NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 7 – Fractions

NCERT Solutions for Class 6 Maths Chapter 7 – Fractions explain the "Fractions" chapter of the Ganita Prakash book in plain, simple language. A fraction is what we use when one whole thing is shared into equal parts. This chapter starts with simple sharing — three guavas weighing 1 kg together, or three rotis shared among four children — and builds from there.

Students learn to write fractions from pictures, mark them on a number line, find how many whole units are in an improper fraction, change mixed numbers into fractions, and use a fraction wall to spot equivalent fractions. The chapter also connects fractions to division, addition and multiplication facts. These solutions are useful for students starting the chapter, for parents helping at home, and for teachers preparing class work. A free printable PDF of these solutions is also available for download.

NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 7 – Fractions

Fractions (New NCERT)
Medium
Q.
Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh ____kg.
Fractions (New NCERT)
Medium
Q.
​Write the following fractions in descending order.
(a) 2516,78,134,1732\frac{25}{16}, \frac{7}{8}, \frac{13}{4}, \frac{17}{32}​​
(b) 34,125,712,54\frac{3}{4}, \frac{12}{5}, \frac{7}{12}, \frac{5}{4}​​
Fractions (New NCERT)
Medium
Q.
46 \frac{4}{6} = ___________ = ___________ = ___________ 
​(Write as many as you can)​
Fractions (New NCERT)
Medium
Q.
​Answer the following questions after looking at the fraction wall:
​Are the lengths 12\frac12 and 36\frac36 equal?​
Fractions (New NCERT)
Medium
Q.
​Answer the following questions after looking at the fraction wall:
​Are  23 \frac{2}{3} and 46 \frac{4}{6} equivalent fractions? Why?​
Fractions (New NCERT)
Medium
Q.
​Answer the following questions after looking at the fraction wall:

​How many pieces of length 16\frac16​ will make a length of 12\frac12​?​

Fractions (New NCERT)
Medium
Q.
​Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.
Fractions (New NCERT)
Medium
Q.
​Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?​
Fractions (New NCERT)
Medium
Q.
​Find the missing numbers:
(a) 5 glasses of juice shared equally among 4 friends is the same as ____________ glasses of juice shared equally among 8 friends. So, 54=?8\frac{5}{4}=\frac{?}{8}​
(b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in ____________ bags. So, 43=12?.\frac{4}{3}=\frac{12}{?} .​​
(c) 7 rods divided among 5 children is the same as rods divided among children. So, 75\frac75​ = ____________​
Fractions (New NCERT)
Medium
Q.
​Express the following fractions in lowest terms:
(a) 1751\frac{17}{51}​​
(b) 64144\frac{64}{144}​​
(c) 126147\frac{126}{147}​​
(d) 525112\frac{525}{112}​​
Fractions (New NCERT)
Medium
Q.
​Rahim mixes 23\frac{2}{3}​ liters of yellow paint with 34\frac{3}{4}​ liters of blue paint to make green paint What is the volume of green paint he has made?​​​​​
Fractions (New NCERT)
Medium
Q.
​Are36,48,510\frac{3}{6}, \frac{4}{8}, \frac{5}{10} equivalent fractions? Why?​​
Fractions (New NCERT)
Medium
Q.
​Geeta bought 25\frac25​ meter of lace and Shamim bought 34\frac34​ meter of the same lace to put a complete border on a table cloth whose perimeter is 1 meter long. Find the total length of the lace they both have bought. Will the lace be sufficient to cover the whole border?​
Fractions (New NCERT)
Medium
Q.
​58−38\frac{5}{8}-\frac{3}{8}​​
Fractions (New NCERT)
Medium
Q.
​79−59\frac{7}{9}-\frac{5}{9}​​
Fractions (New NCERT)
Medium
Q.
​Carry out the following subtractions using Brahmagupta’s method:
(a) 815−315 \frac{8}{15}-\frac{3}{15}​​
(b) 25−415\frac{2}{5}-\frac{4}{15}​​
(c) 56−49\frac{5}{6}-\frac{4}{9}​​
(d) 23−12\frac{2}{3}-\frac{1}{2}​​
Fractions (New NCERT)
Medium
Q.
​Subtract as indicated:
​(a) 134  from 103\rm { (a) }~ \frac{13}{4} \ {~ from ~} \frac{10}{3}

