NCERT Solutions for Class 6 Maths Chapter 7 Fractions - Ganita Prakash
Chapter 7 Fractions NCERT Solutions for Class 6 Maths is available here which will be helpful in covering the entire syllabus and solving the difficult problems given in exercise. You can also Download PDF of Class 6 Maths Chapter 7 Fractions NCERT Solutions which will prove useful guide in making a student confident. The chapter is taken from the new NCERT Mathematics textbook, Ganita Prakash.
These NCERT Solutions for Class 6 will develop you understanding of the chapter and help in gaining good marks in the examinations. We have also provided Chapter 7 Fractions Revision Notes which will help you in completing your homework on time. These NCERT Solutions will help an individual to increase concentration and you can solve questions of supplementary books easily. Students can also check Extra Questions Answer for Fractions Class 6 Maths to prepare for their examination completely.
NCERT Solutions for Chapter 7 Fractions Class 6 Maths
Page 152&153
Figure it Out
Fill in the blanks with fractions.
Question 1. Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh _____kg.
Answer
1/3
Question 2. A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ____ kg.
Answer
1/4
Question 3. Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank ____ glass of sugarcane juice.
Answer
3/4
Question 4. The big fish weighs 1/2 kg. The small one weighs 1/4 kg. Together they weigh ____ kg.
Answer
3/4
Question 5. 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
One and a half means = 1 + 1/2 = 3/2, Three quarters means = 3/4, One and a quarter means = 1 + 1/4 = 5/4, Half means = 1/2, Quarter means = 1/4, Two and a half means = 2 + 1/2 = 5/2
Arrange these fractions from smallest to largest = 1/4 < 1/2 < 3/4 < 5/4 < 3/2 < 5/2.
So, let’s arrange these fraction words in order of size from smallest to larges,
Quarter < Half < Three quarters < One and a quarter < One and a half < Two and a half
Page 155
Question. The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece?
Answer
Page 158
Question 1. Continue this table of 1/2 for 2 more steps.
Answer
Question 2. Can you create a similar table for 1/4?
Answer
Question 3. Make 1/3 using a paper strip. Can you use this to also make 1/6?
Answer
Yes, when you divide each part of this 1/3 it is 1/6.
Question 4. 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
(b) 9 times 1/4 of a roti
Question 5. Match each fractional unit with the correct picture:
Answer
Page 159
Now, can you find the lengths of the various blue lines shown below? Fill in the boxes as well.
Question 1. 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 pink line = OP + PQ = 1/3 + 1/3 = 2/3
Question 2. 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 OT = 1 unit is divided into five equal parts OP, PQ, QR, RS and ST.
Hence length of pink line OQ = OP + PQ = 1/5 + 1/5 = 2/5
Now, length of pink line OS = OP + PQ + QR + RS = 1/5 + 1/5 + 1/5 + 1/5 = 4/5
Hence, OQ = 2/5 or OS = 4/5
Question 3. 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.
Also, OA = 1/8, OB = 2/8, OC = 3/8, OH = 8/8 = 1
Page 160
Question 1. On a number line, draw lines of lengths 1/10, 3/10, and 4/5.
Answer
Question 2. Write five more fractions of your choice and mark them on the number line.
Answer
Five fractions are = 1/5, 2/5, 5/10, 7/10 and 9/10
Question 3. 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, 7/10, 3/4, 1/2etc.
Question 4. 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 black line = 1/2 + 1/2 + 1/2 = 3/2
Question 5. Write the fraction that gives the lengths of the black lines in the respective boxes.
Answer
Page 162
Question 1. How many whole units are there in 7/2?
Answer
There are 3 whole units in 7/2.
Question 2. How many whole units are there in 4/3 and in 7/3?
Answer
(i) There are 1 whole unit in 4/3.
(ii) There are 2 whole units in 7/3.
Figure it Out
Question 1. Figure out the number of whole units in each of the following fractions:
(a) 8/3
(b) 11/5
(c) 9/4
Answer
(a) 8/3
There are 2 whole units in 8/3.
(b) 11/5
There are 2 whole units in 11/5.
(c) 9/4
There are 2 whole units in 9/4.
