NCERT Solutions Class 5 Maths Chapter 2 Fractions

F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T

C L A S S 5 · M AT H S

NCERT Solutions

Chapter 2: Fractions

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

17 – 31 17 55 English

Solutions, notes, sample papers & more at 59 pages

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

CLASS 5 · MATHS · MATH MELA

NCERT Solutions — Chapter 2: Fractions
Chapter 2 of Math Mela is about fractions — the numbers we use for parts of a whole. Tamanna's two
chocolates, Gurpreet's fraction kit, Raman's father's parathas and a family pizza teach four big ideas: a
fraction only makes sense when you know which whole it came from, two fractions can name the same part
(equivalent fractions), fractions can be bigger than 1, and you can compare fractions quickly by holding them
up against 1 or against 1/2.

TEXTBOOK BOOK PAGES

Math Mela (Class 5) 17 – 31

SECTIONS QUESTIONS

17 55

MEDIUM

English

Playing with a Grid — Page 17
Tamanna's chocolates and Grids A, B, C

PLAYING WITH A GRID

Q1 Tamanna is a student of Grade 5. She has two chocolates of different sizes. She says
that 1/3 of one of her chocolates is bigger than 1/2 of the other chocolate. Is that
correct? Explain why this is so.

Yes, Tamanna is correct. She is right because her two chocolates are not the same size.
Look at the two bars in the book. Count the squares.

Page 1 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Big bar: 9 squares

Small bar: 4 squares

1/2 = 2 squares 1/3 = 3 squares

3 squares are more than 2
squares.

The squares are the same size, but the bars are not. So 1/3 of the big bar beats 1/2 of the small bar.

Small chocolate = 2 × 2 = 4 squares

1/2 of it = 4 ÷ 2 = 2 squares

Big chocolate = 3 × 3 = 9 squares

1/3 of it = 9 ÷ 3 = 3 squares

3 squares > 2 squares, so 1/3 of the big chocolate is bigger

Why it happens: A fraction is always a part of something. The 1/3 here is a part of a
big chocolate. The 1/2 is a part of a small chocolate. So the two pieces are cut from
two different wholes, and the bigger whole can give the bigger piece even though
1/3 sounds smaller than 1/2.

Remember the book's rule: To compare two fractions of two wholes, the wholes
from which the fractions are derived must be the same.

Page 2 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Q2 When can we say that 1/2 of something is greater than 1/3 of something?

We can say it when both fractions are taken from the same whole.
Take one paratha. Cut it in 2 equal parts and keep one part — that is 1/2. Now take the same
paratha, cut it in 3 equal parts and keep one part — that is 1/3.

Same paratha cut into 2 parts → 1/2

longer

Same paratha cut into 3 parts → 1/3

shorter

Same paratha, two different cuts. The half is clearly the longer piece.

Same whole, cut into 2 → each part is bigger

Same whole, cut into 3 → each part is smaller

So 1/2 > 1/3

Why it happens: When you share the same thing among more people, each person
gets less. Two friends sharing one paratha get more each than three friends sharing
the same paratha.

Also true: If the wholes are different, 1/2 of a small thing can be smaller than 1/3 of
a big thing — that is exactly what happened with Tamanna's chocolates in Q1. So
always ask first: 1/2 of what?

Page 3 of 59

as e
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

co m
m.
Identify 1/2 of the chocolate (the small bar). Identify 1/3 of the chocolate (the big
e
Q3

m l as
.co
bar).

a g
se m
g l a
a

1/2 of the small bar = 2 squares. 1/3 of the big bar = 3 squares.

om ag
Here is how to find them, step by step.
. c
a s em2 rows of 2 = 4 squares. Big bar: 3 rows of 3 = 9
1. Count the squares in the bar. Small bar:
squares.
a gl
2. Look at the bottom number of the fraction. For 1/2 the bottom number is 2. For 1/3 it is 3.
3. Divide the squares into that many equal groups. 4 squares into 2 equal groups → 2
co m
em.
squares in each group. 9 squares into 3 equal groups → 3 squares in each group.
m l as
.co a g
4. Take one group. That one group is the fraction you wanted.

a s em
agl 1/2 of the small chocolate = 4 ÷ 2 = 2 squares
m a s
agl
1/3 of the big chocolate = 9 ÷ 3 = 3 squares
.co
a s em
agl+ 2 squares = 4 squares, the whole small bar. 3 + 3 + 3 =
Check it yourself: 2 squares
9 squares, the whole big bar. The groups fit exactly, so the parts are equal.

co m
m .
as e
om 1/8 of Grid A in red.
.cShade a g l
a s emQ4

agl
se m
com g l a
. a
Shade any 6 squares. Grid A has 8 columns and 6 rows, so it has 48 small squares. One-eighth
m
ase
of 48 is 6.

agl
Squares in Grid A = 8 × 6 = 48

co m
1/8 of 48 = 48 ÷ 8 = 6 squares
m .
m as e
.co a g l
a s em The easiest 6 squares to shade are one whole column, because a column has exactly 6 squares.

agl
.c
s e m
m a
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 4 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Grid A: 1 column of 6 shaded red
= 1/8

Grid A has 48 squares. Each column of 6 squares is one-eighth of the grid.

Why it happens: The 8 columns are all the same size, and together they make the
whole grid. So each single column is one of 8 equal parts — that is exactly what 1/8
means.

Check it yourself: 6 squares × 8 columns = 48 squares. The eight columns fill the
grid with nothing left over.

Q5 Shade 1/6 of Grid B in blue.

Shade any 8 squares. Grid B is the same size as Grid A: 8 columns and 6 rows, so 48 small
squares.

Page 5 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Squares in Grid B = 8 × 6 = 48

1/6 of 48 = 48 ÷ 6 = 8 squares

One whole row has exactly 8 squares, so shading one full row is the neatest way.

Grid B: 1 row of 8 shaded blue =
1/6

Grid B has 6 rows. Each row of 8 squares is one-sixth of the grid.

Why it happens: The 6 rows are equal and together they make the whole grid, so
one row is one of 6 equal parts — that is 1/6.

Check it yourself: 8 squares × 6 rows = 48 squares. Correct.

Page 6 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Q6 Shade 1/12 of Grid C in yellow.

Shade any 4 squares. Grid C also has 8 × 6 = 48 small squares.

1/12 of 48 = 48 ÷ 12 = 4 squares

A neat way is to shade a block of 2 squares across and 2 squares down, or half a row.

Grid C: a 2 × 2 block = 4
squares = 1/12

Four squares out of 48 is one-twelfth of Grid C.

Why it happens: Twelve blocks of 4 squares fill the grid: 4 × 12 = 48. So each block of
4 is one of 12 equal parts.

Page 7 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Compare the three answers: 1/8 gave 6 squares, 1/6 gave 8 squares, 1/12 gave 4
squares. The grids are the same, so the bigger the bottom number, the smaller the
shaded piece.

Q7 Do you see 1/3 in any of the grids? Mark it.

Yes — 1/3 of any of these grids is 16 squares, which is exactly 2 full rows.

Squares in a grid = 8 × 6 = 48

1/3 of 48 = 48 ÷ 3 = 16 squares

2 rows = 2 × 8 = 16 squares ✓

2 rows shaded = 16 squares = 1/3

The 6 rows split neatly into 3 groups of 2 rows each. Each group is one-third.

Page 8 of 59

as e
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

co m
m.
Why it happens: The grid has 6 rows. Six rows can be shared into 3 equal groups of

m as e
l
2 rows. Each group is one of 3 equal parts of the grid, so each group is 1/3.
.co a g
a s em
gl
aAnother way to mark it: Two rows of 8 is 16 squares. So is a block that is 4 squares
across and 4 squares down. Any 16 squares of the 48 make one-third — but a neat

co m
ag
block is easier to see.
m .
as e
a g l
Fun with Fraction Kit — Page 18
co m
m.
Is 1/3 equal to 2/6? Gurpreet builds a whole

m as e
.co
FUN WITH FRACTION KIT
a g l
a s em
gl Is 1/3 equal to 2/6? Let us find out. Look at the picture and identify the fractions.
a Q1
m a s
m .co agl
l a se
a g

. c om
m a s em part is at the left.
The bar printed on page 18. It is cut into 6 equal parts and the shaded

. co a gl
as em
g l
a ANSWER
se m
com
Yes, 1/3 is equal to 2/6. The picture shows one strip with two shaded parts out of six.
g l a
m . a
ase
gl 1 shaded → 1/3
Seen as 3 big aparts:

co m
m .
o m l a se
m ag
.c Same strip cut again into 6 parts: 2 shaded → 2/6
l a se
ag
.c
s e m
com a
.
em is the same in both. So 1/3 = 2/6. agl
s
The orange length
a
agl One strip, two names. The shaded length never changed.

com
m .
m ase
.co


a g l Page 9 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Strip cut into 3 equal parts, 1 shaded → 1/3

Same strip cut into 6 equal parts, 2 shaded → 2/6

Same shaded length, so 1/3 = 2/6

Why it happens: Cutting each of the 3 big parts into 2 makes 6 small parts. The one
shaded big part becomes 2 shaded small parts. Nothing was added or taken away —
only the cutting changed. Fractions like these are called equivalent fractions.

