NCERT Solutions Class 6 Maths Chapter 7: Fractions

Answers to every “Figure it Out” question and puzzle in Chapter 7, Fractions, of Ganita Prakash (Reprint 2026-27), with the in-text questions that go with them. The page numbers match the book. Short notes: Chapter 7 notes.

Figure it Out: fractional units (pages 152–153)

1. Three guavas of about the same size weigh 1 kg, so each weighs about 1/3 kg (1 ÷ 3).
2. 1 kg of rice in 4 equal packets: each packet is 1/4 kg.
3. 3 glasses of juice shared equally by 4 friends: each drinks 3 ÷ 4 = 3/4 glass.
4. The fish weigh 1/2 kg and 1/4 kg. Since 1/2 = 2/4, together they weigh 2/4 + 1/4 = 3/4 kg.
5. From the smallest to the biggest: quarter (1/4), half (1/2), three quarters (3/4), one and a quarter (1 1/4), one and a half (1 1/2), two and a half (2 1/2).

For the activity on fraction words: in Hindi, for example, people say paav (1/4), aadha (1/2), paune or teen paav (3/4), sava (1 1/4), dedh (1 1/2) and dhai (2 1/2). Collect the words your own family uses.

Pieces of a chikki (pages 154–155)

Are the 1/6 pieces of different shapes the same size? Yes. Each piece is one of 6 equal parts of the same chikki, so each has the same amount of chikki, whatever its shape.

Figure it Out (page 155). The whole chikki is a grid of 6 × 4 = 24 small squares. Count the squares in each piece (a triangle is half of the rectangle around it):

Piece	Small squares	Fraction of the chikki
a. rectangle 1 × 2	2	2/24 = 1/12
b. triangle, half of 3 × 4	6	6/24 = 1/4
c. triangle, half of 3 × 2	3	3/24 = 1/8
d. strip 1 × 4	4	4/24 = 1/6
e. L-shape	3	3/24 = 1/8
f. triangle, half of 2 × 4	4	4/24 = 1/6
g. one square	1	1/24
h. triangle, half of 1 × 2	1	1/24

Folding a strip into eighths (page 157)

2 times 1/8 = 2/8, 4 times 1/8 = 4/8, 6 times 1/8 = 6/8, and 8 times 1/8 = 8/8 = 1. Comparing with the quarter strip: 2/8 = 1/4, 4/8 = 2/4 and 6/8 = 3/4.

Figure it Out: measuring with fractional units (page 158)

1. Two more steps of the table of 1/2: 6 times 1/2 = 6/2 = 3, and 7 times 1/2 = 7/2 = 3 1/2.
2. Table of 1/4: 1/4 = 1 time a quarter; 1/4 + 1/4 = 2/4; 1/4 + 1/4 + 1/4 = 3/4; four quarters = 4/4 = 1; five quarters = 5/4; and so on.
3. Roll the strip into 3 equal layers, moving the folds until the layers match exactly, and press: each part is 1/3. Fold this folded strip in half once more and you get 6 equal parts, each 1/6.
4. a. 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5/4 = 1 1/4 roti (one whole roti and a quarter). b. Nine quarters: 9/4 = 2 1/4 rotis.
5. Count the equal parts of each circle: 1/3 goes with the circle cut into 3 parts, 1/5 with the one in 5 parts, 1/8 with the one in 8 parts, and 1/6 with the one in 6 parts.

Lengths on the number line (page 159)

1. 1 unit is cut into 3 equal parts and the blue line covers 2 of them: 2/3.
2. 1 unit is cut into 5 equal parts. The shorter blue line is 2/5 and the longer one is 4/5.
3. With 8 equal parts the marks are 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 and 8/8 = 1.

Figure it Out: the number line (page 160)

1. Divide 0 to 1 into 10 equal parts. 1/10 is the first mark and 3/10 the third. Since 4/5 = 8/10, 4/5 is the eighth mark (or divide 0 to 1 into 5 parts and take 4).
2. Any five fractions will do, for example 1/2, 1/4, 2/3, 5/6 and 7/8. For each, cut 0 to 1 into as many equal parts as the denominator and count as many parts as the numerator.
3. Endlessly many. Between any two fractions there is always another, for example the one halfway between them, so they never run out.
4. The black line covers 3 halves: 3/2 (= 1 1/2).
5. The space from 1 to 2 is also cut into fifths, so the black lines are 6/5, 7/5, 8/5 and 9/5 long, from the shortest to the longest.

Figure it Out: wholes in a fraction (page 162)

1. 7/2 = 2/2 + 2/2 + 2/2 + 1/2, so it has 3 whole units (7/2 = 3 1/2).
2. 4/3 = 3/3 + 1/3 has 1 whole unit; 7/3 = 3/3 + 3/3 + 1/3 has 2 whole units.

