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NCERT Solutions for Class 5 Maths Chapter 2 Fractions (PDF) – 2027

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NCERT Solutions for Class 5 Maths Chapter 2 Fractions – step-by-step answers to every exercise and in-text question of the chapter, as per the latest NCERT syllabus for 2027. Read them online or download the free question-answer PDF.

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.

NCERT Solutions for Class 5 Maths Chapter 2 Fractions PDF

All the answers are on this page below. The PDF also explains every answer – why it is right and how to check it – so download it for revision.

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NCERT Solutions for Class 5 Maths Chapter 2 Fractions – Questions and Answers

All 55 questions of the chapter (textbook pages 17 – 31) are answered below, in the order of the book – in-text questions, activities and the end-of-chapter exercises. Each answer is written the way you would write it in the exam.

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

Playing with a Grid
Q1Tamanna 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.
Answer

Yes, Tamanna is correct. She is right because her two chocolates are not the same size.

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
Q2When can we say that 1/2 of something is greater than 1/3 of something?
Answer

We can say it when both fractions are taken from the same whole.

Same paratha cut into 2 parts → 1/2 Same paratha cut into 3 parts → 1/3 longer 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
Q3Identify 1/2 of the chocolate (the small bar). Identify 1/3 of the chocolate (the big bar).
small barbig bar
Two chocolate bars made of pieces of the same size.
Answer

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

1/2 of the small chocolate = 4 ÷ 2 = 2 squares
1/3 of the big chocolate = 9 ÷ 3 = 3 squares
Q4Shade 1/8 of Grid A in red.
A
Grid A — 8 squares across and 6 squares down.
Answer

Shade any 6 squares. Grid A has 8 columns and 6 rows, so it has 48 small squares. One-eighth of 48 is 6.

Squares in Grid A = 8 × 6 = 48
1/8 of 48 = 48 ÷ 8 = 6 squares
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.
Q5Shade 1/6 of Grid B in blue.
B
Grid B — 8 squares across and 6 squares down.
Answer

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

Squares in Grid B = 8 × 6 = 48
1/6 of 48 = 48 ÷ 6 = 8 squares
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.
Q6Shade 1/12 of Grid C in yellow.
C
Grid C — 8 squares across and 6 squares down.
Answer

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

1/12 of 48 = 48 ÷ 12 = 4 squares
Grid C: a 2 × 2 block = 4squares = 1/12
Four squares out of 48 is one-twelfth of Grid C.
Q7Do you see 1/3 in any of the grids? Mark it.
ABC
Grids A, B and C, each 8 squares across and 6 squares down.
Answer

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.

Fun with Fraction Kit — Page 18Is 1/3 equal to 2/6? Gurpreet builds a whole

Fun with Fraction Kit
Q1Is 1/3 equal to 2/6? Let us find out. Look at the picture and identify the fractions.
The bar printed on page 18. It is cut into 6 equal parts and the shaded part is at the left.
Answer

Yes, 1/3 is equal to 2/6. The picture shows one strip with two shaded parts out of six.

Seen as 3 big parts: 1 shaded → 1/3 Same strip cut again into 6 parts: 2 shaded → 2/6 The orange length is the same in both. So 1/3 = 2/6.
One strip, two names. The shaded length never changed.
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
Q2Are there two different ways to write the fraction represented by the shaded part?
A bar cut into equal parts. The shaded part is at the left.
Answer

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.
Q3Do 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?
Answer

You need 5 pieces of 1/5.

1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1 whole
1/51/51/51/51/5 5 pieces of 1/5 fill the whole strip 5/5 = 1
The bottom number tells you how many equal pieces make one whole.
Q4One 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.
1/21/41/4
The whole shown on page 18: one 1/2 piece and two 1/4 pieces.
Answer

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

1/21/2 1/41/41/41/4 One 1/2 piece covers two 1/4 pieces exactly
Put the pieces one under the other and the match is easy to see.

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.

Q5What else is equivalent to 1/2? 1/2 = 2/4 = ____ = ____ = ____
Answer

1/2 = 2/4 = 3/6 = 4/8 = 5/10 (and 6/12, and so on).