Q2 Are there two different ways to write the fraction represented by the shaded part?

Yes. The shaded part can be written as 1/3 or as 2/6.

1. Count the big parts. The strip has 3 big parts and 1 of them is shaded. That gives 1/3.
2. Count the small parts. The same strip has 6 small parts and 2 of them are shaded. That
gives 2/6.
3. Compare. Both names describe the very same orange piece, so 1/3 = 2/6.

Did you know? A part can have many names. The same shaded piece is also 3/9 and
4/12 if you cut the strip into 9 or 12 equal parts. These are all equivalent fractions.

Q3 Do you remember how to make a whole with pieces of the same size? How many 1/5
pieces will you need to make a whole?

You need 5 pieces of 1/5.

1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1 whole

Page 10 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

5 pieces of 1/5 fill the whole strip

1/5 1/5 1/5 1/5 1/5

5/5 = 1
The bottom number tells you how many equal pieces make one whole.

Why it happens: The name 1/5 means the whole was cut into 5 equal parts and you
took one. So to build the whole back, you must put all 5 parts together.

The general rule: It takes 2 pieces of 1/2, 3 pieces of 1/3, 8 pieces of 1/8, and 12
pieces of 1/12 to make one whole. The bottom number is the number of pieces you
need.

Q4 One piece of 1/2 and two pieces of 1/4 make a whole. What is the relation between
1/2 and 1/4? Discuss in class.

Two pieces of 1/4 are exactly equal to one piece of 1/2. So 1/2 = 2/4.

One 1/2 piece covers two 1/4 pieces exactly

1/2 1/2

1/4 1/4 1/4 1/4

Put the pieces one under the other and the match is easy to see.

Page 11 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

1/4 + 1/4 = 2/4

2/4 covers the same space as 1/2

So 1/2 = 2/4

Sample answer for the class discussion: When a 1/2 piece is broken into 2 equal parts, each
part is a 1/4 piece. So one half is twice as long as one fourth, and two fourths are needed to
cover one half.

Why it happens: Cutting the whole into 4 parts instead of 2 makes each part half as
big. Twice as many pieces, each half the size — the total stays the same.

Q5 What else is equivalent to 1/2? 1/2 = 2/4 = ____ = ____ = ____

1/2 = 2/4 = 3/6 = 4/8 = 5/10 (and 6/12, and so on).
Here is the method, in steps you can copy.

1. Start with 1/2. Top number 1, bottom number 2.
2. Pick a number to multiply by — say 3.
3. Multiply the top and the bottom by that same number. 1 × 3 = 3 and 2 × 3 = 6, so you get
3/6.
4. Repeat with 4, 5, 6 … to get 4/8, 5/10, 6/12.

1/2 = (1×2)/(2×2) = 2/4

1/2 = (1×3)/(2×3) = 3/6

1/2 = (1×4)/(2×4) = 4/8

1/2 = (1×5)/(2×5) = 5/10

1/2 = (1×6)/(2×6) = 6/12

Page 12 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

1/

2/

3/

4/

Four strips of the same length. The blue part stops at the same place every time — that is what
equivalent means.

Check it yourself: In every one of these fractions the bottom number is exactly
double the top number. That is the family mark of one-half.

Let Us Do — Page 19
Making a whole from kit pieces; how many small pieces fit inside a bigger piece

LET US DO

Q1 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) 1/3 = ___ = ___ = ___ (b) 1/4 = ___ = ___ = ___ (c) 1/5 = ___ = ___ = ___
(d) 1/6 = ___ = ___ = ___

Multiply the top number and the bottom number by the same number each time.

Page 13 of 59

as e
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

co m
m.
PART FRACTION ×2 ×3 ×4

m 1/3 ase
(a)
.co
2/6 3/9
a g l 4/12

se m
g
(b)
l a
a
1/4 2/8 3/12 4/16

(c) 1/5 2/10 3/15 4/20

co m 2/12
(d) 1/6
e m . 3/18 4/24 ag
g l as
What you see with the kit: a
Two 1/6 pieces sit exactly on one 1/3 piece → 1/3 = 2/6.
co m
Two 1/8 pieces sit exactly on one 1/4 piece → 1/4 = 2/8. Three 1/12 pieces also cover one 1/4
em.
c o m
piece → 1/4 = 3/12.
g l as
.
Twom1/10 pieces cover one 1/5 piece → 1/5 = 2/10. a
l a se 1/12 pieces cover one 1/6 piece → 1/6 = 2/12.
ag Two

m a s
.co one 1/3 piece
Two 1/6 pieces exactly cover
m agl
l a se
1/3 ag

co m
m .
m
1/6 1/6
as e
.co a g l
se m
g l a
a Line the kit pieces up under each other — that is the proof, not just the numbers.

se m
com g l a
m . a
ase
Tip: Some of these pieces are not in the kit (there is no 1/16 or 1/24 piece). You can

agl
still write those fractions, because the rule about multiplying works for every
number.

co m
m .
o m l a se
m .c Do you see how to generate equivalent fractions foragany given fraction? Discuss in
se
Q2

a
agl
class.

.c
s e m
m a
agl

. co
e m
Yes. Multiply the top number and the bottom number by the same number.

g l as
a
Sample answer for the class discussion:

1. Choose any counting number — 2, 3, 4, 5 …

co m
m .
m ase
.co


a g l Page 14 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

2. Multiply the numerator (the top number) by it.
3. Multiply the denominator (the bottom number) by the same number.
4. The new fraction shows the same part of the whole. It is an equivalent fraction.

Example: 3/4

3/4 = (3×2)/(4×2) = 6/8

3/4 = (3×5)/(4×5) = 15/20

Why it happens: Multiplying the bottom number by 3 means every part is cut into 3
smaller parts. Multiplying the top number by 3 means you now hold 3 times as many
of those smaller parts. Three times as many pieces, each a third as big — the
amount you are holding does not change.

It works backwards too: Divide the top and the bottom by the same number and
you also get an equivalent fraction. 6/8 = (6÷2)/(8÷2) = 3/4.

Q3 Find the following using your kit. You can also shade and check by shading. A. How
many 1/6s make 1/3? (The shaded part is 1/3. Identify 1/6 in the same whole and
find how many 1/6s fit into 1/3.)

Two 1/6s make 1/3.
The figure in the book is a whole cut into 6 equal boxes (3 across, 2 down). The shaded part is
the first column — that is 2 boxes.

Page 15 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Whole = 6 equal boxes. Shaded = 1
column = 2 boxes.

1/6

1/6

1 column of 3 columns = 1/3, and it
holds 2 boxes = 2/6.
Two one-sixth boxes fill one one-third column.

Whole = 6 equal boxes, so each box = 1/6

Shaded column = 1 of 3 columns = 1/3

The shaded column holds 2 boxes

So 2 sixths = 1 third, that is 2/6 = 1/3

Check it yourself: 2 boxes × 3 columns = 6 boxes, the whole figure. Correct.

Q4 B. How many 1/8s make (a) 1/4? (b) 1/2?

(a) Two 1/8s make 1/4. (b) Four 1/8s make 1/2.
The figures in the book are wholes cut into 8 equal boxes (4 across, 2 down). Each box is 1/8.

Page 16 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

(a) 1/4 = 2 boxes of 1/8 (b) 1/2 = 4 boxes of 1/8

1/4 = 2/8 1/2 = 4/8

Shade one of the four columns for 1/4, and two of the four columns for 1/2.

(a) Whole = 8 boxes. 1/4 of 8 = 8 ÷ 4 = 2 boxes → 1/4 = 2/8

(b) 1/2 of 8 = 8 ÷ 2 = 4 boxes → 1/2 = 4/8

Why it happens: Each 1/4 piece can be cut into 2 equal bits, and each bit is a 1/8.
Each 1/2 piece can be cut into 4 such bits.

Check it yourself: 2 boxes × 4 quarters = 8 boxes ✓, and 4 boxes × 2 halves = 8
boxes ✓.

Q5 C. How many 1/12s make (a) 1/2? (b) 1/3? (c) 1/4? (d) 1/6?

(a) 6 (b) 4 (c) 3 (d) 2 pieces of 1/12.
Each figure in the book is a whole cut into 12 equal boxes (4 across, 3 down). Each box is 1/12.
Divide 12 by the bottom number of the fraction.

PART FRACTION WORKING BOXES OF 1/12 NEEDED EQUIVALENT FRACTION

(a) 1/2 12 ÷ 2 6 1/2 = 6/12

(b) 1/3 12 ÷ 3 4 1/3 = 4/12

(c) 1/4 12 ÷ 4 3 1/4 = 3/12

(d) 1/6 12 ÷ 6 2 1/6 = 2/12

Page 17 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

1/4 of 12 boxes = 3
1/2 of 12 boxes = 6 boxes boxes

1/2 = 6/12 1/4 = 3/12
Twelfths make it easy: shade whole columns and count the boxes.

Look at the pattern: As the pieces get smaller (1/2 → 1/3 → 1/4 → 1/6), the number
of twelfths needed also gets smaller (6 → 4 → 3 → 2). That makes sense — a smaller
piece needs fewer boxes to fill it.