Figure it Out: mixed fractions (page 162)

1. a. 8/3 = 2 2/3: 2 wholes. b. 11/5 = 2 1/5: 2 wholes. c. 9/4 = 2 1/4: 2 wholes.
2. Almost all. When the numerator is a multiple of the denominator, the fraction is a whole number, like 8/4 = 2, and there is no fractional part left to write. Every other fraction greater than 1 can be written as a mixed fraction.
3. a. 9/2 = 4 1/2 b. 9/5 = 1 4/5 c. 21/19 = 1 2/19 d. 47/9 = 5 2/9 e. 12/11 = 1 1/11 f. 19/6 = 3 1/6

Figure it Out: mixed fractions to fractions (page 163)

Count the fractional units in the whole part and add the rest:

• a. 3 1/4 = 12/4 + 1/4 = 13/4
• b. 7 2/3 = 21/3 + 2/3 = 23/3
• c. 9 4/9 = 81/9 + 4/9 = 85/9
• d. 3 1/6 = 18/6 + 1/6 = 19/6
• e. 2 3/11 = 22/11 + 3/11 = 25/11
• f. 3 9/10 = 30/10 + 9/10 = 39/10

The fraction wall (page 164)

1. Yes, 1/2 = 3/6: they end at the same place on the wall.
2. Yes. 1/3 = 2/6, so two thirds equal four sixths: 2/3 = 4/6. They are the same length.
3. 3 pieces of 1/6 make 1/2.
4. 2 pieces of 1/6 make 1/3.

Figure it Out: equivalent fractions (page 165)

1. Yes. In 3/6, 4/8 and 5/10 the numerator is exactly half of the denominator, so each is equal to 1/2. On the fraction wall all three end at the 1/2 line.
2. For example 1/3 (dividing both by 2) and 4/12 (multiplying both by 2). 3/9 also works.
3. 4/6 = 2/3 = 6/9 = 8/12 = 10/15 = 12/18 = …

Figure it Out: sharing rotis and cakes (page 166)

1. Cut each roti into 4 quarters. The 12 quarters give each child 3 of them: 3/4 roti. Division fact: 3 ÷ 4 = 3/4. Addition fact: 3 = 3/4 + 3/4 + 3/4 + 3/4. Multiplication fact: 3 = 4 × 3/4.
2. Each child gets 2/4 = 1/2 roti. Division fact: 2 ÷ 4 = 1/2. Addition fact: 2 = 1/2 + 1/2 + 1/2 + 1/2. Multiplication fact: 2 = 4 × 1/2.
3. Anil gets 2 ÷ 5 = 2/5 cake. For 10 children to get the same share you need 4 cakes, because 4/10 = 2/5. Put the two groups together and 6 cakes are shared by 15 children: 6/15 = 2/5, the same share again.

Equal shares (page 168)

2 rotis among 3, 4 among 6, 6 among 9: every child gets the same, 2/3, because 4/6 and 6/9 both simplify to 2/3. In each pair, the numerator and the denominator of 2/3 have been multiplied by the same number (2 or 3).

Figure it Out (page 168).

• a. 5/4 = 10/8: 10 glasses shared by 8 friends.
• b. 4/3 = 12/9: 12 kg in 9 bags.
• c. 7/5 = 14/10: 14 rotis shared by 10 children (21 rotis by 15 children also works).

Which group gets more? (pages 169–170)

More units, same number of children: each child’s share grows. That is why 1/5 < 2/5 and 3/7 < 4/7, and since 1/2 = 4/8, also 1/2 < 5/8.

1. Group 1 gets 3/4 glass each and Group 2 gets 7/10. With the denominator 20: 3/4 = 15/20 and 7/10 = 14/20, so each child in Group 1 gets more.
2. 4/7 against 5/7: each child in Group 2 gets more.

The second pair was easier to compare, because the number of children, the denominator, is the same.

Same fractional units for pairs (page 172)

Using the smallest common denominator:

• a. 7/2 and 3/5 → 35/10 and 6/10
• b. 8/3 and 5/6 → 16/6 and 5/6
• c. 3/4 and 3/5 → 15/20 and 12/20
• d. 6/7 and 8/5 → 30/35 and 56/35
• e. 9/4 and 5/2 → 9/4 and 10/4
• f. 1/10 and 2/9 → 9/90 and 20/90
• g. 8/3 and 11/4 → 32/12 and 33/12
• h. 13/6 and 1/9 → 39/18 and 2/18

Any common multiple works; for a., 70/20 and 12/20 is also correct.

Figure it Out: lowest terms (page 173)

• a. 17/51: 51 = 3 × 17, so divide both by 17: 1/3.
• b. 64/144: the HCF is 16: 4/9.
• c. 126/147: 126 = 6 × 21 and 147 = 7 × 21, so divide by 21: 6/7.
• d. 525/112: both are multiples of 7 (525 = 7 × 75, 112 = 7 × 16): 75/16.