Question 2. Can all fractions greater than 1 be written as such mixed numbers?
Answer
Yes, all fractions greater than 1 can be written as mixed numbers. A mixed number consists of a whole number and a proper fraction (fraction less than 1).
Question 3. Write the following fractions as mixed fractions (e.g., 
)
(a) 9/2
(b) 9/5
(c) 21/19
(d) 47/9
(e) 12/11
(f) 19/6
Answer
(a) 9/2
(b) 9/5
(c) 21/19
(d) 47/9
(e) 12/11
(f) 19/6
Page 163
Question. Write the following mixed numbers as fractions:
Page 164
Answer the following questions after looking at the fraction wall.
Question 1. Are the lengths 1/2 and 3/6 equal?
Answer
Yes, here lengths 1/2 and 3/6 = 1/2
Lengths are equal.
Question 2. Are 2/3 and 4/6 equivalent fractions? Why?
Answer
Yes, lengths 2/3 and 4/6 = 1/3 are equivalent fraction, as they have same length.
Question 3. How many pieces of length 1/6 will make a length of 1/2?
Answer
Total no. of pieces = 
Hence three pieces of length 1/6 will make a length of 1/2.
Question 4. How many pieces of length 1/6 will make a length of 1/3?
Answer
Total no. of pieces = 
Hence two pieces of length 1/6 will make a length of 1/3.
Page 165
Figure it Out
Question 1. Are 3/6, 4/8, 5/10 equivalent fractions? Why?
Answer
Yes, 3/6, 4/8, 5/10 are equivalent fractions because they all simplify to 1/2.
Question 2. Write two equivalent fractions for 2/6.
Answer
Therefore, 4/12, 6/18 are two equivalent fractions for 2/6.
Question 3. 
(Write as many as you can)
Answer
Page 166
Figure it Out
Question 1. Three rotis are shared equally by four children. Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts and multiplication facts.
Fraction of roti each child gets is _______ .
Division fact:
Addition fact:
Multiplication fact:
Compare your picture and answers with your classmates!
Answer
As 3 rotis are divided equally among 4 children:
(i) Each roti is divided into 4 equal parts.
(ii) Each child receives 1/4 share from each roti.
Fraction of roti each child gets = 1/4+1/4+1/4=3/4
Division fact:
3 wholes divided in 4 parts
3 ÷ 4 = 3/4
Addition fact:
Four times 3/4 added gives 3 wholes
= 3/4 + 3/4 + 3/4 + 3/4
= 12/4 = 3
Multiplication fact:
4 parts of 3/4 make 3 wholes
4 × 3/4 = 3
Question 2. 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
As 2 rotis have to be shared equally by 4 children we divide each roti in 4 parts and give
(a) 1 part of each roti to each child as shown below:
(b) 2 parts to each child as shown below
Division fact:
2 wholes divide in 4 parts
2 ÷ 4 or 2/4 = 1/2
Addition fact:
2/4 + 2/4 + 2/4 + 2/4 = 8/4 = 2
Multiplication fact:
4 × 2/4 = 2
Q3: Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?
Answer
Anil is in a group where 2 cakes were divided equally among 5 children.
Each cake gets divided into 5 parts and Anil gets one part from each cake i.e. 1/5 + 1/5 = 2/5
Page 168
Figure it Out
Question. 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.
Here, the amount of juice each friend gets when 5 glasses are shared among 4 friends = number of glasses number of friends = 5/4
Now to determine how many glasses of juice would be needed to give each of the 8 friends the same amount = 8 × 5/4 = 10 glasses
So, 10 glasses of juice shared equally among 8 friends is the same as 5 glasses of juice shared equally among 4 friends.
∴ 5/4 = 10/8
(b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in ______ bags.
So, 
Answer
Let x is the number of bags for 12 kg of potatoes, where each bag has the same amount of potatoes then
12 kg/x bags = 4/3 kg per bag
⇒ 12 × 3 = 4 × x
⇒ 36 = 4x
⇒ x = 36/4
⇒ x = 9
∴ 4/3 = 12/9
(c) 7 rods divided among 5 children is the same as rods divided among children. So, 7/5 = ______
So, 
Answer
Dividing 7 rotis among 4 children gives 7 each child = 7/5 of a roti. We can find an equivalent fraction by multiplying both the numerator and the denominator by the same number. For example, multiplying both by 2.