​(b) 185 from 233\rm { (b) } ~\frac{18}{5} \ { from } ~\frac{23}{3}

(c) 297  from  457 \rm(c)~\frac{29}{7} \ {~ from ~~} \frac{45}{7} ​​​
Fractions (New NCERT)
Medium
Q.
​Solve the following problems:
(a) Jaya’s school is 710\frac7{10}​ km from her home. She takes an auto for 12\frac12​ km from her home daily, and then walks the remaining distance to reach her school. How much does she walk daily to reach the school?
(b) Jeevika takes 103\frac{10}3​ minutes to take a complete round of the park and her friend Namit takes 134\frac{13}4​ minutes to do the same. Who takes less time and by how much?​
Fractions (New NCERT)
Medium
Q.
​Answer the following questions after looking at the fraction wall:

​How many pieces of length 16\frac16​ will make a length of 13 \frac{1}{3}​?​

Fractions (New NCERT)
Medium
Q.
​Three rotis are shared equally by four children, show the division in the picture and write a fraction of how much each child gets. Also, write the corresponding division facts, addition facts, and, multiplication facts.
​The fraction of roti each child gets is ___________
Division fact:
Addition fact:
Multiplication fact:
Compare your picture and answer with your classmates!​
Fractions (New NCERT)
Medium
Q.
​Write following fractions ascending order.
(a) 710,1115,25\frac{7}{10}, \frac{11}{15}, \frac{2}{5}

(b) 1924,56,712 \frac{19}{24}{,}\frac{5}{6}{,}\frac{7}{12}​​
Fractions (New NCERT)
Medium
Q.
​Write two equivalent fractions for 26\frac26.​
Fractions (New NCERT)
Medium
Q.
​Write the following mixed numbers as fractions
(a) 314\frac14​​​
(b) 723\frac23​​
(c) 949\frac49​​
(d) 316\frac16​​
(e) 2311\frac3{11}​​
(f) 3910\frac9{10}​​
Fractions (New NCERT)
Medium
Q.
​A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is _________ kg.​
Fractions (New NCERT)
Medium
Q.
​Write five more fractions of your choice and mark them on the number line.​
Fractions (New NCERT)
Medium
Q.
​Four friends ordered 3 glasses of sugarcane juice and shared it equally. Each one drank ____________ glass of sugarcane juice.​
Fractions (New NCERT)
Medium
Q.
The big fish weighs  12\ \frac{1}{2}​. The small one weighs  14\ \frac{1}{4}. Together they weigh ____ kg.
Fractions (New NCERT)
Medium
Q.
​Arrange these fraction words in order of size from the smallest to the biggest in the empty box below: One and a half, three quarters, one and a quarter, half, quarter, two and a half​
Fractions (New NCERT)
Medium
Q.
​The figure below shows different fractional units of a whole chikki. How much of a whole chikki is each piece?

Fractions (New NCERT)
Medium
Q.
a) Continue this table of  12 \ \frac{1}{2}\  21​ ​ for 2 more steps.​
b) ​Can you create a similar table for 14 \frac{1}{4}​​ ?​​
Fractions (New NCERT)
Medium
Q.
Make 13\frac{1}{3}​  using a paper strip. Can you use this to also make ​16\frac{1}{6}?​
Fractions (New NCERT)
Medium
Q.
​Draw a picture and write an addition statement as above to show:
​(a) 5 times 14\frac{1}{4}​ of a roti
(b) 9 times 14\frac{1}{4}​ of a roti​
Fractions (New NCERT)
Medium
Q.
​Match each fractional unit with the correct picture:
​​
Fractions (New NCERT)
Medium
Q.
​On a number line, draw lines of length ​110,310,\frac{1}{10}{,}\frac{3}{10}{,}  and 45\frac{4}{5}​​
Fractions (New NCERT)
Medium
Q.
​How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.​
Fractions (New NCERT)
Medium
Q.
​Write the following fractions as mixed fractions (e.g. ​92\frac92=412\frac12)
(a) 92\frac92

