}{9}$$ is bigger than $$\frac{1}{10}$$. So, $$\frac{6}{9}>\frac{6}{10}$$

(f) $$\frac{7}{9}$$ ____ $$\frac{7}{11}$$

Solution:
$$\frac{7}{9}$$ ____ $$\frac{7}{11}$$

Here, $$\frac{1}{9}$$ is bigger than $$\frac{1}{11}$$. So, $$\frac{7}{9}>\frac{7}{11}$$

NCERT Textbook Pages 24-28

Fractions Greater Than 1

Raman’s father makes nice soft parathas. He cuts the parathas either into halves (2 equal parts) or fourths (4 equal parts) before serving them. He asks his children (Raman and Radhika) each day to find out the number of parathas he made.

Maa took 5 pieces of $$\frac{1}{2}$$ paratha. How many parathas did she eat?

Dadiji had 7 pieces of $$\frac{1}{2}$$ paratha. How many parathas did she eat?

Solution:

= 7 pieces of $$\frac{1}{2}$$ paratha
= $$\frac{7}{2}$$ parathas
= 3 + $$\frac{1}{2}$$ parathas
= 3$$\frac{1}{2}$$ parathas.

So, dadiji ate 3$$\frac{1}{2}$$ parathas.

Raman ate 6 pieces of $$\frac{1}{2}$$ paratha, Dadaji ate 7 pieces of $$\frac{1}{2}$$ paratha and Baba ate 5 pieces of $$\frac{1}{2}$$ paratha. How many parathas did each of them eat?

Use the number line to find the answer.

Solution:

In the given number lines, each segment represents $$\frac{1}{2}$$​. Since Raman ate 6 pieces of $$\frac{1}{2}$$  parathas, mark 6 points on the number line.

$$\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{6}{2}$$

Therefore, Raman ate 3 parathas.

Dadaji ate 7 pieces of $$\frac{1}{2}$$ paratha. So, mark 7 points on number line.

$$\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{7}{2}=3 \frac{1}{2}$$

Therefore, dadaji ate 3$$\frac{1}{2}$$ parathas.

Baba ate 5 pieces of $$\frac{1}{2}$$ paratha. So, mark 5 points on number line.

$$\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{5}{2}=2 \frac{1}{2}$$

Therefore, Baba are 2$$\frac{1}{2}$$ parathas.

How many parathas were made on this day? Find out.

Solution:

Maa ate 2½ parathas, which is equal to 5/2.

Radhika ate 3 parathas, which is equal to 6/2.

Dadiji ate 3½ parathas, which is equal to 7/2.

Raman ate 3½ parathas, which is equal to 6/2.

Dadaji ate 3½ parathas, which is equal to 7/2.

Baba ate 2½ parathas, which is equal to 5/2.

The total number of parathas made on this day was $$\frac{5}{2}+\frac{6}{2}+\frac{7}{2}+\frac{6}{2}+\frac{7}{2}+\frac{5}{2}=\frac{36}{2}$$ = 18 parathas.

Raman ate 7 pieces of $$\frac{1}{4}$$, Radhika ate 6 pieces of $$\frac{1}{4}$$, Maa ate 8 pieces of $$\frac{1}{4}$$, Dadiji ate 10 pieces of $$\frac{1}{4}$$, and Baba ate 12 pieces of $$\frac{1}{4}$$ paratha. Use a number line to find out how many parathas were eaten by each of them.

Solution:

On the given number lines, divide the distance between 0 and 1 into four equal parts. Each part represents  $$\frac{1}{4}$$​.

Since Raman ate 7 pieces of  $$\frac{1}{4}$$ paratha, mark 7 points on the number line.

Therefore, Raman ate $$\frac{7}{4}$$ parathas or 1 $$\frac{3}{4}$$ parathas.

Radhika ate 6 pieces of $$\frac{1}{4}$$ paratha. So, mark 6 points on number line.

Therefore, Radhika ate $$\frac{6}{4}$$ = 1$$\frac{1}{2}$$ parathas.

Maa ate 8 pieces of $$\frac{1}{4}$$ paratha. So, mark 8 points on number line.