Figure it Out: comparing fractions (page 174)

1. a. 8/3 = 16/6 and 5/2 = 15/6, so 8/3 > 5/2. b. 4/9 = 28/63 and 3/7 = 27/63, so 4/9 > 3/7. c. 7/10 = 49/70 and 9/14 = 45/70, so 7/10 > 9/14. d. Same denominator: 12/5 > 8/5. e. 5/2 = 10/4, so 9/4 < 5/2.
2. a. With the denominator 30: 7/10 = 21/30, 11/15 = 22/30, 2/5 = 12/30. Ascending: 2/5 < 7/10 < 11/15. b. With the denominator 24: 19/24, 5/6 = 20/24, 7/12 = 14/24. Ascending: 7/12 < 19/24 < 5/6.
3. a. With the denominator 32: 25/16 = 50/32, 7/8 = 28/32, 13/4 = 104/32, 17/32. Descending: 13/4 > 25/16 > 7/8 > 17/32. b. With the denominator 60: 3/4 = 45/60, 12/5 = 144/60, 7/12 = 35/60, 5/4 = 75/60. Descending: 12/5 > 5/4 > 3/4 > 7/12.

Adding on a number line (pages 175–177)

Meena and her brother ate 3/4 of the chikki, so 1/4 is left. On a number line, 4/7 + 6/7 means 4 hops of 1/7 and then 6 more: 10 hops end at 10/7 = 1 3/7, the same as adding the numerators.

Figure it Out: adding fractions (page 179)

1. Using Brahmagupta’s method:
   • a. 2/7 + 5/7 + 6/7 = 13/7 = 1 6/7
   • b. 3/4 + 1/3 = 9/12 + 4/12 = 13/12 = 1 1/12
   • c. 2/3 + 5/6 = 4/6 + 5/6 = 9/6 = 3/2 = 1 1/2
   • d. 2/3 + 2/7 = 14/21 + 6/21 = 20/21
   • e. 3/4 + 1/3 + 1/5 = 45/60 + 20/60 + 12/60 = 77/60 = 1 17/60
   • f. 2/3 + 4/5 = 10/15 + 12/15 = 22/15 = 1 7/15
   • g. 4/5 + 2/3 = 12/15 + 10/15 = 22/15 (the same as f., in the other order)
   • h. 3/5 + 5/8 = 24/40 + 25/40 = 49/40 = 1 9/40
   • i. 9/2 + 5/4 = 18/4 + 5/4 = 23/4 = 5 3/4
   • j. 8/3 + 2/7 = 56/21 + 6/21 = 62/21 = 2 20/21
   • k. 3/4 + 1/3 + 1/5 = 77/60 (the same sum as e.)
   • l. 2/3 + 4/5 + 3/7 = 70/105 + 84/105 + 45/105 = 199/105 = 1 94/105
   • m. 9/2 + 5/4 + 7/6 = 54/12 + 15/12 + 14/12 = 83/12 = 6 11/12
2. 2/3 + 3/4 = 8/12 + 9/12 = 17/12 = 1 5/12 litres of green paint.
3. 2/5 + 3/4 = 8/20 + 15/20 = 23/20 = 1 3/20 m. That is more than 1 m, so yes, the lace is enough, with 3/20 m to spare.

Figure it Out: subtracting with the same denominator (page 181)

1. 5/8 − 3/8 = 2/8 = 1/4
2. 7/9 − 5/9 = 2/9
3. 10/27 − 1/27 = 9/27 = 1/3

On a number line, 6/7 − 4/7 means starting at 6/7 and going back 4 hops of 1/7, which ends at 2/7. In the example 3/4 − 2/3, we multiply 3/4 by 3/3 and 2/3 by 4/4 so that both get the denominator 12, a common multiple of 4 and 3.

Figure it Out: subtracting with different denominators (page 182)

1. a. 8/15 − 3/15 = 5/15 = 1/3 b. 2/5 − 4/15 = 6/15 − 4/15 = 2/15 c. 5/6 − 4/9 = 15/18 − 8/18 = 7/18 d. 2/3 − 1/2 = 4/6 − 3/6 = 1/6
2. a. 10/3 − 13/4 = 40/12 − 39/12 = 1/12 b. 23/3 − 18/5 = 115/15 − 54/15 = 61/15 = 4 1/15 c. 45/7 − 29/7 = 16/7 = 2 2/7
3. a. Jaya walks 7/10 − 1/2 = 7/10 − 5/10 = 2/10 = 1/5 km. b. 10/3 = 40/12 and 13/4 = 39/12, so Namit takes less time, by 1/12 minute.

Puzzle: different fractional units that add up to 1 (pages 184–185)

1. Three different fractional units: 1/2 + 1/3 + 1/6 = 1. It is the only way (changing the order does not count).
2. Four different fractional units: there are exactly six ways.
   • 1/2 + 1/3 + 1/7 + 1/42
   • 1/2 + 1/3 + 1/8 + 1/24
   • 1/2 + 1/3 + 1/9 + 1/18
   • 1/2 + 1/3 + 1/10 + 1/15
   • 1/2 + 1/4 + 1/5 + 1/20
   • 1/2 + 1/4 + 1/6 + 1/12

Why only these? The biggest fraction must be 1/2, because even 1/3 + 1/4 + 1/5 + 1/6 is less than 1. Then the other three must make 1/2, which forces the second to be 1/3 or 1/4, and the last two to make 1/6 or 1/4. Check one: 1/2 + 1/4 + 1/6 + 1/12 = 6/12 + 3/12 + 2/12 + 1/12 = 12/12 = 1.