Let Us Do (Question 3) — Page 20
Building a whole out of chosen kit pieces

LET US DO

Q1 Do as instructed using your fraction kit: Make a whole using only 1/6 and 1/12
pieces.

One good answer: five 1/6 pieces and two 1/12 pieces.

5 × 1/6 = 5/6

2 × 1/12 = 2/12 = 1/6
5/6 + 1/6 = 6/6 = 1 whole

Page 18 of 59

as e
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

co m
m.
m pieces + two 1/12 pieces = one whole ase
Five 1/6
m .
e 1/6
co agl
g l as 1/6 1/6 1/6 1/6 1/12 1/12
a
om = 1
5/6 + 2/12 = 10/12 + 2/12 = 12/12
.c ag
s e m
a
agl
The last one-sixth space is filled by two one-twelfth pieces.

Other correct answers (each row makes exactly one whole):
co m
em.
m l as
.co g
PIECES OF 1/6 PIECES OF 1/12 CHECK

m a
l a se
g
5 2 10/12 + 2/12 = 1
a
s
4 4 8/12 + 4/12 = 1

m a
m .co agl
se
3 6 6/12 + 6/12 = 1

g l a
2
a 8 4/12 + 8/12 = 1

co m
1 10 2/12 + 10/12 = 1

m .
m as e
.co a g
Why it happens: One 1/6 piece is the same size as two 1/12 pieces. So every timel
s m remove a 1/6 piece you can put two 1/12 pieces in its place, and the whole is still
eyou
a
gl full.
a
se m
com g l a
m . a
e
as1/4, and 1/2 pieces.
Q2
g l
Make a whole using 1/12,
a
co m
m .
One 1/2 piece + one 1/4 piece + three 1/12 pieces = one whole.
m ase
.co
Change every piece into twelfths first, because 12 works for 2, 4 and 12.
a g l
a s em1. 1/2 = 6/12 (since 12 ÷ 2 = 6)
agl 2. 1/4 = 3/12 (since 12 ÷ 4 = 3)
.c
s e m
m a
3. That is 6/12 + 3/12 = 9/12 so far.

m .
4. 12/12 − 9/12 = 3/12, so add three 1/12 pieces.
e
co agl
g l as
a

co m
m .
m as e
.co


a g l Page 19 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

1/2 + 1/4 + 1/12 + 1/12 + 1/12

= 6/12 + 3/12 + 3/12

= 12/12 = 1 whole

1/2 1/4 1/12 1/12 1/12

6/12 + 3/12 + 3/12 = 12/12 = 1
Three different sizes of piece, one full strip.

Another correct answer: two 1/4 pieces + one 1/4 piece + three 1/12 pieces will not
do, because it has no 1/2. But 1/2 + two 1/12 + ... always check the total comes to
exactly 12/12.

Q3 Make a whole using any five pieces of the same size.

Use five 1/5 pieces.

1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1 whole

Five equal pieces, so each piece must be 1/5

1/5 1/5 1/5 1/5 1/5

5/5 = 1
If five equal pieces make one whole, each piece is one-fifth.

Page 20 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Why it happens: If all five pieces are the same size and they exactly fill the whole,
then the whole has been cut into 5 equal parts. That is what 1/5 means. No other
same-size piece will work — five 1/4 pieces would be too much (5/4) and five 1/6
pieces too little (5/6).

Q4 Make a whole using any seven pieces.

One good answer: five 1/6 pieces and two 1/12 pieces — that is 7 pieces in all.

5/6 + 2/12

= 10/12 + 2/12

= 12/12 = 1 whole (pieces used: 5 + 2 = 7)

Another answer: one 1/2 piece and six 1/12 pieces — also 7 pieces.

1/2 + 6/12 = 6/12 + 6/12 = 12/12 = 1 whole (pieces used: 1 + 6 = 7)

1 + 6 = 7 pieces, and they fill the strip exactly

1/2

six 1/12 pieces

Seven pieces of two different sizes, filling one whole.

How to invent your own: Turn every piece into twelfths. Then just make seven
numbers of twelfths add up to 12 — for example 6 + 2 + 1 + 1 + 1 + 1 = 12 gives 1/2 +
1/6 + four 1/12 pieces, which is also 7 pieces.

Page 21 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Q5 Play in a group with this kit and find other interesting combinations to make a
whole. Write or draw your findings.

Work in a group. One child lays pieces on the whole strip, another writes down the fractions,
and the group checks that the total is exactly 1.
Sample answer — findings written by a group:

COMBINATION WE MADE NUMBER OF PIECES CHECK IN TWELFTHS

1/2 + 1/3 + 1/6 3 6/12 + 4/12 + 2/12 = 12/12

1/2 + 1/4 + 1/4 3 6/12 + 3/12 + 3/12 = 12/12

1/3 + 1/3 + 1/6 + 1/6 4 4/12 + 4/12 + 2/12 + 2/12 = 12/12

1/4 + 1/4 + 1/4 + 1/6 + 1/12 5 3/12 + 3/12 + 3/12 + 2/12 + 1/12 = 12/12

1/2 + 1/6 + 1/6 + 1/12 + 1/12 5 6/12 + 2/12 + 2/12 + 1/12 + 1/12 = 12/12

Twelve 1/12 pieces 12 12/12

Two things our group noticed:

1. Every combination adds up to 12 twelfths. Twelfths work well because 2, 3, 4, 6 and 12 all
divide 12.
2. The more pieces you use, the smaller the pieces have to be.

Try this at home: Make a whole using pieces that are all different sizes. 1/2 + 1/3 +
1/12 + 1/12 works: 6/12 + 4/12 + 1/12 + 1/12 = 12/12.

Making Equivalent Fractions — Pages 20–21

Page 22 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Sameer draws more lines; the 1/3 family and the 2/5 family

MAKING EQUIVALENT FRACTIONS

Q1 Sameer has shaded one-third of the following figures. He draws horizontal lines to
divide the shapes into more equal parts. Name the fraction shaded in each figure.

The four figures printed on page 20. In each one the same middle strip is shaded, but
the figure is cut into more and more equal parts.

The four figures show 1/3, 2/6, 3/9 and 4/12 — and all four are the same shaded amount.

FIGURE LINES SAMEER DREW TOTAL EQUAL PARTS SHADED PARTS FRACTION

1st none 3 1 1/3

2nd 1 line 6 2 2/6

3rd 2 lines 9 3 3/9

4th 3 lines 12 4 4/12

Page 23 of 59

ase
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m .co a g
l a se
a g

co m
m . ag
2/6 se
1/3
a 3/9 4/12
agl
The yellow column never changes width. Only the number of lines changes.

co m
se m.
c o m l a
gthe same while its
Why it happens: A horizontal line cuts every part into smaller parts, but it does not
addm or. remove any colour. So the shaded amount stays exactly
a
l a se
a g name changes. Fractions like 1/3, 2/6, 3/9 and 4/12 that show the same part of a
whole are called equivalent fractions.

m a s
em
.co agl
a s
l into more equal parts and find fractions equivalent
Divide the wholes given g
Q2 a below
to 1/3. Write them in the boxes below the images.

co m
m .
m as e
.co a g l
emit further, then count.
Each figure is already cut into 3 columns with the middle one shaded. Draw horizontal lines to

a s
gl
cut

a 1. Draw 4 horizontal lines in the first figure. Now there are 3 × 5 = 15 small parts and 5 are

se m
com a
shaded → 5/15.

. a g l
em figure. Now 3 × 7 = 21 parts, 7 shaded → 7/21.
2. Draw 5 horizontal lines in the second figure. Now 3 × 6 = 18 parts, 6 shaded → 6/18.
3. Draw 6 horizontal lines in thesthird
a
agl

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
a s e
. com 6/18 agl
5/15
as em 7/21
g l
a to write in the boxes. The yellow strip is the same width in all three.
The three answers

co m
m .
m ase
.co


a g l Page 24 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

5/15 : 15 ÷ 5 = 3 ✓ equivalent to 1/3

6/18 : 18 ÷ 6 = 3 ✓

7/21 : 21 ÷ 7 = 3 ✓

Other correct answers: any fraction whose bottom number is 3 times its top
number — 8/24, 10/30, 20/60 and so on. Just make sure your figure really is cut into
equal parts.

Q3 Do you see any pattern in all the equivalent fractions that you found? 1/3 = 2/6 = 3/9
= 4/12 = ____ = ____ = ____ = □/24 = □/36

1/3 = 2/6 = 3/9 = 4/12 = 5/15 = 6/18 = 7/21 = 8/24 = 12/36
The pattern: the bottom number is always 3 times the top number.

FRACTION 1/3 2/6 3/9 4/12 5/15 6/18 7/21 8/24 12/36

Top × 3 1×3=3 2×3=6 3×3=9 4×3=12 5×3=15 6×3=18 7×3=21 8×3=24 12×3=36

How to fill the last two boxes:

1. □/24: ask "3 times what gives 24?" 24 ÷ 3 = 8, so the box is 8.
2. □/36: ask "3 times what gives 36?" 36 ÷ 3 = 12, so the box is 12.