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
1/2 2/4 3/6 4/8
Four strips of the same length. The blue part stops at the same place every time — that is what equivalent means.

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

Let Us Do
Q1In 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 = ___ = ___ = ___
Answer

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

PartFraction× 2× 3× 4
(a)1/32/63/94/12
(b)1/42/83/124/16
(c)1/52/103/154/20
(d)1/62/123/184/24
Q2Do you see how to generate equivalent fractions for any given fraction? Discuss in class.
Answer

Yes. Multiply the top number and the bottom number by the same number.

Sample answer for the class discussion:

  1. Choose any counting number — 2, 3, 4, 5 …
  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.
Q3Find 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.)
The whole is cut into boxes. The shaded part is 1/3.
Answer

Two 1/6s make 1/3.

1/61/6 Whole = 6 equal boxes. Shaded = 1column = 2 boxes. 1 column of 3 columns = 1/3, and itholds 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
Q4B. How many 1/8s make (a) 1/4? (b) 1/2?
(a) for 1/4 (b) for 1/2
The two wholes printed on page 19, each cut into 8 equal boxes.
Answer

(a) Two 1/8s make 1/4. (b) Four 1/8s make 1/2.

(a) 1/4 = 2 boxes of 1/8 1/4 = 2/8 (b) 1/2 = 4 boxes of 1/8 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
Q5C. How many 1/12s make (a) 1/2? (b) 1/3? (c) 1/4? (d) 1/6?
(a) (b) (c) (d)
The four wholes printed on page 19, each cut into 12 equal boxes.
Answer

(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.

PartFractionWorkingBoxes of 1/12 neededEquivalent fraction
(a)1/212 ÷ 261/2 = 6/12
(b)1/312 ÷ 341/3 = 4/12
(c)1/412 ÷ 431/4 = 3/12
(d)1/612 ÷ 621/6 = 2/12
1/2 of 12 boxes = 6 boxes 1/2 = 6/12 1/4 of 12 boxes = 3boxes 1/4 = 3/12
Twelfths make it easy: shade whole columns and count the boxes.

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

Let Us Do
Q1Do as instructed using your fraction kit: Make a whole using only 1/6 and 1/12 pieces.
Answer

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

five 1/6 pieces = 5/6
two 1/12 pieces = 2/12 = 1/6
5/6 + 1/6 = 6/6 = 1 whole
1/61/61/61/61/6 1/121/12 Five 1/6 pieces + two 1/12 pieces = one whole 5/6 + 2/12 = 10/12 + 2/12 = 12/12 = 1
The last one-sixth space is filled by two one-twelfth pieces.
Q2Make a whole using 1/12, 1/4, and 1/2 pieces.
Answer

One 1/2 piece + one 1/4 piece + three 1/12 pieces = one whole.

1/2 + 1/4 + 1/12 + 1/12 + 1/12
= 6/12 + 3/12 + 3/12
= 12/12 = 1 whole
1/21/41/121/121/12 6/12 + 3/12 + 3/12 = 12/12 = 1
Three different sizes of piece, one full strip.
Q3Make a whole using any five pieces of the same size.
Answer

Use five 1/5 pieces.

1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 5/5 = 1 whole
1/51/51/51/51/5 Five equal pieces, so each piece must be 1/5 5/5 = 1
If five equal pieces make one whole, each piece is one-fifth.
Q4Make a whole using any seven pieces.
Answer

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)
1/2 six 1/12 pieces 1 + 6 = 7 pieces, and they fill the strip exactly
Seven pieces of two different sizes, filling one whole.
Q5Play in a group with this kit and find other interesting combinations to make a whole. Write or draw your findings.
Answer

Sample answer — findings written by a group:

Combination we madeNumber of piecesCheck in twelfths
1/2 + 1/3 + 1/636/12 + 4/12 + 2/12 = 12/12
1/2 + 1/4 + 1/436/12 + 3/12 + 3/12 = 12/12
1/3 + 1/3 + 1/6 + 1/644/12 + 4/12 + 2/12 + 2/12 = 12/12
1/4 + 1/4 + 1/4 + 1/6 + 1/1253/12 + 3/12 + 3/12 + 2/12 + 1/12 = 12/12
1/2 + 1/6 + 1/6 + 1/12 + 1/1256/12 + 2/12 + 2/12 + 1/12 + 1/12 = 12/12
Twelve 1/12 pieces1212/12

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.