So, 7 rotis divided among 5 children is the same as 14 rotis divided among 10 children
∴ 7/5 = 14/10
Page 172
Question. Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.
(a) 7/2 and 3/5
(b) 8/3 and 5/6
(c) 3/4 and 3/5
(d) 6/7 and 8/5
(e) 9/4 and 5/2
(f) 1/10 and 2/9
(g) 8/3 and 11/4
(h) 13/6 and 1/9
Answer
(a) 7/2 and 3/5
Here, the denominators are 2 and 5.
And least common multiple of 2 and 5 is 10.
Hence for both fractions let’s have same denominator of 10.
Now for 7/2 multiply both the numerator and the denominator by 5.
And for 3/5 multiply both the numerator and the denominator by 2, we get,
Hence, the equivalent fractions with the same denominator are:
35/10 and 6/10
(b) 8/3 and 5/6
Given fractions are 8/3 and 5/6
Here, the denominators are 3 and 6.And least common multiple of 3 and 6 is 6.
Now for 8/3 multiply both the numerator and the denominator by 2.
5/6 already have a denominator 6.
Hence, the equivalent fractions with the same denominator are:
16/6 and 5/6
(c) 3/4 and 3/5
Answer
Here, the denominators are 4 and 5.
And least common multiple of 4 and 5 is 20.
Now for 3/4 multiply both the numerator and the denominator by 5.
And for 3/5 multiply both the numerator and the denominator by 4, we get
So, the equivalent fractions with the same denominator are:
15/20 and 12/20
(d) 6/7 and 8/5
Answer
Here, the denominators are 7 and 5.
And least common multiple of 7 and 5 is 35.
Now for 6/7 multiply both the numerator and the denominator by 5.
And for 8/5 multiply both the numerator and the denominator by 7, we get
So, the equivalent fractions with the same denominator are:
30/35 and 56/35
(e) 9/4 and 5/2
Answer
Here, the denominators are 4 and 2.
And least common multiple of 4 and 2 is 4.
Now for 5/2 multiply both the numerator and the denominator by 2.
and 9/4 already have a denominator 4
So, the equivalent fractions with the same denominator are:
9/4 and 10/4
(f) 1/10 and 2/9
Answer
Here, the denominators are 10 and 9.
And least common multiple of 10 and 9 is 90.
Now for 1/10 multiply both the numerator and the denominator by 9.
And for 2 multiply both the numerator and the denominator by 10, we get
So, the equivalent fractions with the same denominator are:’
9/90 and 20/90
(g) 8/3 and 11/4
Answer
Here, the denominators are 3 and 4.
And least common multiple of 3 and 4 is 12.
Now for 8/3 multiply both the numerator and the denominator by 4.
And for 11/4 multiply both the numerator and the denominator by 3, we get
So, the equivalent fractions with the same denominator are:
32/12 and 33/12
(h) 13/6 and 1/9
Answer
Here, the denominators are 6 and 9.
And least common multiple of 6 and 9 is 18.
Now for 13/6 multiply both the numerator and the denominator by 3.
And for 1/9 multiply both the numerator and the denominator by 2, we get
So, the equivalent fractions with the same denominator are:
39/18 and 2/18
Page 173
Question 1. Express the following fractions in lowest terms:
(a) 17/51
(b) 64/144
(c) 126/147
(d) 525/112
Answer
(a) 17/51
which is the lowest term.
(b) 64/144
Here 64 and 144 are both multiples of 16. So we divide both by 16.
(c) 126/147
Here, 126/147
[∵ HCF of 126 and 147 is 7 × 3 = 21]
(d) 525/112
Here 525 and 112 are both multiples of 7, we divide both by 7.
Page 174
Figure it Out
Question 1. Compare the following fractions and justify your answers:
(a) 8/3, 5/2
(b) 4/9, 3/7
(c) 7/10, 9/14
(d) 12/5, 8/5
(e) 9/4, 5/2
Answer
(a) 8/3, 5/2
L.C.M of 3 and 2 is 6.