□/24 → 24 ÷ 3 = 8 → 8/24

□/36 → 36 ÷ 3 = 12 → 12/36

Check it yourself: 8/24 — divide top and bottom by 8 and you get 1/3 ✓. 12/36 —
divide top and bottom by 12 and you get 1/3 ✓.

Q4 How do you know when a fraction is equivalent to another? Discuss in class.

Two fractions are equivalent when one can be made from the other by multiplying (or
dividing) the top and the bottom by the same number.

Page 25 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Sample answer for the class discussion — three ways to check:

1. The multiplying check. Is 3/5 equivalent to 12/20? Ask: 5 × what = 20? The answer is 4. Now
do the same to the top: 3 × 4 = 12 ✓. So yes, they are equivalent.
2. The dividing check. Make both fractions as small as they will go. 6/8 becomes 3/4, and 9/12
also becomes 3/4. Same simplest form, so they are equivalent.
3. The picture check. Shade both fractions on two strips of the same length. If the shaded
lengths end at the same place, the fractions are equivalent.

3/5 and 12/20 → 5 × 4 = 20 and 3 × 4 = 12 → equivalent

2/3 and 3/4 → 3 × ? = 4 has no whole-number answer → not equivalent

Why it happens: Multiplying the bottom by 4 chops every part into 4 smaller parts.
Multiplying the top by 4 means you now hold 4 times as many of these smaller parts.
You end up holding exactly the same amount, so the two fractions must be equal.

Page 26 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Q5 The below pictures show 2/5 of a whole. Find the different fractions that are
equivalent to 2/5 and write your fractions below each image. 2/5 = 4/10 = ____ = ____ =
□/50 = □/100

2 4
5 10

The four pictures printed on page 21. Each one shows the same shaded amount. Under
the first two the book has already written the fraction; under the last two the boxes are
empty.

2/5 = 4/10 = 6/15 = 8/20 = 20/50 = 40/100
Each picture is a whole cut into 5 rows with 2 rows shaded. Cutting it into columns as well gives
the next fraction.

PICTURE COLUMNS DRAWN TOTAL PARTS SHADED PARTS FRACTION

1st 1 5×1=5 2 2/5

2nd 2 5 × 2 = 10 4 4/10

3rd 3 5 × 3 = 15 6 6/15

4th 4 5 × 4 = 20 8 8/20

Page 27 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

2/5 4/10 6/15 8/20
Same purple area every time; only the number of boxes changes.

Now the last two boxes:

1. □/50: 5 × 10 = 50, so multiply the top by 10 too: 2 × 10 = 20. The answer is 20/50.
2. □/100: 5 × 20 = 100, so 2 × 20 = 40. The answer is 40/100.

Check it yourself: In every fraction here, the bottom number is 2 and a half times
the top — or more simply, divide the top and bottom by their common number and
you always come back to 2/5. 40/100 ÷ 20 = 2/5 ✓.

Let Us Do — Page 22
Practising equivalent fractions

LET US DO

Q1 Fill in the blanks with equivalent fractions. There may be more than one answer. (a)
1/7 = ____ (b) 2/3 = ____ (c) 3/4 = ____ (d) 3/5 = ____

Multiply the top and the bottom by the same number. Any such answer is correct.

PART GIVEN ×2 ×3 ×4 × 10

(a) 1/7 2/14 3/21 4/28 10/70

(b) 2/3 4/6 6/9 8/12 20/30

(c) 3/4 6/8 9/12 12/16 30/40

(d) 3/5 6/10 9/15 12/20 30/50

Page 28 of 59

as e
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

Working for (b), step by step:
co m
em.
m 2. as
1. Start with 2/3.

. conumber a g l
3. Top:s2e×m2 = 4. Bottom: 3 × 2 = 6.
2. Choose the

a
agSol 2/3 = 4/6.
4.

co m
.
Check it yourself: Divide your answer back by the same number and you must land
em✓. ag
a s
on the original fraction. 9/12 ÷ 3 = 3/4

agl

co m
m.
✓
e
Put a tick ( ) against the fractions that are equivalent. (a) 2/3 and 3/4 (b) 3/5 and

as
Q2

m l
.co
6/10 (c) 4/12 and 2/6 (d) 6/9 and 1/3
a g
se m
g l a
a (a) ✗ (b) ✓ (c) ✓ (d) ✗

m a s
m .co agl
ase
PART PAIR TEST EQUIVALENT?

(a) 2/3 and 3/4
a gl
3 × ? = 4 — no whole number works. Also 2/3 in smallest form is 2/3, No ✗
and 3/4 is 3/4.

. comYes ✓
m
(b)
e
3/5 and 5 × 2 = 10 and 3 × 2 = 6

com l as
6/10

. a g
m
ase
✓
agl
(c) 4/12 and 4/12 ÷ 4 = 1/3 and 2/6 ÷ 2 = 1/3 — both are 1/3 Yes
2/6

✗
se m
com a
(d)
l
6/9 and 1/3 6/9 ÷ 3 = 2/3, and 2/3 is not 1/3 No

. a g
m
lase
agout of nine shaded
6/9 — six parts

co m
m .
m ase
.co a g l
se m
g l a
a c
m .
1/3 — one part out of three. The red lengths are
m a s e
.co
different, so 6/9 ≠ 1/3.
m agl
l a se
a g
Part (d) shown as strips: 6/9 fills two-thirds of the strip, not one-third.

co m
m .
m as e
.co


a g l Page 29 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

A quick eye-test: In (d), 6 is more than half of 9, so 6/9 is more than 1/2 — while 1/3
is less than 1/2. They cannot possibly be equal.

Q3 Fill in the boxes such that the fractions become equivalent. (a) 2/5 = □/10 (b) 3/4 =
□/16 (c) 4/7 = 8/□ (d) 5/9 = 25/□

(a) 4 (b) 12 (c) 14 (d) 45
The method is the same every time: find what the number you can see was multiplied by, then
do the same to the other number.

PART QUESTION MULTIPLIED BY WORKING ANSWER

(a) 2/5 = □/10 10 ÷ 5 = 2 2×2=4 2/5 = 4/10

(b) 3/4 = □/16 16 ÷ 4 = 4 3 × 4 = 12 3/4 = 12/16

(c) 4/7 = 8/□ 8÷4=2 7 × 2 = 14 4/7 = 8/14

(d) 5/9 = 25/□ 25 ÷ 5 = 5 9 × 5 = 45 5/9 = 25/45

Working for (b), step by step:

1. Look at the two bottom numbers: 4 and 16.
2. Ask: 4 times what is 16? 16 ÷ 4 = 4.
3. Do the same to the top: 3 × 4 = 12.
4. So the box is 12, and 3/4 = 12/16.

Check it yourself: Divide the answer by the number you used. 25/45 ÷ 5 = 5/9 ✓,
and 8/14 ÷ 2 = 4/7 ✓.

Comparing Fractions — Same Denominator — Pages 22–23

Page 30 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Sevi and Shami share a piece of chikki

COMPARING FRACTIONS — SAME DENOMINATOR LET US DO

Q1 Sevi and Shami divided a piece of chikki between themselves. Sevi ate 1/3 and
Shami ate the rest, that is, 2/3. Who ate more?

Shami ate more.

Sevi ate 1 piece of 1/3

Shami ate 2 pieces of 1/3

2 pieces > 1 piece, so 2/3 > 1/3

Sevi: 1/3 of the chikki

Shami: 2/3 of the chikki

Shami's orange bar is longer, so Shami ate more.
Same chikki, same size of piece — so just count the pieces.

Why it happens: The chikki was cut into 3 equal pieces, so every piece is the same
size. When the pieces are the same size, whoever has more pieces has more chikki.
The bottom numbers are the same, so we only need to look at the top numbers: 2 >
1.

The rule: When two fractions have the same denominator (the same bottom
number), the one with the bigger numerator (top number) is bigger.

Page 31 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Q2 Compare the fractions given below using < and > signs. (a) 1/4 ___ 3/4 (b) 3/5 ___ 4/5
(c) 5/7 ___ 2/7 (d) 7/8 ___ 3/8 (e) 5/10 ___ 6/10 (f) 2/6 ___ 1/6

Every pair here has the same bottom number, so just compare the top numbers.

PART PAIR COMPARE THE TOP NUMBERS ANSWER

(a) 1/4 and 3/4 1<3 1/4 < 3/4

(b) 3/5 and 4/5 3<4 3/5 < 4/5

(c) 5/7 and 2/7 5>2 5/7 > 2/7

(d) 7/8 and 3/8 7>3 7/8 > 3/8

(e) 5/10 and 6/10 5<6 5/10 < 6/10

(f) 2/6 and 1/6 2>1 2/6 > 1/6

Part (a): the pieces are the same size, so 3 pieces
beat 1 piece.

1/

3/

With the same denominator, the taller count always wins.

Careful: This shortcut works only when the bottom numbers are the same. For 3/8
and 3/7 you cannot compare the tops — that is the next section.

Comparing Fractions — Same Numerator — Page 23

Page 32 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

4/6 paratha or 4/5 paratha?

