NCERT Class 6 Mathematics Chapter 7 Fractions

By Parimol Roy / NCERT Class 6 Mathematics

NCERT Class 6 Mathematics Chapter 7 Fractions Solutions in English Medium As Per CBSE New Syllabus to each chapter is provided in the list so that you can easily browse through different chapters NCERT Class 6 Mathematics Chapter 7 Fractions Notes and select need one. NCERT Class 6 Mathematics Chapter 7 Fractions Question Answers Download PDF. NCERT Class 6 Solutions for Maths in English Medium.

NCERT Class 6 Mathematics Chapter 7 Fractions

Also, you can read the NCERT book online in these sections Solutions by Expert Teachers as per Central Board of Secondary Education (CBSE) Book guidelines. NCERT Class 6 Mathematics Chapter 7 Fractions Textual Solutions are part of All Subject Solutions. Here we have given NCERT Class 6 Maths in English Medium Solutions. CBSE Class 6 Mathematics Textbook Solutions in English for All Chapters, You can practice these here.

Fractions

Chapter: 7

TEXTUAL SOLUTIONS

Figure it Out (Page No. 152 – 153)

Fill in the blanks with fractions.

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

Ans: 1/3

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

Ans: 1/4

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

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

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

Ans:

Given the weighs of big fish = 1/2 kg and the weighs of small fish = 1/4 kg

Total weight of both fish = 1/2 + 1/4 = 2 + 1/4 kg

= 3/4 kg

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.

Ans:

∴ 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.

Figure it Out (Page No. 155)

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

Ans: (a)

Total no. of pieces formed of given size = 12

Required fraction = 1/12

(b)

Total no. of pieces formed of given size = 4

Required fraction = 1/4

(c)

Total no. of pieces formed of given size = 8

Required fraction = 1/8

(d)

Total no. of pieces formed of given size = 6

Required fraction = 1/6

(e)

Total no. of pieces formed of given size = 8

Required fraction = 1/8

(f)

Total no. of pieces formed of given size = 8

Required fraction = 1/8

(g)

Total no. of pieces formed of given size = 24

Required fraction = 1/24

(h)

Total no. of pieces formed of given size = 12

Required fraction = 1/12

Figure it Out (Page No. 158)

1. Continue this table of 1/2 for 2 more steps.

Ans:

2. Can you create a similar table for 1/4?

Ans: Yes.

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

Ans: 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 6 again the above strip.

4. Draw a picture and write an addition statement as above to show:

(a) 5 times 1/4 of a roti.

Ans:

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.

Ans:

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

5. Match each fractional unit with the correct picture:

Ans:

Figure it Out (Page No. 160)

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

Ans:

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.

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

Ans: The fractions are 3/5,1/3,5/7,2/5 and 1/8.

Their number line representations are:

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

Ans: There are an infinite number of fractions between 0 and 1.

Example: 3/5,4/5,7/10 1/2 etc.

4. What is the length of the pink 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 pink line is y units long. Write the fraction that gives the length of the black line in the box.

Ans: Length of black line is 1/2;

Length of black line is 1/2 + 1/2 + 1/2

Fraction that gives length of black line = 3/2

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

Ans:

Intext Questions:

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 pink line in the box or in your notebook. (Page 159)

Ans: Here the 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

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

Ans: 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 OS = 4/5

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

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

Ans:

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

Figure it Out (Page No. 162)

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

Ans: 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.

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

Ans: 4/3 = 1/3 + 1/3 + 1/3 + 1/3 = 1 + 1/3

So, there are 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.

Figure it Out (Page No. 162)

1. Figure out the number of whole units in each of the following fractions:

(a) 8/3

(b) 11/5

Ans: (a) 2

(b) 2

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

Ans: Yes.

3. Write the following fractions as mixed fractions (e.g. 9/2 = 4 1/2)

(a) 9/2

Ans: = 4 1/2

(b) 9/5

Ans: = 1 4/5

(c) 21/19

Ans: = 1 2/19

(d) 47/9

Ans: = 5 2/9

(e) 12/11

Ans: = 1 1/11

(f) 19/6

Ans: = 3 1/6

Figure it Out (Page No. 163)

1. Write the following mixed numbers as fractions:

(a) 3 1/4

(b) 7 2/3

(d) 3 1/6

(e) 2 3/11

(f) 3 9/10

Ans:

Figure it Out (Page No. 165)

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

Ans: 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, 3/6,4/8,5/10 are equivalent fractions.