(b) 4/9, 3/7
Given fractions are 4/9 and 3/7.
Here LCM of denominators 9 and 7 is 63.
then multiplying and dividing 4/9 by 7 and 3/7 by 9 then
(c) 7/10, 9/14
Given fractions are 7/10 and 9/14.
Here LCM of denominators 10 and 14 is 70.
then multiplying and dividing 7/10 by 7 and 9/14 by 5 then
(d) 12/5, 8/5
Given fractions are 12/5, 8/5
Since, the denominators of both the fractions are same, then the fraction with the larger numerator is greater.
Here, 12/5 > 8/5
(e) 9/4, 5/2
Given fractions are 9/4, 5/2.
then multiplying and dividing 5/2 by 2 and
Equivalent fractions with 4 are
9/4 < 10/4
∴ 9/4 < 5/2
Question 2. Write following fractions in ascending order.
(a) 7/10, 11/15, 2/5
(b) 19/24, 5/6, 7/12
Answer
(a) 7/10, 11/15, 2/5
The given fractions are 7/10, 11/15, 2/5
Let us find LCM of denominator 10, 15, 5
∴ LCM of 10, 15 and 5 = 2 × 3 × 5 = 30
Now let us make denominator of each fractions as LCM
Hence given fractions in ascending order are: 25,710115
(b) 19/24, 5/6, 7/12
The given fractions are 19/24, 5/6, 7/12
Here LCM of 24, 6, 12 is 24.
On arranging in ascending Order, we get
14/24, 19/24, 20/24
⇒ 7/12, 19/24, 5/6
Question 3. Write the following fractions descending order.
(a) 25/16, 7/8, 13/4, 17/32
(b) 3/4, 12/5, 7/12, 5/4
Answer
(a) 25/16, 7/8, 13/4, 17/32
Let us find LCM of denominator 16, 8, 4, 32
LCM of 16, 8,4, 32 = 2 × 2 × 2 × 2 × 2 = 32
Now let us make denominator of each fractions as LCM thus
On arranging in descending order, we get
Hence given fractions in descending order are 13/4, 25/16, 7/8 and 17/32.
(b) 3/4, 12/5, 7/12, 5/4
Answer
Here LCM of 4, 5, 12, 4 is 60
Now let us make denominator of each fraction as LCM then
Hence fractions in descending order are
12/5 > 5/4 > 3/4 > 7/12
Page 179
Figure it Out
Question 1. Add the following fractions using Brahmagupta’s method:
(a) 2/7 + 5/7 + 6/7
(b) 3/4 + 1/3
(c) 2/3 + 5/6
(d) 2/3 + 2/7
(e) 3/4 + 1/3 + 1/5
(f) 2/3 + 4/5
(g) 4/5 + 2/3
(h) 3/5 + 5/8
(i) 9/2 + 5/4
(j) 8/3 + 2/7
(k) 3/4 + 1/3 + 1/5
(l) 2/3 + 4/5 + 3/7
(m) 9/2 + 5/4 + 7/6
Answer
(a) 2/7 + 5/7 + 6/7
Here,
(b) 3/4 + 1/3
∴ Equivalent fraction of 3/4 with denominators 12 is 9/12 and equivalent fraction of 1/3 with denominators 12 is 4/12
(c) 2/3 + 5/6
Now LCM of 3 and 6 is 6.
Expressing as equivalent fractions with denominators 6, we get
Expressing as equivalent fractions with denominators 21, we get
To add 2/3 + 2/7, start by finding the least common denominator (LCD) of the two fractions. The denominators are 3 and 7, and their LCD is 21.
Next, rewrite each fraction with a denominator of 21.
2/3 is equivalent to 14/21 because 2×7=14 i.e. 2 times 7 = 14.
2/7 is equivalent to 6/21, because 2×3=6 i.e. 2 times 3 = 6.
Now that the fractions have the same denominator, add them together:
The final result is 20/2
(e) 3/4 + 1/3 + 1/5
Now LCM of 4, 3, 5 is 60.