(b) ​95\frac95

(c) ​2119\frac{21}{19}

(d) 479\frac{47}9

(e) ​1211\frac{12}{11}

(f) 196\frac{19}6

​
Fractions (New NCERT)
Medium
Q.
What is the length of the blue line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is 12.\frac{1}{2} . So, the blue line is 12\frac{1}{2}​ units long. Write the fraction that gives the length of the black line in the box.

Fractions (New NCERT)
Medium
Q.
​Write the fraction that gives the lengths of the black lines in the respective boxes.
Fractions (New NCERT)
Medium
Q.
Here, the fractional unit is dividing a length of 1 unit into three equal parts. Write the fraction that gives the length of the blue line in the box or in your notebook.
Fractions (New NCERT)
Medium
Q.
Here, a unit is divided into 5 equal parts. Write the fraction that gives the length of the blue lines in the respective boxes or in your notebook.
Fractions (New NCERT)
Medium
Q.
​Now, a unit is divided into 8 equal parts. Write the appropriate fractions in your notebook
 Solution: Here number line OH is divided into 8 equal parts OA, AB, BC, CD, DE, EF, FG and GH.
Fractions (New NCERT)
Medium
Q.
​How many whole units are there in 72\frac{7}{2}​?​
Fractions (New NCERT)
Medium
Q.
​How many whole units are there in 43\frac{4}{3}​ and in 73\frac{7}{3}​?​
Fractions (New NCERT)
Medium
Q.
​Figure out the number of whole units in each of the following fractions:
​(a) 83\frac 83​
(b) 115\frac {11}5​​
(c) ​94\frac94​​
Fractions (New NCERT)
Medium
Q.
​Can all fractions greater than 1 be written as such mixed numbers?​
Fractions (New NCERT)
Medium
Q.
​1027−127 \frac{10}{27}-\frac{1}{27}​​

NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 7 – Fractions

Class 6 Maths Chapter 7 Fractions Solutions

Figure it Out (Page 153)

Q1. Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh ____ kg.

Answer:
Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh 1/3 kg.

Q2. A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ________ kg.

Answer:
A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is 1/4 kg.

Q3. Four friends ordered 3 glasses of sugarcane juice and shared it equally. Each one drank _______ glass of sugarcane juice.

Answer:
As total quantity is 3 which is to be divided into four equal parts. So, the required fraction is 3/4.

Q4. The big fish weighs 1/2 kg. The small one weighs 1/4 kg. Together they weigh ____ kg.

Answer:

Together they weigh = 1/2 + 1/4 = 3/4 kg

Q5. Arrange these fraction words in order of size from the smallest to the biggest in the empty box below: One and a half, three quarters, one and a quarter, half, quarter, two and a half.

Answer:


∴ The fractions from smallest to the biggest are as follows: quarter, half, three quarters, one and a quarter, one and a half, two and a half.

Q6. The figure below shows different fractional units of a whole chikki. How much of a whole chikki is each piece?

Answer:

(a)

fractional units

Total no. of pieces formed of given size = 12
Required fraction = 1/12

(b)

fraction

Total no. of pieces formed of given size = 4
Required fraction = 1/4

(c)

angle

Total no. of pieces formed of given size = 8
Required fraction = 1/8

(d)

pieces formed of given size

Total no. of pieces formed of given size = 6
Required fraction = 1/6

(e)

Total no. of pieces formed of given size

Total no. of pieces formed of given size = 8
Required fraction = 1/8

(f)

Fraction

Total no. of pieces formed of given size = 8
Required fraction = 1/8

(g)

Total no. of pieces

Total no. of pieces formed of given size = 24
Required fraction = 1/24

(h)

Total no. of pieces formed of given size

Total no. of pieces formed of given size = 12
Required fraction = 1/12

Figure it Out (Page No. 158)

Q7. (a) Continue this table of 1/2 for 2 more steps. (b) Can you create a similar table for 1/4?