2. Write two equivalent fractions for 2/6.

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

3. 4/6 = ___________ = ___________ = ___________ = ___________________ (Write as many as you can)

Ans: Here,

Answer the following questions after looking at the fraction wall: [Page 164]

Intext Questions:

1. Are the lengths 1/2 and 3/6 equal?

Ans: Yes, here lengths 1/2 and 3/6 = 1/2

Lengths are equal.

2. Are 2/3 and 4/6 equivalent fractions? Why?

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

3. How many pieces of length 1/6 will make a length of 1/2?

Ans: Total no.of pieces:

= ½ / ⅙ = 1/2 * 6\1 = 6/2 = 3

Hence three pieces of length 1//6 will make a length of 1/2

4. How many pieces of length 1/6 will make a length of 1/3?

Ans: Total no. of pieces:

= ⅓ / ⅙ = ⅓ * 6/1 = 6/3 = 2

Hence two pieces of length 1/6 will make a length of 1/3.

Figure it Out (Page No. 166)

1. 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!

Ans: 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

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.

Ans: 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 rod.

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 = 2/4 + 2/4 + 2/4 + 2/4

The multiplication fact is 2 = 4 × 2/4

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

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

Figure it Out (Page No. 168 – 169)

1. 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, 5/4 = ?/8.

(b) 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in ____________ bags. So, 4/3 = 12/?.

Ans: (a) 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) Here 4 kg of potatoes divided equally in 3 bags then amount of potatoes per bag = 4 kg/3 bags = 4/3 kg per bag

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) 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.

7 × 2/5 × 2 = 14/10

So, 7 rotis divided among 5 children is the same as 14 rotis divided among 10 children

∴ 7/5 = 14/10

Intext Questions:

1. Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. (Page 172)

(a) 7/2 and 3/5

Ans: Given fractions are 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.

7/2 = 7 × 5/2 × 5 = 35/10

And for 3/5 multiply both the numerator and the denominator by 2, we get,

3 × 2/5 × 2 = 6/10

Hence, the equivalent fractions with the same denominator are:

35/10 and 6/10

(b) 8/3 and 5/6

Ans: Given fractions are 8 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.

8/3 = 8 × 2/3 × 2 = 16/6

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

Ans: Given fractions are 3/4 and 3/5

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.

3/4 = 3 × 5/4 × 5 = 15/20

And for 3/5 multiply both the numerator and the denominator by 4, we get

3/5 = 3 × 4/5 × 4 = 12/20

So, the equivalent fractions with the same denominator are:

15/20 and 12/20

(d) 6/7 and 8/5

Ans: Given fractions are 6/7 and 8/5

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.

6/7 = 6 × 5/7 × 5 = 30/35

And for 8/5 multiply both the numerator and the denominator by 7, we get

8/5 = 8 × 7/5 × 7 = 56/35

So, the equivalent fractions with the same denominator are:

30/35 and 56/35

(e) 9/4 and 5/2

Ans: Given fractions are 9/4 and 5/2

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.

5/2 = 5 × 2/2 × 2 = 10/4

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

Ans: Given fractions are and 1/10 and 2/9

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.

1/10 = 1 × 9/10 × 9 = 9/90

And for 2 multiply both the numerator and the denominator by 10, we get

2/9 = 2 × 10/9 × 10 = 20/90

So, the equivalent fractions with the same denominator are:’

9/90 and 20/90

(g) 8/3 and 11/4

Ans: Given fractions are 8/3 and 11/4

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.

8/3 = 8 × 4/3 × 4 = 32/12

And for 11/4 multiply both the numerator and the denominator by 3, we get

11/4 = 11 × 3/4 × 3 = 33/12

So, the equivalent fractions with the same denominator are:

32/12 and 33/12

(h) 13/6 and 1/9

Ans: Given fractions are 13/6 and 1/9

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.