Expressing as equivalent fractions with denominators 60, we get
(f) 2/3 + 4/5
Now LCM of 3 and 5 is 15
Expressing as equivalent fractions with denominators 15, we get
(g) 4/5 + 2/3
Now LCM of 5 and 3 is 15
Thus, expressing as equivalent fractions with denominators 15, we get
(h) 3/5 + 5/8
Here LCM of 5 and 8 is 40Expressing as equivalent fractions with denominators 40, we get
(i) 9/2 + 5/4
Now LCM of 2 and 4 is 4.
Expressing as equivalent fractions with denominators 4, we get
(j) 8/3 + 2/7
Here LCM of 3 and 7 is 21Expressing as equivalent fractions with denominators 21, we get
(k) 3/4 + 1/3 + 1/5
Now LCM of 4, 3, 5 is 60Expressing as equivalent fractions with denominators 60, we get
(l) 2/3 + 4/5 + 3/7
Now LCM of 3, 5 and 7 is 105.
Expressing as equivalent fractions with denominators 105, we get
Here LCM of 2, 4, 6 is 12.
Now expressing as equivalent fractions with denominators 12, we get
Question 2. Rahim mixes 2/3 litres of yellow paint with 3/4 litres of blue paint to make green paint. What is the volume of green paint he has made?
Answer
Given quantity of yellow paint = 2/3 litres
and quality of blue paint = 3/4 litres
Volume of green paint made
= 2/3 litres + 3/4 litres
Here LCM of 3 and 4 is 12
Now expressing as equivalent fractions with denominator 12, we get
Question 3. Geeta bought 2/5 meter of lace and Shamim bought 3/4 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?
Answer
Given length of lace bought by Geeta = 2/5 meter
and length of lace bought by Shamim = 3/4 meter
Total length of lace = 2/5 + 3/4
LCM of 5 and 4 is 20
Now expressing as equivalent fractions with denominator 20, we get
Total lace required = Perimeter = 1 m
Hence total lace Geeta and Shamim have together is sufficient to cover the whole border.
Page 181
Figure it Out
Question 1. 5/8 - 3/8
Answer
Q2. 7/9 - 5/9
Answer
Q3. 10/27 - 1/27
Answer
Page 182
Figure it Out
Question 1. Carry out the following subtractions using Brahmagupta’s method:
(a) 8/15 - 3/15
(b) 2/5 - 4/15
(c) 5/6 - 4/9
(d) 2/3 - 1/2
Answer
Here LCM of 5 and 15 is 15. Fractional unit for both fractions should be 1/15
(c) Given, 5/6 - 4/9
Hence LCM of 6 and 9 is 18. Fractional unit for both fractions should be 1/18 then
(d) Given, 2/3 - 1/2
Here LCM of 3 and 2 is 6. Fractional unit for both fractions should be 1/6
Question 2. Subtract as indicated:
(a) 13/4 from 10/3
(b) 18/5 from 22/3
(c) 29/7 from 45/7
Answer
(a) Given, 10/3 - 13/4
Here, LCM of 3 and 4 is 12.Fractional unit for both fractions should be 1/12
(b) Here, 23/3 - 18/5
Now, LCM of 3 and 5 is 15.
Fractional unit = 1/15 for both fractions
Hence,
(c) Given, 45/7 - 29/7
Here fractional = 1/7 for both fractions.
Question 3. Solve the following problems:
a. Java’s school is 7/10 km from her home. She takes an auto for 1/2 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 10/3 minutes to take a complete round of the park and her 13 friend Namit takes 13/4 minutes to do the same. Who takes less time and by how much?
Answer
LCM of 10 and 2 is 10.
Hence Jaya walks 1/5 km or 200 meters to reach her school.
(b) Time taken by Jeevika to cover 1 round of park = 10/3 mm
Time taken by Namit to cover 1 round of 13 park= 13/4 min
To find who takes less time we need to compare 10/3 and 13/4
Here, LCM of 3 and 4 is 12
[Expressing fractions in fractional unit 1/12]
Hence Namit takes less time
Namit takes 1/2 of minutes less than Jeevika.