Making Equivalent Fractions — Pages 20–21Sameer draws more lines; the 1/3 family and the 2/5 family

Making Equivalent Fractions
Q1Sameer 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.
Answer

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

FigureLines Sameer drewTotal equal partsShaded partsFraction
1stnone311/3
2nd1 line622/6
3rd2 lines933/9
4th3 lines1244/12
1/3 2/6 3/9 4/12
The yellow column never changes width. Only the number of lines changes.
Q2Divide the wholes given below into more equal parts and find fractions equivalent to 1/3. Write them in the boxes below the images.
The three wholes printed on page 21, each with one-third shaded, and an empty box under each.
Answer

Write 5/15, 6/18 and 7/21 in the three boxes. Draw 4, 5 and 6 horizontal lines in the three figures. Now 5 of 15, 6 of 18 and 7 of 21 equal parts are shaded.

5/15 6/18 7/21
The three answers to write in the boxes. The yellow strip is the same width in all three.
Q3Do you see any pattern in all the equivalent fractions that you found? 1/3 = 2/6 = 3/9 = 4/12 = ____ = ____ = ____ = □/24 = □/36
Answer

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.

Fraction1/32/63/94/125/156/187/218/2412/36
Top × 31×3=32×3=63×3=94×3=125×3=156×3=187×3=218×3=2412×3=36
□/24 → 24 ÷ 3 = 8 → 8/24
□/36 → 36 ÷ 3 = 12 → 12/36
Q4How do you know when a fraction is equivalent to another? Discuss in class.
Answer

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.

3/5 and 12/20 → 5 × 4 = 20 and 3 × 4 = 12 → equivalent
2/3 = 8/12 but 3/4 = 9/12 → not equivalent
Q5The 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
25
410
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.
Answer

2/5 = 4/10 = 6/15 = 8/20 = 20/50 = 40/100

PictureColumns drawnTotal partsShaded partsFraction
1st15 × 1 = 522/5
2nd25 × 2 = 1044/10
3rd35 × 3 = 1566/15
4th45 × 4 = 2088/20
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.

Let Us Do — Page 22Practising equivalent fractions

Let Us Do
Q1Fill 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 = ____
Answer

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

PartGiven× 2× 3× 4× 10
(a)1/72/143/214/2810/70
(b)2/34/66/98/1220/30
(c)3/46/89/1212/1630/40
(d)3/56/109/1512/2030/50
Q2Put a tick (✓) against the fractions that are equivalent. (a) 2/3 and 3/4 (b) 3/5 and 6/10 (c) 4/12 and 2/6 (d) 6/9 and 1/3
Answer

(a) ✗   (b) ✓   (c) ✓   (d) ✗

PartPairTestEquivalent?
(a)2/3 and 3/42/3 = 8/12 but 3/4 = 9/12, and 8/12 ≠ 9/12No ✗
(b)3/5 and 6/105 × 2 = 10 and 3 × 2 = 6Yes ✓
(c)4/12 and 2/64 ÷ 4 = 1, 12 ÷ 4 = 3 → 1/3; 2 ÷ 2 = 1, 6 ÷ 2 = 3 → 1/3Yes ✓
(d)6/9 and 1/36 ÷ 3 = 2, 9 ÷ 3 = 3 → 6/9 = 2/3, not 1/3No ✗
Q3Fill 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/□
Answer

(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.