COMPARING FRACTIONS — SAME NUMERATOR LET US DO

Q1 One child says, ‘I ate 4/6 paratha yesterday evening.’ The other says, ‘I ate 4/5
paratha yesterday evening.’ Between Sevi and Shami, can you tell who ate more?
Use your fraction kit to find the answer.

The one who ate 4/5 — Shami — ate more.
Both children ate 4 pieces. So the answer depends on whose pieces were bigger.

1. Take out the 1/5 pieces and the 1/6 pieces from your kit.
2. Put one 1/5 piece on top of one 1/6 piece. The 1/5 piece sticks out — it is bigger.
3. Both children ate 4 pieces. Shami's 4 pieces were each bigger.
4. So Shami ate more: 4/5 > 4/6.

Sevi: 4 pieces of 1/6 = 4/6

Shami: 4 pieces of 1/5 = 4/5

Same number of pieces, but the fifths are longer. So
4/5 > 4/6.
Both parathas are the same size. Only the cutting is different.

Why it happens: Cutting a paratha into 6 makes smaller pieces than cutting it into 5.
So each 1/6 is smaller than each 1/5. Four small pieces come to less than four bigger
pieces.

Page 33 of 59

as e
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

co m
m.
Do the following pictures help you reason? Share your thoughts in the class.
e
Q2

m l as
m .co a g
l a se
a g
1 1 1 1
co m
. ag
6 6 5 5
e m
1
g l a1s
6 a 6 1 1
5 5
com
1 1
.
1
5 em
6 6
m a s
m .co agl
l a se
a g Sevi’s paratha Shami’s paratha

s
The two parathas printed on page 23 — one cut into 5 equal pieces, the other into 6
m a
.co agl
equal pieces.

se m
g l a
a

co m
.
Yes, the pictures settle it at once. The two parathas in the pictures are the same size, but one
m
m for the class discussion:
is cut into 5 pieces and the other into 6.
as e
. coanswer a g l
em
Sample

a s
agl The whole is the same in both pictures — one paratha.
1.

m
2. The paratha cut into 5 has fewer, bigger pieces. The one cut into 6 has more, smaller pieces.

a se
com l
3. So one 1/6 piece is smaller than one 1/5 piece.
. a g
m
ase
4. Each child ate 4 pieces, so the one with the bigger pieces ate more. Therefore 4/6 < 4/5.

1/6 < 1/5
agl

co m
4 × (1/6) < 4 × (1/5)
m .
m as e
.co
So 4/6 < 4/5
a g l
se m
g l a
a c
.
The rule: When two fractions have the same numerator (the same top number),

s e m
a
the one with the smaller denominator is bigger — because its pieces are bigger.
m
e m . co agl
g l as
a

co m
m .
m ase
.co


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Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Q3 Compare the following fractions using < and > signs. (a) 3/8 ___ 3/7 (b) 4/9 ___ 4/10 (c)
2/7 ___ 2/5 (d) 5/7 ___ 5/6 (e) 6/9 ___ 6/10 (f) 7/9 ___ 7/11

Every pair has the same top number. So look at the bottom numbers: the smaller bottom
number means bigger pieces, and therefore the bigger fraction.

PART PAIR WHICH PIECE IS BIGGER? ANSWER

(a) 3/8 and 3/7 1/7 is bigger than 1/8 3/8 < 3/7

(b) 4/9 and 4/10 1/9 is bigger than 1/10 4/9 > 4/10

(c) 2/7 and 2/5 1/5 is bigger than 1/7 2/7 < 2/5

(d) 5/7 and 5/6 1/6 is bigger than 1/7 5/7 < 5/6

(e) 6/9 and 6/10 1/9 is bigger than 1/10 6/9 > 6/10

(f) 7/9 and 7/11 1/9 is bigger than 1/11 7/9 > 7/11

3/8 — the whole is cut into 8

3/7 — the whole is cut into 7

Same 3 pieces each time, but sevenths are longer.
So 3/8 < 3/7.
Part (a) drawn on two strips of the same length.

Remember it this way: More people sharing one paratha means a smaller share
each. A bigger bottom number means a smaller piece.

Fractions Greater Than 1 — Pages 24–26

Page 35 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Raman's father cuts the parathas into halves

FRACTIONS GREATER THAN 1

Q1 Raman's father cuts the parathas into halves (2 equal parts) or fourths (4 equal
parts) before serving them. Maa took 5 pieces of 1/2 paratha. How many parathas
did she eat?

Maa ate 5/2 parathas, that is 2 1/2 parathas.
Name the quantity first: we need the number of parathas, and each piece is half a paratha.

1. Maa took 5 pieces. Each piece is 1/2 paratha.
2. 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 5/2 parathas.
3. Group the halves in twos, because 2 halves make 1 whole paratha.
(1/2 + 1/2) + (1/2 + 1/2) + 1/2 = 1 + 1 + 1/2.
4. So Maa ate 2 whole parathas and 1 half = 2 1/2 parathas.

5 pieces of 1/2 paratha = 5/2 parathas
= 2 + 1/2 parathas

= 2 1/2 parathas

5 jumps of 1/2 land on 5/2, which is 2 1/2

0 1/2 2/2 = 1 3/2 4/2 = 2 5/2

Divide 0 to 1 into two equal parts. Each part is 1/2. Five such jumps take you past 2.

Check it yourself: 2 1/2 parathas is 2 whole ones (4 halves) plus 1 half = 5 halves ✓.

Page 36 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Q2 Raman's sister Radhika took 6 pieces of 1/2 paratha. How many parathas did she
eat?

Radhika ate 6/2 parathas, which is exactly 3 parathas.

1. Radhika took 6 pieces, each of 1/2 paratha.
2. Add them: 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 6/2 parathas.
3. Pair them up — every 2 halves make 1 whole:
(1/2 + 1/2) + (1/2 + 1/2) + (1/2 + 1/2) = 1 + 1 + 1.
4. So Radhika ate 3 whole parathas, with nothing left over.

6/2 parathas = 6 ÷ 2 = 3 parathas

6 jumps of 1/2 land exactly on 3

0 1/2 1 3/2 2 5/2 3

Six halves land exactly on a whole number, so there is no half left over.

Compare with Q1: Maa's 5 halves left one half over, so her answer was a mixed
number. Radhika's 6 halves paired up perfectly, so her answer is a whole number.

Q3 Dadiji had 7 pieces of 1/2 paratha. How many parathas did she eat? Find out.

Dadiji ate 7/2 parathas, that is 3 1/2 parathas.

1. Dadiji had 7 pieces, each 1/2 paratha, so she ate 7/2 parathas.
2. Pair the halves: (1/2+1/2) + (1/2+1/2) + (1/2+1/2) + 1/2.
3. Three pairs make 3 whole parathas, and one half is left.
4. So she ate 3 1/2 parathas.

Page 37 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

7 ÷ 2 = 3 with 1 left over

7/2 = 3 + 1/2 = 3 1/2 parathas

7 jumps of 1/2 reach 7/2, one half past 3

0 1/2 1 3/2 2 5/2 3 7/2

7/2 sits exactly halfway between 3 and 4.

Check it yourself: 3 1/2 parathas = 3 wholes (6 halves) + 1 half = 7 halves ✓.

Page 38 of 59

ase
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

co m
m.
Raman ate 6 pieces of 1/2 paratha, Dadaji ate 7 pieces of 1/2 paratha and Baba ate 5
e
Q4

om the answer.
pieces of 1/2 paratha. How many parathas did each of them eat? Use the number
cfind g l as
. a
em
line to

a s
a gl
Quantity of Raman’s paratha

co m
em . ag
as
0 1

a g
Quantity of Dadaji’s paratha
l

co m
m.
0 1

m ase
.coQuantity of Baba’s paratha a g l
se m
g l a
a 0 1

m a s
e m . coon agl
as
The three number lines printed page 25. Each small step is half a paratha.

a g l

co m
.

se m
m a
Raman 3 parathas · Dadaji 3 1/2 parathas · Baba 2 1/2 parathas.
o
.c number line, mark 0, then step forward one half at a time
a l
gand count the steps.
m
On each

l a se
ag PERSON PIECES OF 1/2 AS A FRACTION WHERE IT LANDS PARATHAS EATEN
se m
Raman 6 6/2
com
exactly on 3 3
g l a
m . a
ase
agl 5/2
Dadaji 7 7/2 half a step past 3 3 1/2

Baba 5 half a step past 2 2 1/2

co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
em . co agl
g l as
a

co m
m .
m as e
.co


a g l Page 39 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Raman
6/2 =
3

0 1 2 3

Dadaji 7/2 = 3 1/2

0 1 2 3

Baba 5/2 = 2
1/2
0 1 2 3

Three number lines, each with a half-step tick. Count the steps from 0.

Who ate the most? Dadaji, with 3 1/2 parathas. Compare 7/2, 6/2 and 5/2 — same
bottom number, so the biggest top number wins.

Q5 How many parathas were made on this day? Find out.

18 parathas were made on this day.
On the halves day, all six members of Raman's family ate. Count every half piece and then
change the halves into whole parathas.