[Image: Q7_question_pictograph.png]

Answer:

(a)

Fractional Units

1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 6 times half
1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 7 times half

(b) Yes. A similar table can be made for 1/4 by adding 1/4 to itself again and again, in the same way.

Q8. Make 1/3 using a paper strip. Can you use this to also make 1/6?

Answer:
Take a strip of paper.

Fold the strip into three equal parts and then open up.

Yes, we can also make 1/6 using a paper strip by folding the above strip 6 times again.

Q9. Draw a picture and write an addition statement as above to show:
(a) 5 times 1/4 of a roti
(b) 9 times 1/4 of a roti

Answer:

(a)

5 times 1/4 of a roti
= 1/4 + 1/4 + 1/4 + 1/4 + 1/4

(b)

9 times 1/4 of a roti
= 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4

Q10. Match each fractional unit with the correct picture:

Answer:

  • 1/3 → the circle divided into 3 equal parts, with 1 part shaded
  • 1/5 → the circle divided into 5 equal parts, with 1 part shaded
  • 1/6 → the circle divided into 6 equal parts, with 1 part shaded
  • 1/8 → the circle divided into 8 equal parts, with 1 part shaded

Q11. What is the length of the blue line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is 1/2. So, the blue line is 1/2 units long. Write the fraction that gives the length of the black line in the box.

Answer:
Length of blue line is 1/2.
Length of black line is 1/2 + 1/2 + 1/2
Fraction that gives length of black line = 3/2

Q12. Here, the fractional unit is dividing a length of 1 unit into three equal parts. Write the fraction that gives the length of the blue line in the box or in your notebook.

Answer:
Here number line OR is divided into three equal parts OP, PQ and QR.
Hence length of blue line = OP + PQ = 1/3 + 1/3 = 2/3

Q13. Here, a unit is divided into 5 equal parts. Write the fraction that gives the length of the blue lines in the respective boxes or in your notebook.

Answer:
Here number line from 0 to 1 unit is divided into five equal parts.
Hence length of the first blue line from bottom = 1/5 + 1/5 = 2/5
Now, length of the second blue line from bottom = 1/5 + 1/5 + 1/5 + 1/5 = 4/5

Q14. Now, a unit is divided into 8 equal parts. Write the appropriate fractions in your notebook.

Answer:
Here number line OH is divided into 8 equal parts OA, AB, BC, CD, DE, EF, FG and GH.

Hence, OA = 1/8, OB = 2/8, OC = 3/8, OH = 8/8 = 1

Q15. On a number line, draw lines of length 1/10, 3/10 and 4/5.

Answer:

Divide the unit into 10 equal parts and point A represents 1/10.

Divide a unit into 10 equal parts and point B represents 3/10.

Divide a unit into 5 equal parts and point C represents 4/5.

Q16. Write five more fractions of your choice and mark them on the number line.

Answer:
The fractions are 3/5, 1/3, 5/7, 2/5 and 1/8.
Their number line representations are:

(a) 3/5

(b) 1/3

(c) 5/7

(d) 2/5

(e) 1/8

Q17. How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.

Answer:
There are an infinite number of fractions between 0 and 1.
Example: 3/5, 4/5, 7/10 etc.

Q18. Write the fraction that gives the lengths of the black lines in the respective boxes.

Answer:

The fractions are 6/5, 7/5, 8/5, 9/5 and 2 (or 10/5). Note that 1 can also be written as 5/5.

Q19. How many whole units are there in 7/2?

Answer:
7/2 = 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 = 3 + 1/2
So, there are 3 whole units in 7/2.

Q20. How many whole units are there in 4/3 and in 7/3?

Answer:
4/3 = 1/3 + 1/3 + 1/3 + 1/3 = 1 + 1/3
So, there is 1 whole unit in 4/3.