Therefore, Maa ate $$\frac{8}{4}$$ or 2 parathas.

Dadiji ate 10 pieces of $$\frac{1}{4}$$ paratha. So, mark 10 points on number line.

= $$\frac{10}{4}$$ = 2 + $$\frac{2}{4}$$ = 2$$\frac{2}{4}$$ = 2$$\frac{1}{2}$$

Therefor, Dadaji ate $$\frac{10}{2}$$. or 2$$\frac{1}{2}$$ parathas 12 point on number line.

= 1 + 1 + 1 = 3
Therefore, Baba ate 3 parathas.

How many parathas were made on this day? Find out.

Solution:

Here is the rephrased version in clear, simple English, keeping all values exactly the same:

• Dadaji ate 9/49/49/4 parathas.
  
  

• Raman ate 7/47/47/4 parathas.
  
  

• Radhika ate 6/46/46/4 parathas.
  
  

• Maa ate 8/48/48/4 parathas.
  
  

• Dadiji ate 10/410/410/4 parathas.
  
  

• Baba ate 12/412/412/4 parathas.
  
  

So, the total number of parathas prepared that day is:

= $$\frac{9}{4}+\frac{7}{4}+\frac{6}{4}+\frac{8}{4}+\frac{10}{4}+\frac{12}{4}$$

= $$\frac{9+7+6+8+10+12}{4}=\frac{52}{4}$$

= 13 parathas

NCERT Textbook Page 28

Let Us Do

Question 1.
Use parathas and number lines to show the following fractions in your notebook.

(a) $$\frac{2}{3}$$ and $$\frac{5}{3}$$

Solution:

Draw a number line and divide each unit (0 to 1, 1 to 2) into 3 equal parts. Count 2 of these parts from O and mark that point as $$\frac{2}{3}$$. Similarly, count 5 of these $$\frac{1}{3}$$ parts from 0 and mark it as $$\frac{5}{3}$$.

(b) $$\frac{3}{4}$$ and $$\frac{5}{4}$$

Solution:

Draw a number line and divide each unit (0 to 1 and 1 to 2) into 4 equal parts. Count 3 of these $$\frac{1}{4}$$ parts from 0 and mark as $$\frac{3}{4}$$. Similarly, count 5 of these $$\frac{1}{4}$$ parts from 0 and mark as $$\frac{5}{4}$$.

(c) $$\frac{4}{8}$$ and $$\frac{9}{8}$$

Solution:

Draw a number line and divide each unit (0 to 1, 1 to 2) into 8 equal parts. Count 4 of these $$\frac{1}{8}$$ parts from O and mark as Similarly, count 9 of these $$\frac{1}{8}$$ parts from 0 and mark as $$\frac{9}{8}$$.

Question 2.

Circle the fractions that are greater than one (whole). How do you know? Discuss your reasoning in the class.

Solution:

Draw a number line and show the given fractions on it.

• If a fraction lies to the right of 1, it is greater than 1.
  
  

• If a fraction lies to the left of 1, it is less than 1.
  
  

• If a fraction is exactly at 1, it is equal to 1.
  
  

NCERT Textbook Page 29

Let Us Do

Question 1.
Compare the following fractions using 1 as a reference. Share your reasoning in the class.

(a) $$\frac{8}{7}$$ ____ $$\frac{9}{15}$$

Solution:
Since, $$\frac{8}{7}$$ is more than 1 and $$\frac{9}{15}$$ is less than 1.
So, $$\frac{8}{7}>\frac{9}{15}$$

(b) $$\frac{13}{20}$$ ____ $$\frac{17}{15}$$

Solution:
Since, $$\frac{13}{20}$$ is less than 1 and $$\frac{17}{15}$$ is more than 1.
So, $$\frac{13}{20}<\frac{17}{15}$$ .

(c) $$\frac{7}{6}$$ ____ $$\frac{8}{8}$$

Solution:
Since, $$\frac{7}{2}$$ is more than 1 and $$\frac{8}{8}$$ is equal to 1.
So, $$\frac{7}{6}>\frac{8}{8}$$.