Page 40 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

PERSON PIECES OF 1/2 EATEN PARATHAS

Maa 5 2 1/2

Radhika 6 3

Dadiji 7 3 1/2

Raman 6 3

Dadaji 7 3 1/2

Baba 5 2 1/2

Total 36 18

1. Add up all the half pieces. 5 + 6 + 7 + 6 + 7 + 5 = 36 pieces.
2. Remember that 2 halves make 1 paratha.
3. Divide. 36 ÷ 2 = 18.

Total = 36/2 parathas

36 ÷ 2 = 18 parathas

Why we add first: Every piece on the table came from a paratha that Raman's father
cut. If we know how many half pieces were served in all, we know how many
parathas were cut, because each paratha gave exactly 2 halves.

Check it yourself: Add the parathas instead: 2 1/2 + 3 + 3 1/2 + 3 + 3 1/2 + 2 1/2 = 18
✓.

Fractions Greater Than 1 (Fourths) — Pages 26–27
Another day: the parathas are cut into fourths

FRACTIONS GREATER THAN 1

Q1 Another day, Raman's father cut all the parathas in 1/4. Dadaji took 9 pieces of 1/4
paratha. How many parathas did he eat?

Dadaji ate 9/4 parathas, that is 2 1/4 parathas.

Page 41 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

1. Each piece is 1/4 paratha, and Dadaji took 9 pieces, so he ate 9/4 parathas.
2. 4 one-fourths make 1 whole paratha. Group the 9 pieces in fours.
(1/4+1/4+1/4+1/4) + (1/4+1/4+1/4+1/4) + 1/4
3. That is 1 + 1 + 1/4.
4. So Dadaji ate 2 1/4 parathas.

9 ÷ 4 = 2 with 1 left over

9/4 = 2 + 1/4 = 2 1/4 parathas

9 jumps of 1/4 land on 9/4, one quarter past 2

0 1/4 2/4 3/4 1 5/4 6/4 7/4 2 9/4

Divide 0 to 1 into four equal parts. Each part is 1/4. Nine such jumps reach 9/4.

Check it yourself: 2 1/4 parathas = 2 wholes (8 quarters) + 1 quarter = 9 quarters ✓.

Q2 Raman ate 7 pieces of 1/4, Radhika ate 6 pieces of 1/4, Maa ate 8 pieces of 1/4, Dadiji
ate 10 pieces of 1/4, and Baba ate 12 pieces of 1/4 paratha. Use a number line to find
out how many parathas were eaten by each of them.

Raman 1 3/4 · Radhika 1 1/2 · Maa 2 · Dadiji 2 1/2 · Baba 3 parathas.
The method is the same each time: divide the number of pieces by 4, because 4 quarters
make one whole paratha.

Page 42 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

PERSON PIECES OF 1/4 FRACTION DIVIDE BY 4 PARATHAS EATEN

Raman 7 7/4 7 ÷ 4 = 1 rem 3 1 3/4

Radhika 6 6/4 6 ÷ 4 = 1 rem 2 1 2/4 = 1 1/2

Maa 8 8/4 8 ÷ 4 = 2 rem 0 2

Dadiji 10 10/4 10 ÷ 4 = 2 rem 2 2 2/4 = 2 1/2

Baba 12 12/4 12 ÷ 4 = 3 rem 0 3

Raman 7/4 = 1 3/4

0 1 2 3
Radhika 6/4 = 1 1/2

Maa 8/4 = 2

Dadiji 10/4 = 2 1/2

Baba 12/4 = 3

Five number lines, each with quarter ticks. The arrow ends where the person's total sits.

Tip: 2/4 is the same as 1/2, so 6/4 is 1 1/2 and 10/4 is 2 1/2. Always write the fraction
in its simplest form at the end.

Q3 How many parathas were made on this day? Find out.

13 parathas were made on this day.
On the fourths day, all six members of the family ate. Count all the quarter pieces, then change
them into whole parathas.

Page 43 of 59

as e
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

co m
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PERSON PIECES OF 1/4 PARATHAS

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Dadaji
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9 2 1/4
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Raman 7 1 3/4

Radhika 6 1 1/2

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Maa 8
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Dadiji 10
a 2 1/2

Baba 12 3
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Total 52 13

. a g
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agl2. 4 quarters make 1 paratha.
1. Add all the quarter pieces. 9 + 7 + 6 + 8 + 10 + 12 = 52 pieces.

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3. Divide. 52 ÷ 4 = 13.
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Total = 52/4 parathas

52 ÷ 4 = 13 parathas a

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Check it yourself: Add the parathas instead: 2 1/4 + 1 3/4 + 1 1/2 + 2 + 2 1/2 + 3. The

m .c 1/4 and 3/4 make 1; the halves 1/2 and 1/2 makea1.g So 2 + 1 + 1 + 1 + 2 + 3 +
ase3 = 13 ✓.
quarters

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se m
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Sharing the Pizzas — Pages e27–28
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Two pizzas, six slices, one family
agl

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Raman's family of 6 members ordered 2 pizzas and cut each pizza into 3 equal slices
emgave their slices to
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so that each family member had one slice. Dadiji and Dadaji
gl much pizza do each of them
.co Raman, and Maa and Baba gave theirs to Radhika. aHow
se m
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Raman has 1 whole pizza and Radhika has 1 whole pizza. Dadiji, Dadaji, Maa and Baba
m agl
have nothing left.
l a se
agEach pizza was cut into 3 equal slices, so one slice = 1/3 of a pizza.
Name the quantities first.

co m
m .
m ase
.co


a g l Page 44 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

1. 2 pizzas × 3 slices = 6 slices, and there are 6 members. So each member gets 1 slice = 1/3
pizza.
2. Raman keeps his own 1/3 and receives Dadiji's 1/3 and Dadaji's 1/3.
1/3 + 1/3 + 1/3 = 3/3 = 1 whole pizza.
3. Radhika keeps her own 1/3 and receives Maa's 1/3 and Baba's 1/3.
1/3 + 1/3 + 1/3 = 3/3 = 1 whole pizza.
4. Dadiji, Dadaji, Maa and Baba gave their slices away, so each of them has 0.

his own slice + 2 gifted slices = 1 whole pizza

0 1/3 2/3 3/3 = 1
Raman: 1/3 + 1/3 + 1/3 = 3/3 = 1
Three one-third jumps land exactly on 1 — a whole pizza.

Raman = 1/3 + 1/3 + 1/3 = 3/3 = 1 pizza
Radhika = 1/3 + 1/3 + 1/3 = 3/3 = 1 pizza

Dadiji = Dadaji = Maa = Baba = 0

Check it yourself: 1 pizza + 1 pizza + 0 + 0 + 0 + 0 = 2 pizzas — exactly what the
family ordered. Nothing was lost.

Q2 Raman could eat only 2 slices of pizza. So, he gave 1 to Radhika. How much pizza
does Radhika have now?

Radhika now has 4/3 pizzas, that is 1 1/3 pizzas. Raman is left with 2/3 of a pizza.

1. Radhika already had 3 slices, that is 3/3 = 1 whole pizza.
2. Raman gives her 1 more slice, which is 1/3 of a pizza.
3. Add: 1/3 + 1/3 + 1/3 + 1/3 = 4/3 pizzas.
4. Three thirds make 1 whole, and one third is left. So 4/3 = 1 1/3 pizzas.

Page 45 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Radhika = 3/3 + 1/3 = 4/3 = 1 + 1/3 = 1 1/3 pizzas

Raman = 3/3 − 1/3 = 2/3 pizza

4 slices of 1/3 = 4/3 = 1 1/3 pizzas

0 1/3 2/3 3/3 = 1 4/3

The fourth one-third step takes Radhika past the whole pizza mark.

Why 4/3 is more than 1: The top number 4 is bigger than the bottom number 3.
That means Radhika has more thirds than are needed to make one whole, so she
has more than one pizza.

Check it yourself: Radhika 4/3 + Raman 2/3 = 6/3 = 2 whole pizzas ✓ — the two
pizzas the family ordered.

Let Us Do — Page 28
Showing fractions on number lines; spotting fractions greater than 1

LET US DO

Q1 Use parathas and number lines to show the following fractions in your notebook.
(a) 2/3 and 5/3 (b) 3/4 and 5/4 (c) 4/8 and 9/8

The steps are the same for each pair.

1. Look at the bottom number. It tells you how many equal parts to cut each paratha (and
each unit on the number line) into.
2. Draw the number line from 0 to 2 (or 0 to 3) and mark every one of those small steps.
3. Count the top number of steps from 0 and mark the point.

Page 46 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

PART FRACTION CUT EACH PARATHA INTO TAKE IN PARATHAS

(a) 2/3 3 parts 2 pieces less than 1

(a) 5/3 3 parts 5 pieces 1 2/3

(b) 3/4 4 parts 3 pieces less than 1

(b) 5/4 4 parts 5 pieces 1 1/4

(c) 4/8 8 parts 4 pieces 1/2

(c) 9/8 8 parts 9 pieces 1 1/8

2/3 5/3

0 1 2

3/4 5/4

0 1 2

4/8 9/8

Top line thirds, middle line fourths, bottom line eighths. The purple dot is less than 1 each time; the
red dot is more than 1.