PartQuestionMultiplied byWorkingAnswer
(a)2/5 = □/1010 ÷ 5 = 22 × 2 = 42/5 = 4/10
(b)3/4 = □/1616 ÷ 4 = 43 × 4 = 123/4 = 12/16
(c)4/7 = 8/□8 ÷ 4 = 27 × 2 = 144/7 = 8/14
(d)5/9 = 25/□25 ÷ 5 = 59 × 5 = 455/9 = 25/45

Comparing Fractions — Same Denominator — Pages 22–23Sevi and Shami share a piece of chikki

Comparing Fractions — Same DenominatorLet Us Do
Q1Sevi 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?
Answer

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.
Q2Compare 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
Answer

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

PartPairCompare the top numbersAnswer
(a)1/4 and 3/41 < 31/4 < 3/4
(b)3/5 and 4/53 < 43/5 < 4/5
(c)5/7 and 2/75 > 25/7 > 2/7
(d)7/8 and 3/87 > 37/8 > 3/8
(e)5/10 and 6/105 < 65/10 < 6/10
(f)2/6 and 1/62 > 12/6 > 1/6

Comparing Fractions — Same Numerator — Page 234/6 paratha or 4/5 paratha?

Comparing Fractions — Same NumeratorLet Us Do
Q1One 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.
Answer

The child who ate 4/5 paratha (the boy in the picture) ate more. Both ate 4 pieces, but a 1/5 piece is bigger than a 1/6 piece (lay one on top of the other with your kit). So 4/5 > 4/6.

4 pieces of 1/6 = 4/6 4 pieces of 1/5 = 4/5 Same number of pieces, but the fifths are longer. So4/5 > 4/6.
Both parathas are the same size. Only the cutting is different.
Q2Do the following pictures help you reason? Share your thoughts in the class.
1515151515
Cut into 5 equal pieces
161616161616
Cut into 6 equal pieces
The two parathas printed on page 23 — one cut into 5 equal pieces, the other into 6 equal pieces.
Answer

Yes. The two parathas are the same size, but one is cut into 5 equal pieces and the other into 6. So a 1/6 piece is smaller than a 1/5 piece, and 4 small pieces are less than 4 bigger pieces.

1/6 < 1/5
4 pieces of 1/6 < 4 pieces of 1/5
So 4/6 < 4/5
Q3Compare 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
Answer

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.

PartPairWhich piece is bigger?Answer
(a)3/8 and 3/71/7 is bigger than 1/83/8 < 3/7
(b)4/9 and 4/101/9 is bigger than 1/104/9 > 4/10
(c)2/7 and 2/51/5 is bigger than 1/72/7 < 2/5
(d)5/7 and 5/61/6 is bigger than 1/75/7 < 5/6
(e)6/9 and 6/101/9 is bigger than 1/106/9 > 6/10
(f)7/9 and 7/111/9 is bigger than 1/117/9 > 7/11

Fractions Greater Than 1 — Pages 24–26Raman’s father cuts the parathas into halves

Fractions Greater Than 1
Q1Raman’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?
Answer

Maa ate 5/2 parathas, that is 2 1/2 parathas.

5 pieces of 1/2 paratha = 5/2 parathas
= 2 + 1/2 parathas
= 2 1/2 parathas
01/22/2 = 13/24/2 = 25/2 5 jumps of 1/2 land on 5/2, which is 2 1/2
Divide 0 to 1 into two equal parts. Each part is 1/2. Five such jumps take you past 2.
Q2Raman’s sister Radhika took 6 pieces of 1/2 paratha. How many parathas did she eat?
Answer

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

6/2 parathas = 6 ÷ 2 = 3 parathas
01/213/225/23 6 jumps of 1/2 land exactly on 3
Six halves land exactly on a whole number, so there is no half left over.
Q3Dadiji had 7 pieces of 1/2 paratha. How many parathas did she eat? Find out.
Answer

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

7 ÷ 2 = 3 with 1 left over
7/2 = 3 + 1/2 = 3 1/2 parathas
01/213/225/237/2 7 jumps of 1/2 reach 7/2, one half past 3
7/2 sits exactly halfway between 3 and 4.
Q4Raman ate 6 pieces of 1/2 paratha, Dadaji ate 7 pieces of 1/2 paratha and Baba ate 5 pieces of 1/2 paratha. How many parathas did each of them eat? Use the number line to find the answer.
Quantity of Raman’s paratha01Quantity of Dadaji’s paratha01Quantity of Baba’s paratha01
The three number lines printed on page 25. Each small step is half a paratha.
Answer

Raman 3 parathas  ·  Dadaji 3 1/2 parathas  ·  Baba 2 1/2 parathas.