(d) $$\frac{6}{6}$$ ____ $$\frac{19}{12}$$

Solution:
Since, $$\frac{6}{6}$$ is equal to 1 and $$\frac{19}{12}$$ is more than 1.
So, $$\frac{6}{6}<\frac{19}{12}$$.

(e) $$\frac{12}{9}$$ ____ $$\frac{4}{5}$$

Solution:
Since, $$\frac{12}{9}$$ is more than 1 and $$\frac{4}{5}$$ is less than 1.
So $$\frac{12}{9}>\frac{4}{5}$$

(f) $$\frac{15}{5}$$ ____ $$\frac{16}{4}$$

Solution:
Since, $$\frac{15}{5}$$ = 3, and $$\frac{16}{4}$$ = 4
So, $$\frac{15}{5}<\frac{16}{4}$$ as 3 < 4.

NCERT Textbook Page 30

Let Us Do

Question 1.
Circle the fractions below that are equal to A.

Solution:

Question 2.

Some fractions are written in the box below. Circle the fractions that are less than half. How do you know? Discuss your reasoning in the class.

Solution:

NCERT Textbook Page 31

Let Us Do

Question 1.
Compare the following fractions. Where possible, compare the fractions with —.

Solution:

Here, $$\frac{2}{9}$$ ia less than $$\frac{1}{2}$$ and $$\frac{4}{7}$$ is more than $$\frac{1}{2}$$. So, $$\frac{2}{9}<\frac{4}{7}$$

Here, $$\frac{11}{14}$$ is more than $$\frac{1}{2}$$ and $$\frac{7}{20}$$ is less than $$\frac{1}{2}$$. So, $$\frac{11}{14}>\frac{7}{20}$$.

Here, $$\frac{5}{7}$$ is more than $$\frac{1}{2}$$ and $$\frac{3}{9}$$ is less than $$\frac{1}{2}$$. So, $$\frac{5}{7}>\frac{3}{9}$$.

Here, $$\frac{6}{7}$$ is more than $$\frac{1}{2}$$ and $$\frac{4}{10}$$ is less than $$\frac{1}{2}$$. So, $$\frac{6}{7}>\frac{4}{10}$$.

Here, $$\frac{9}{17}$$ is more than $$\frac{1}{2}$$ and $$\frac{3}{15}$$ is less than $$\frac{1}{2}$$. So, $$\frac{9}{17}>\frac{3}{15}$$.

Here, $$\frac{7}{12}$$ is more than $$\frac{1}{2}$$ and $$\frac{3}{11}$$ is less than $$\frac{1}{2}$$. So, $$\frac{7}{12}>\frac{3}{11}$$.

Here, $$\frac{1}{3}$$ is more than $$\frac{1}{2}$$ and $$\frac{5}{9}$$ is less than $$\frac{1}{2}$$. So, $$\frac{1}{3}<\frac{5}{9}$$.

Here, $$\frac{3}{9}$$ is more than $$\frac{1}{2}$$ and $$\frac{4}{7}$$ is less than $$\frac{1}{2}$$. So, $$\frac{3}{9}<\frac{4}{7}$$.

Try this:

If the length of an ant is $$\frac{1}{4}$$ cm—then what is the total length of 16 such ants walking in a line? Use the number line given below.

Solution:

As the length of an ant is $$\frac{1}{4}$$ cm

= $$\frac{16}{4}$$ cm

= 4 cm

Hence, 

total length of 16 such ants = 4 cm

Class 5 Maths Fractions – Key Concepts and Exam Tips

Grasping the basics of fractions is crucial for success in Maths. This chapter helps students compare, identify, and convert equivalent fractions using fun activities and visual aids for clearer understanding.

By reviewing NCERT Solutions Class 5 Maths Mela Chapter 2 Fractions (2025-26), students will build strong calculation skills. Understanding fractions greater than one and comparing fractions makes solving daily maths problems much easier.

Always practice with your fraction kit and grids for depth. Regular revision and working on different question types will boost your confidence in fractions and help you score higher in your exams.