With parathas: for 5/3, take 2 parathas, cut each into 3 equal pieces, and pick up 5 pieces. You
get one whole paratha and 2 pieces left over, so 5/3 = 1 2/3.

Notice: In each pair, the first fraction is less than 1 (top smaller than bottom) and the
second is more than 1 (top bigger than bottom).

Page 47 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Q2 Circle the fractions that are greater than one (whole). How do you know? Discuss
your reasoning in the class. [7/9, 2/5, 5/4, 3/9, 7/3, 2/3, 7/11, 13/11, 5/7, 9/4, 4/9, 12/5,
9/4, 12/8]

Circle these: 5/4, 7/3, 13/11, 9/4, 12/5, 9/4 (it appears twice) and 12/8.
How to know: compare the top number with the bottom number. If the top is bigger, the
fraction is more than one whole.

FRACTION TOP VS BOTTOM GREATER THAN 1?

7/9 7<9 No

2/5 2<5 No

5/4 5>4 Yes — circle it

3/9 3<9 No

7/3 7>3 Yes — circle it

2/3 2<3 No

7/11 7 < 11 No

13/11 13 > 11 Yes — circle it

5/7 5<7 No

9/4 9>4 Yes — circle it

4/9 4<9 No

12/5 12 > 5 Yes — circle it

9/4 9>4 Yes — circle it

12/8 12 > 8 Yes — circle it

Sample answer for the class discussion: The bottom number tells us how many pieces make
one whole. If we are holding more pieces than that, we must have more than one whole. In 12/8,
eight-eighths already make one whole paratha, and we have 12 pieces — four more. So 12/8 = 1
4/8 = 1 1/2.

Page 48 of 59

as e
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

co m
e m.
5/4 = 1 1/4 · 7/3 = 2 1/3 · 13/11 = 1 2/11
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9/4 = 2 1/4 · 12/5 = 2 2/5 · 12/8 = 1 1/2
m a g
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aWatch out for one more case: if the top and the bottom are equal — like 9/9 — the

co m
fraction is exactly 1, not greater than 1. There is no such fraction in this box, but
there is one in the next exercise.
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Comparing Fractions With Reference to 1 (a whole) — Page 29com
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7/8 paratha or 8/6 paratha?

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COMPARING FRACTIONS WITH REFERENCE TO 1

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LET US DO

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Let us compare some more fractions. One child says, ‘I ate 7/8 paratha yesterday
s
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evening.’ The other says, ‘I ate 8/6 paratha yesterday evening.’ Between Sevi and

s em
Shami can you tell who ate less?
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Sevi, who ate 7/8 of a paratha, ate less.
. c om
Do not compare 7 with 8, or 8 with 6. Compare each fraction with 1 wholemparatha instead.
o m l a se
g So 7/8 is less than 1.
.c 8 eighths make one whole paratha, but she ate only 7 ofathem.
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s2.e 8/6: 6 sixths make one whole paratha, and he ate 8 of them — two more than a whole. So
1. 7/8:

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a 8/6 is more than 1.

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3. Something less than 1 must be smaller than something more than 1.

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4. So 7/8 < 8/6, and Sevi ate less.

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7/8 8/6
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1 acts as a fence. 7/8 stops before it; 8/6 crosses it.

com
m .
m ase
.co


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Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

7/8 < 1 and 1 < 8/6

So 7/8 < 8/6

Why this trick works: 1 is a fence in the middle. Any fraction on the left of the fence
is smaller than any fraction on the right of it. You never have to make the bottom
numbers the same.

Q2 Compare the following fractions using 1 as a reference. Share your reasoning in the
class. (a) 8/7 ___ 9/15 (b) 13/20 ___ 17/15 (c) 7/6 ___ 8/8 (d) 6/6 ___ 19/12 (e) 12/9 ___ 4/5 (f)
15/5 ___ 16/4

For each fraction, first ask: is it less than 1, equal to 1, or more than 1?

PART FIRST FRACTION SECOND FRACTION ANSWER

(a) 8/7 : 8 > 7, so more than 1 9/15 : 9 < 15, so less than 1 8/7 > 9/15

(b) 13/20 : 13 < 20, less than 1 17/15 : 17 > 15, more than 1 13/20 < 17/15

(c) 7/6 : 7 > 6, more than 1 8/8 : 8 = 8, exactly 1 7/6 > 8/8

(d) 6/6 : 6 = 6, exactly 1 19/12 : 19 > 12, more than 1 6/6 < 19/12

(e) 12/9 : 12 > 9, more than 1 4/5 : 4 < 5, less than 1 12/9 > 4/5

(f) 15/5 = 3 16/4 = 4 15/5 < 16/4

Part (f) needs one extra step — both fractions are more than 1, so the fence at 1 does not
separate them.

1. 15/5 means 15 fifths. Five fifths make 1, so 15 ÷ 5 = 3.
2. 16/4 means 16 fourths. Four fourths make 1, so 16 ÷ 4 = 4.
3. 3 < 4, so 15/5 < 16/4.

Sample answer for the class discussion: Comparing with 1 is the fastest way when
one fraction has a top number smaller than its bottom and the other has a top
number bigger. If both are on the same side of 1, you need another method — work
them out as whole numbers or mixed numbers, as in part (f).

Page 50 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Comparing Fractions with Reference to 1/2 — Pages 29–30
Half as the second fence

COMPARING FRACTIONS WITH REFERENCE TO 1/2 LET US DO

Q1 Circle the fractions below that are equal to 1/2. [2/4, 3/5, 5/7, 7/14, 5/10, 8/16, 5/9,
6/12, 10/20, 6/8]

Circle these six: 2/4, 7/14, 5/10, 8/16, 6/12 and 10/20.
The test: a fraction is half when the bottom number is exactly double the top number.

FRACTION IS THE BOTTOM DOUBLE THE TOP? EQUAL TO 1/2?

2/4 2×2=4✓ Yes — circle it

3/5 3 × 2 = 6, not 5 No

5/7 5 × 2 = 10, not 7 No

7/14 7 × 2 = 14 ✓ Yes — circle it

5/10 5 × 2 = 10 ✓ Yes — circle it

8/16 8 × 2 = 16 ✓ Yes — circle it

5/9 5 × 2 = 10, not 9 No

6/12 6 × 2 = 12 ✓ Yes — circle it

10/20 10 × 2 = 20 ✓ Yes — circle it

6/8 6 × 2 = 12, not 8 No

Page 51 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

2/

6/

6/

2/4 and 6/12 stop exactly in the middle. 6/8 goes past
the middle, so it is not half.
The green bars end at the halfway mark. The red bar does not.

Check it yourself: Divide the top and the bottom of each circled fraction by their
common number and you always get 1/2. 10/20 ÷ 10 = 1/2 ✓, 8/16 ÷ 8 = 1/2 ✓.

Q2 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. [3/9, 2/4, 12/15, 8/15,
11/12, 3/15, 4/8, 1/3, 7/11, 11/16, 15/31, 6/18]

Circle these five: 3/9, 3/15, 1/3, 15/31 and 6/18.
The test (one step): double the top number. If the doubled number is less than the bottom
number, the fraction is less than half.

Page 52 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

FRACTION DOUBLE THE TOP COMPARE WITH THE BOTTOM LESS THAN HALF?

3/9 3×2=6 6<9 Yes — circle it

2/4 2×2=4 4=4 No — it is exactly half

12/15 12 × 2 = 24 24 > 15 No — more than half

8/15 8 × 2 = 16 16 > 15 No — just more than half

11/12 11 × 2 = 22 22 > 12 No

3/15 3×2=6 6 < 15 Yes — circle it

4/8 4×2=8 8=8 No — it is exactly half

1/3 1×2=2 2<3 Yes — circle it

7/11 7 × 2 = 14 14 > 11 No

11/16 11 × 2 = 22 22 > 16 No

15/31 15 × 2 = 30 30 < 31 Yes — circle it

6/18 6 × 2 = 12 12 < 18 Yes — circle it

Sample answer for the class discussion: Half of the whole means half of the pieces. So work
out half of the bottom number and compare it with the top number. Half of 9 is 4 1/2, and 3 is
less than 4 1/2, so 3/9 is less than half. Half of 31 is 15 1/2, and 15 is just below it, so 15/31 is
only a tiny bit less than half. Doubling the top number is the same test without any half-
numbers.

Careful with 8/15 and 15/31. They look almost the same, but 8 is just above half of
15 while 15 is just below half of 31. Always do the doubling — do not guess by
looking.

Q3 Now let us compare fractions using 1/2. One child says, ‘I ate 5/8 paratha yesterday
evening.’ The other says, ‘I ate 3/6 paratha yesterday evening.’ Who do you think ate
more paratha?

The one who ate 5/8 — Sevi — ate more paratha.

1. Check 3/6 against half. Double the top: 3 × 2 = 6, and the bottom is 6. They match, so 3/6 is
exactly half.

Page 53 of 59

as e
Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

2. Check 5/8 against half. Double the top: 5 × 2 = 10, and the bottom is 8. 10 is more than 8, so
co m
5/8 is more than half.
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3. More than half beats exactly half.
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4. So 5/8 > 3/6.