PersonPieces of 1/2As a fractionWhere it landsParathas eaten
Raman66/2exactly on 33
Dadaji77/2half a step past 33 1/2
Baba55/2half a step past 22 1/2
Raman 6/2 = 3 01234 Dadaji 7/2 = 3 1/2 01234 Baba 5/2 = 2 1/2 01234
Three number lines, each with a half-step tick. Count the steps from 0.
Q5How many parathas were made on this day? Find out.
Answer

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.

PersonPieces of 1/2 eatenParathas
Maa52 1/2
Radhika63
Dadiji73 1/2
Raman63
Dadaji73 1/2
Baba52 1/2
Total3618
Total = 36/2 parathas
36 ÷ 2 = 18 parathas

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

Fractions Greater Than 1
Q1Another 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?
Answer

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

9 ÷ 4 = 2 with 1 left over
9/4 = 2 + 1/4 = 2 1/4 parathas
01/42/43/415/46/47/429/4 9 jumps of 1/4 land on 9/4, one quarter past 2
Divide 0 to 1 into four equal parts. Each part is 1/4. Nine such jumps reach 9/4.
Q2Raman 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.
Quantity of Raman’s paratha 0 1 Quantity of Radhika’s paratha 0 1 Quantity of Maa’s paratha 0 1 Quantity of Dadiji’s paratha 0 1 Quantity of Baba’s paratha 0 1
The five number lines printed on page 27.
Answer

Raman 1 3/4  ·  Radhika 1 1/2  ·  Maa 2  ·  Dadiji 2 1/2  ·  Baba 3 parathas.

PersonPieces of 1/4FractionDivide by 4Parathas eaten
Raman77/47 ÷ 4 = 1 rem 31 3/4
Radhika66/46 ÷ 4 = 1 rem 21 2/4 = 1 1/2
Maa88/48 ÷ 4 = 2 rem 02
Dadiji1010/410 ÷ 4 = 2 rem 22 2/4 = 2 1/2
Baba1212/412 ÷ 4 = 3 rem 03
Raman 7/4 = 1 3/4 0123 Radhika 6/4 = 1 1/2 0123 Maa 8/4 = 2 0123 Dadiji 10/4 = 2 1/2 0123 Baba 12/4 = 3 0123
Five number lines, each with quarter ticks. The arrow ends where the person’s total sits.
Q3How many parathas were made on this day? Find out.
Answer

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.

PersonPieces of 1/4Parathas
Dadaji92 1/4
Raman71 3/4
Radhika61 1/2
Maa82
Dadiji102 1/2
Baba123
Total5213
Total = 52/4 parathas
52 ÷ 4 = 13 parathas

Sharing the Pizzas — Pages 27–28Two pizzas, six slices, one family

Q1Raman’s family of 6 members ordered 2 pizzas and cut each pizza into 3 equal slices so that each family member had one slice. Dadiji and Dadaji gave their slices to Raman, and Maa and Baba gave theirs to Radhika. How much pizza do each of them have after this?
Answer

Raman has 1 whole pizza and Radhika has 1 whole pizza. Dadiji, Dadaji, Maa and Baba have nothing left.

01/32/33/3 = 1 his own slice + 2 gifted slices = 1 whole pizza 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
Q2Raman could eat only 2 slices of pizza. So, he gave 1 to Radhika. How much pizza does Radhika have now?
Answer

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

Radhika = 3/3 + 1/3 = 4/3 = 1 + 1/3 = 1 1/3 pizzas
Raman = 3/3 − 1/3 = 2/3 pizza
01/32/33/3 = 14/3 4 slices of 1/3 = 4/3 = 1 1/3 pizzas
The fourth one-third step takes Radhika past the whole pizza mark.