7/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 = 2 + 1/3
So, there are 2 whole units in 7/3.

Q21. Figure out the number of whole units in each of the following fractions:
(a) 8/3 (b) 11/5 (c) 9/4

Answer:
(a) 2
(b) 2
(c) 2

Q22. Can all fractions greater than 1 be written as such mixed numbers?

Answer:
Yes.

Q23. Write the following mixed numbers as fractions:
(a) 3¼ (b) 7⅔ (c) 9 4/9 (d) 3⅙ (e) 2 3/11 (f) 3 9/10

Answer:
(a) 3¼ = (3 × 4 + 1)/4 = 13/4
(b) 7⅔ = (7 × 3 + 2)/3 = 23/3
(c) 9 4/9 = (9 × 9 + 4)/9 = 85/9
(d) 3⅙ = (3 × 6 + 1)/6 = 19/6
(e) 2 3/11 = (2 × 11 + 3)/11 = 25/11
(f) 3 9/10 = (3 × 10 + 9)/10 = 39/10

Q24. Answer the following question after looking at the fraction wall: Are the lengths 1/2 and 3/6 equal?

Answer:
Yes, here lengths 1/2 and 3/6 = 1/2.
Lengths are equal.

Q25. Answer the following question after looking at the fraction wall: Are 2/3 and 4/6 equivalent fractions? Why?

Answer:
Yes, lengths 2/3 and 4/6 = 1/3 are equivalent fractions, as they have the same length.

Q26. Answer the following question after looking at the fraction wall: How many pieces of length 1/6 will make a length of 1/2?

Answer:
Total no. of pieces = (1/2) ÷ (1/6) = (1/2) × (6/1) = 6/2 = 3
Hence three pieces of length 1/6 will make a length of 1/2.

Q27. Answer the following question after looking at the fraction wall: How many pieces of length 1/6 will make a length of 1/3?

Answer:
Total no. of pieces = (1/3) ÷ (1/6) = (1/3) × (6/1) = 6/3 = 2
Hence two pieces of length 1/6 will make a length of 1/3.

Q28. Are 3/6, 4/8 and 5/10 equivalent fractions? Why?

Answer:
Here, simplest form of 3/6 = (3 ÷ 3)/(6 ÷ 3) = 1/2 [HCF of 3 and 6 is 3]
and simplest form of 4/8 is (4 ÷ 4)/(8 ÷ 4) = 1/2 [HCF of 4 and 8 is 4]
and simplest form of 5/10 is (5 ÷ 5)/(10 ÷ 5) = 1/2 [HCF of 5 and 10 is 5]
Hence, 3/6, 4/8 and 5/10 are equivalent fractions.

Q29. Write two equivalent fractions for 2/6.

Answer:
From the fraction wall we can choose any two fractions that denote the same length as 2/6:
2/6 = 1/3 = 3/9

Q30. Three rotis are shared equally by four children. Show the division in the picture and write a fraction of how much each child gets. Also, write the corresponding division facts, addition facts, and multiplication facts.

Answer:
One roti is shared as shown in the figure below:

The four shares must be equal to each other!
Similar distribution will be done for the second and third roti also.
So, each child will get 3/4 a piece of roti.
The division fact is 3 ÷ 4 = 3/4
The addition fact is 3 = 3/4 + 3/4 + 3/4 + 3/4
The multiplication fact is 3 = 4 × 3/4

Q31. Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.

Answer:
One roti is shared as shown in the figure below:

The four shares must be equal to each other!
A similar distribution will be done for the second roti also.
So, each child will get 1/4 part from a roti.
So, the total fraction of roti received by each child from 2 rotis = 2/4 = 1/2
The division fact is 2 ÷ 4 = 2/4
The addition fact is 2 = 2/4 + 2/4 + 2/4 + 2/4
The multiplication fact is 2 = 4 × 2/4

Q32. Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?

Answer:
Anil would get 2/5 part of the cake.

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