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Sevi: 5/8 paratha
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Shami: 3/6 paratha
a

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l a se the halfway line
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The dashed line is exactly half the paratha. Sevi's orange bar crosses it; Shami's stops on it.

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3/6 = 1/2 (exactly half)
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5/8 > 4/8 = 1/2 (more than half)

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So 5/8 > 3/6
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s m the doubling test works: A fraction is half when it has half as many pieces as
eWhy
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a
eighths — one piece more than half.
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Let Us Do — Page 31 agl
Comparing fractions using 1/2 wherever possible
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Compare the following fractions. Where possible, compare the fractions with 1/2.
a c
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2/9 and 4/7 · 11/14 and 7/20 · 5/7 and 3/9 · 6/7 and 4/10 · 9/17 and 3/15 · 7/12 and 3/11
· 1/3 and 5/9 · 3/9 and 4/7
s e m
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ag1/2 by doubling its top number. Every pair here has one fraction
Test each fraction against
below half and one above half, so the comparison is settled at once.

co m
m .
m ase
.co


a g l Page 54 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

PAIR FIRST FRACTION VS 1/2 SECOND FRACTION VS 1/2 ANSWER

2/9 and 4/7 2 × 2 = 4 < 9 → less than 1/2 4 × 2 = 8 > 7 → more than 1/2 2/9 < 4/7

11/14 and 7/20 11 × 2 = 22 > 14 → more than 1/2 7 × 2 = 14 < 20 → less than 1/2 11/14 > 7/20

5/7 and 3/9 5 × 2 = 10 > 7 → more than 1/2 3 × 2 = 6 < 9 → less than 1/2 5/7 > 3/9

6/7 and 4/10 6 × 2 = 12 > 7 → more than 1/2 4 × 2 = 8 < 10 → less than 1/2 6/7 > 4/10

9/17 and 3/15 9 × 2 = 18 > 17 → more than 1/2 3 × 2 = 6 < 15 → less than 1/2 9/17 > 3/15

7/12 and 3/11 7 × 2 = 14 > 12 → more than 1/2 3 × 2 = 6 < 11 → less than 1/2 7/12 > 3/11

1/3 and 5/9 1 × 2 = 2 < 3 → less than 1/2 5 × 2 = 10 > 9 → more than 1/2 1/3 < 5/9

3/9 and 4/7 3 × 2 = 6 < 9 → less than 1/2 4 × 2 = 8 > 7 → more than 1/2 3/9 < 4/7

2/9 4/7

0 1/2 1
2/9 sits left of 1/2, 4/7 sits right of it. So 2/9 < 4/7.
1/2 is a fence in the middle of the number line, just as 1 was a fence before.

Notice how close some are. 9/17 is only a whisker above half (half of 17 is 8 1/2)
and 8/15 in the earlier exercise was only a whisker above half too. Always do the
doubling; a picture alone can trick you.

Try This — Page 31

Page 55 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Sixteen ants in a line

TRY THIS

Q1 If the length of an ant is 1/4 cm — then what is the total length of 16 such ants
walking in a line? Use the number line given below.

0
1
4 cm

The number line printed on page 31, with 16 ants walking one behind the other. One ant
is 1/4 cm long.

The 16 ants together are 4 cm long.
Name the quantity first: we need a total length in centimetres. Each ant adds 1/4 cm.

1. One ant is 1/4 cm long.
2. 16 ants together = 16 pieces of 1/4 cm = 16/4 cm.
3. 4 quarters make 1 cm, so group the 16 quarters into fours: 4 groups.
4. 16 ÷ 4 = 4. The line of ants is 4 cm long.

16 × 1/4 cm = 16/4 cm

16 ÷ 4 = 4 cm

16 ants, each 1/4 cm — 16 small steps

0 1 cm 2 cm 3 cm 4 cm
Every 4 ants cover 1 cm, so 16 ants cover 4 cm.
The small ticks are quarter-centimetres. Sixteen of them reach the 4 cm mark.

Page 56 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Why it happens: Four ants standing nose to tail are 1/4 + 1/4 + 1/4 + 1/4 = 4/4 = 1
cm. There are 4 such groups of 4 ants in 16, so the line is 4 × 1 cm = 4 cm.

Check it yourself: Work backwards. 4 cm has 4 × 4 = 16 quarter-centimetres, and
each ant fills one of them. That is exactly 16 ants ✓.

Fun with Relations — Page 31
A family puzzle to close the chapter

FUN WITH RELATIONS

Q1 If the only brother of your father's sister had a child, what would be the child's
relationship with you?

The child is you yourself — or your own brother or sister.
Untangle the puzzle one link at a time.

1. Your father's sister is your aunt — your bua.
2. Bua's only brother — bua has just one brother, and your father is her brother. So this
person is your own father.
3. Your father's child is you, or one of your brothers and sisters.
4. So the child in the puzzle is you (or your sibling).

her only brother his child
Father's sister Your father You!

(your bua)

Follow the arrows one step at a time and the puzzle
unwinds.
Bua → her only brother is your father → his child is you.

Reading a relationship puzzle is like reading a fraction: take it one step at a time.

Page 57 of 59

Class 5 Maths Chapter 2 Fractions AglaSem · NCERT Solutions

Try this: Make your own puzzle for a friend. For example — who is the son of my
mother's only sister's husband? (Answer: your cousin, your mausi's son.)

Chapter at a glance
A fraction is a part of a whole. In 1/3, the bottom number 3 (the denominator) tells how
many equal parts the whole was cut into. The top number 1 (the numerator) tells how many
of those parts we took. Cut a chapati into 4 equal parts and take 3 — you have 3/4 of the
chapati.
The whole matters. Tamanna says 1/3 of one chocolate is bigger than 1/2 of the other, and
she is right — her chocolates are different sizes. 1/2 of a 4-square bar is 2 squares; 1/3 of a
9-square bar is 3 squares. To compare two fractions fairly, both must come from the same
whole. Then 1/2 is always more than 1/3.
Equivalent fractions name the same part with different numbers. Cut a 1/2 piece into 2
equal bits and you get two 1/4 bits, so 1/2 = 2/4. Cut each part into more parts and both
numbers grow together: 1/3 = 2/6 = 3/9 = 4/12. To make one, multiply the top and the
bottom by the same number. 2/5 = (2×3)/(5×3) = 6/15.
Same denominator — count the pieces. If the pieces are the same size, more pieces
means more. 2/3 > 1/3, because 2 pieces of one-third beat 1 piece of one-third.
Same numerator — bigger bottom, smaller piece. Cut a paratha into 6 and each piece is
smaller than if you cut it into 5. So 1/6 < 1/5, and therefore 4/6 < 4/5. The bigger the
denominator, the smaller each piece.
Fractions greater than 1. Two halves make one whole, so 5 halves = 5/2 = 2 wholes and 1
half = 2 1/2. Four one-fourths make one whole, so 9 one-fourths = 9/4 = 2 1/4. On a number
line you just keep stepping the same-sized jump past 1.
Compare with 1. If the top is smaller than the bottom, the fraction is less than 1. If the top
is bigger, it is more than 1. If they are equal, it is exactly 1. So 7/8 < 1 and 8/6 > 1, which
settles 7/8 < 8/6 without any other work.
Compare with 1/2. Double the top. If the doubled top is less than the bottom, the fraction
is less than half. 3/9: double 3 to get 6, and 6 is less than 9, so 3/9 < 1/2. 5/8: double 5 to get
10, and 10 is more than 8, so 5/8 > 1/2. One fraction below half and one above half — the
comparison is done.

Page 58 of 59

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Class 5 Maths Chapter 2 Fractions
a g l AglaSem · NCERT Solutions

co m
m.
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m l a se
m .co WHAT IT MEANS ag EXAMPLE
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WORD WHERE IT APPEARS

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Whole The full thing before it is cut Page 17, the two chocolates One full paratha

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Fraction A number for a part of a whole Chapter title, page 17 3/4 of a chapati

a sem Comparing Fractions — Same
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Denominator The bottom number — how many In 2/3, the
equal parts the whole was cut into Denominator, page 22 denominator is 3

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Numerator The top number — how many Comparing Fractions — Same In 2/3, the numerator

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parts were taken Numerator, page 23 is 2

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Equal parts
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Parts of exactly the same size

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fractions Equivalent Fractions, page 20

omFun with Fraction Kit, page 18
same part of the same whole

Cut-out pieces of 1/2, 1/3, 1/4, .c
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Fraction kit Two 1/4 pieces cover
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1/6, 1/8, 1/12 … used to build one 1/2 piece
whole

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Number line A straight line where 0 to 1 is split Pages 24–28 1/4, 2/4, 3/4, 4/4 = 1
into equal steps
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Top number bigger than the
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Fractions Greater Than 9/4 = 2 1/4

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than bottom number page 24

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A whole number and a fraction Pages 24 and 26 5/2 = 2 1/2

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written together

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Reference A known fraction you compare Pages 29 and 30 Comparing with 1
(benchmark) others against and with 1/2

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Half One of two equal parts, 1/2 Comparing Fractions with 6/12 = 1/2
Reference to 1/2, page 29
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a g l Page 59 of 59