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

Let Us Do
Q1Use 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
Answer

Count equal steps from 0 to mark each fraction. 2/3, 3/4 and 4/8 are less than 1. 5/3 = 1 2/3, 5/4 = 1 1/4 and 9/8 = 1 1/8 are more than 1.

PartFractionCut each paratha intoTakeIn parathas
(a)2/33 parts2 piecesless than 1
(a)5/33 parts5 pieces1 2/3
(b)3/44 parts3 piecesless than 1
(b)5/44 parts5 pieces1 1/4
(c)4/88 parts4 pieces1/2
(c)9/88 parts9 pieces1 1/8
012 2/3 5/3 012 3/4 5/4 012 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.
Q2Circle 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]
Answer

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.

FractionTop vs bottomGreater than 1?
7/97 < 9No
2/52 < 5No
5/45 > 4Yes — circle it
3/93 < 9No
7/37 > 3Yes — circle it
2/32 < 3No
7/117 < 11No
13/1113 > 11Yes — circle it
5/75 < 7No
9/49 > 4Yes — circle it
4/94 < 9No
12/512 > 5Yes — circle it
9/49 > 4Yes — circle it
12/812 > 8Yes — circle it

Comparing Fractions With Reference to 1 (a whole) — Page 297/8 paratha or 8/6 paratha?

Comparing Fractions With Reference to 1Let Us Do
Q1Let us compare some more fractions. One child says, ‘I ate 7/8 paratha yesterday evening.’ The other says, ‘I ate 8/6 paratha yesterday evening.’ Between Sevi and Shami can you tell who ate less?
Answer

The child who ate 7/8 paratha (the girl in the picture) ate less. 7/8 is less than 1 whole paratha, but 8/6 is more than 1 whole.

01 7/8 8/6 before 1 after 1
1 acts as a fence. 7/8 stops before it; 8/6 crosses it.
7/8 < 1  and  1 < 8/6
So 7/8 < 8/6
Q2Compare 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
Answer

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

PartFirst fractionSecond fractionAnswer
(a)8/7 : 8 > 7, so more than 19/15 : 9 < 15, so less than 18/7 > 9/15
(b)13/20 : 13 < 20, less than 117/15 : 17 > 15, more than 113/20 < 17/15
(c)7/6 : 7 > 6, more than 18/8 : 8 = 8, exactly 17/6 > 8/8
(d)6/6 : 6 = 6, exactly 119/12 : 19 > 12, more than 16/6 < 19/12
(e)12/9 : 12 > 9, more than 14/5 : 4 < 5, less than 112/9 > 4/5
(f)15/5 = 316/4 = 415/5 < 16/4

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

Comparing Fractions with Reference to 1/2Let Us Do
Q1Circle 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]
Answer

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.

FractionIs the bottom double the top?Equal to 1/2?
2/42 × 2 = 4 ✓Yes — circle it
3/53 × 2 = 6, not 5No
5/75 × 2 = 10, not 7No
7/147 × 2 = 14 ✓Yes — circle it
5/105 × 2 = 10 ✓Yes — circle it
8/168 × 2 = 16 ✓Yes — circle it
5/95 × 2 = 10, not 9No
6/126 × 2 = 12 ✓Yes — circle it
10/2010 × 2 = 20 ✓Yes — circle it
6/86 × 2 = 12, not 8No
2/4 6/12 6/8 2/4 and 6/12 stop exactly in the middle. 6/8 goes pastthe middle, so it is not half.
The green bars end at the halfway mark. The red bar does not.
Q2Some 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]
Answer

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.

FractionDouble the topCompare with the bottomLess than half?
3/93 × 2 = 66 < 9Yes — circle it
2/42 × 2 = 44 = 4No — it is exactly half
12/1512 × 2 = 2424 > 15No — more than half
8/158 × 2 = 1616 > 15No — just more than half
11/1211 × 2 = 2222 > 12No
3/153 × 2 = 66 < 15Yes — circle it
4/84 × 2 = 88 = 8No — it is exactly half
1/31 × 2 = 22 < 3Yes — circle it
7/117 × 2 = 1414 > 11No
11/1611 × 2 = 2222 > 16No
15/3115 × 2 = 3030 < 31Yes — circle it
6/186 × 2 = 1212 < 18Yes — circle it
Q3Now 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?
Answer

The child who ate 5/8 paratha (the girl in the picture) ate more. 3/6 is exactly half, but 5/8 is more than half.

5/8 paratha 3/6 paratha the halfway line
The dashed line is exactly half the paratha. The 5/8 bar crosses it; the 3/6 bar stops on it.
3/6 = 1/2  (exactly half)
5/8 > 4/8 = 1/2  (more than half)
So 5/8 > 3/6

Let Us Do — Page 31Comparing fractions using 1/2 wherever possible

Let Us Do
Q1Compare the following fractions. Where possible, compare the fractions with 1/2. 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
Answer

Test each fraction against 1/2 by doubling its top number. Every pair here has one fraction below half and one above half, so the comparison is settled at once.

PairFirst fraction vs 1/2Second fraction vs 1/2Answer
2/9 and 4/72 × 2 = 4 < 9 → less than 1/24 × 2 = 8 > 7 → more than 1/22/9 < 4/7
11/14 and 7/2011 × 2 = 22 > 14 → more than 1/27 × 2 = 14 < 20 → less than 1/211/14 > 7/20
5/7 and 3/95 × 2 = 10 > 7 → more than 1/23 × 2 = 6 < 9 → less than 1/25/7 > 3/9
6/7 and 4/106 × 2 = 12 > 7 → more than 1/24 × 2 = 8 < 10 → less than 1/26/7 > 4/10
9/17 and 3/159 × 2 = 18 > 17 → more than 1/23 × 2 = 6 < 15 → less than 1/29/17 > 3/15
7/12 and 3/117 × 2 = 14 > 12 → more than 1/23 × 2 = 6 < 11 → less than 1/27/12 > 3/11
1/3 and 5/91 × 2 = 2 < 3 → less than 1/25 × 2 = 10 > 9 → more than 1/21/3 < 5/9
3/9 and 4/73 × 2 = 6 < 9 → less than 1/24 × 2 = 8 > 7 → more than 1/23/9 < 4/7

Try This — Page 31Sixteen ants in a line

Try This
Q1If 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.
014cm
The number line printed on page 31, with 16 ants walking one behind the other. One ant is 1/4 cm long.
Answer

The 16 ants together are 4 cm long.

16 pieces of 1/4 cm = 16/4 cm
16 ÷ 4 = 4 cm
01 cm2 cm3 cm4 cm 16 ants, each 1/4 cm — 16 small steps 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.

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

Fun with Relations
Q1If the only brother of your father’s sister had a child, what would be the child’s relationship with you?
Answer

The child is you yourself — or your own brother or sister. Your father’s sister (your bua) has only one brother, and that is your father. Your father’s child is you or your sibling.

Father’s sister (your bua) Your father You (or your brother/sister) her only brother his child
Reading a relationship puzzle is like reading a fraction: take it one step at a time.

Chapter 2 of 15 – Maths

Also for This Chapter

NCERT Solutions Class 5 Maths Chapter 2 Fractions – Overview

ClassClass 5
SubjectMaths
Chapter2 – Fractions
Textbook pages17 – 31
Questions solved55
Session2027
FormatFull answers on this page + PDF

NCERT Solutions Class 5 Maths Chapter 2 – FAQs

Where can I download NCERT Solutions Class 5 Maths Chapter 2 Fractions PDF?

Read every answer on this page, or download the free PDF from the table at the top.

Is this for the 2027 session?

Yes, it follows the latest NCERT Class 5 Maths book for 2027.

How many questions are solved in NCERT Class 5 Maths Chapter 2?

All 55 questions of the chapter (textbook pages 17 – 31) – the in-text questions, activities and the end-of-chapter exercises.

How should I use these solutions?

Read the chapter in the NCERT book first, attempt the questions yourself, then check your answers here.

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