13/6 = 13 × 3/6 × 3 = 39/18

for 1/9 multiply both the numerator and the denominator by 2, we get

1/9 = 1 × 2/9 × 2 = 2/18

So, the equivalent fractions with the same denominator are:

39/18 and 2/18

Figure it Out (Page No. 173)

1. Express the following fractions in lowest terms:

(a) 17/51

Ans: 1/3

(b) 64/144

Ans: 4/9

(c) 126/147

Ans: 6/7

(d) 525/112

Ans: 75/16

Figure it Out (Page No. 174)

1. Compare the following fractions and justify your answers:

(a) 8/3,5/2

(b) 4/9,3/7

(d) 12/5,8/5

(e) 9/4,5/2

Ans:

2. Write following fractions ascending order.

(a) 7/10,11/15,2/5

Ans: 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: 2/5,7/10 11/5

(b) 19/24,5/6,7/12

Ans: 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

3. Write the following fractions in descending order.

(a) 25/16,7/8,13/4,17/32

Ans:

(b) 3/4,12/5,7/12,5/4

Ans:

Figure it Out (Page No. 179)

1. Add the following fractions using Brahmagupta’s method:

(a) 2/7 + 5/7 + 6/7

Ans: 2/7 + 5/7 + 6/7

= 2 + 5 + 6/7 = 13/7

= 1 6/7

(b) 3/4 + 1/3

Ans: 3/4 + 1/3 = 3/4 × 3/3 + 1/3 × 4/4

= 9/12 + 4/12

= 9 + 4/12

= 13/12

= 1 1/12

(c) 2/3 + 5/6

Ans: 2/3 + 5/6 =2/3 × 2/2 + 5/6

4/6 + 5/6 = 9/6 = 3/2

= 1 1/2

(d) 2/3 + 2/7

Ans: 2/3 + 2/7 = 2/3 × 7/7 + 2/7 × 3/3

= 14/21 + 6/21 = 20/21

(e) 3/4 + 1/3 + 1/5

Ans: 45/60 + 20/60 + 12/60

= 77/60

= 1 17/60

(f) 2/3 + 4/5

Ans: 10/15 + 12/15 = 22/15

= 1 7/15

(g) 4/5 + 2/3

Ans: 12/15 + 10/15 = 22/15

= 1 7/15

(h) 3/5 + 5/8

Ans: 24/40 + 25/40 = 49/40

= 9/40

(i) 9/2 + 5/4

Ans: 18/4 + 5/4 = 23/4

= 5 3/4

(j) 8/3 + 2/7

Ans: 56/21 + 6/21 = 62/21

= 2 20/21

(k) 3/4 + 1/3 + 1/5

Ans: 45/60 + 20/60 + 12/60 = 77/60

= 1 17/60

(l) 2/3 + 4/5 + 3/7

Ans: 70/105 + 84/105 + 45/105 = 199/105

= 1 94/105

(m) 9/2 + 5/4 + 7/6

Ans: 54/12 + 15/12 + 14/12 = 83/12

= 11/12

2. Rahim mixes 2/3 liters of yellow paint with 3/4 liters of blue paint to make green paint What is the volume of green paint he has made?

Ans: Quantity of yellow paint added = 2/3 litres

Quantity of blue paint added = 3/4 litres

Total quantity of green paint made = 2/3 + 3/4

LCM of 3 and 4 is 12.

2/3 = 2/3 × 4/4 = 8/12

3/4 = 3/4 × 3/3 = 9/12

8/12 + 9/12 = 8 + 9/12 = 17/12

So, the total quantity of paint made is 17/12 liters.

3. Geeta bought 2/5 meter of lace and Shamim bought ¾ 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?

Ans: Length of lace bought by Geeta = 2/5 m

Length of lace bought by Shamim = 3/4 m

Total length of lace bought = 2/5 + 3/4

LCM of 5 and 4 is 20.

2/5 = 2/5 × 4/4 = 8/20

3/4 = 3/4 × 5/5 = 15/20

8/20 + 15/20 = 23/20 = 1 3/20

This length is more than 1 m. So, lace is more than sufficient or will be left extra after covering the border.

Figure it Out (Page No. 181)

1. 5/8 − 3/8

Ans: Given 5/8 − 3/8

As fractional unit is same i.e., 1/8 we shall simply subtract numerators keeping fractional unit as 1/8

Then 5/8 − 3/8 = 5−3/8

= 2/8 = 1/4 (representing in simplest form)

2. 7/9 − 5/9

Ans: Given 7/9 − 5/9

As fractional unit is same i.e., 1/9 we shall simply subtract numerators keeping fractional unit as 1/9 7/9 − 5/9

= 7−5/9 = 2/9

3. 10/27 − 1/27 10/27 − 1/27

Ans: Here 10/27 − 1/27

= 10−1/27

= 9/27 = 1/03

Figure it Out (Page No. 182)

1. Carry out the following subtractions using Brahmagupta’s method:

(a) 8/15 − 3/15

Ans: Given 8/15 − 3/15

Fractional unit for both fractions is 1/15 then

8/15 − 3/15 = 8−3/15

= 5/15 = 1/3

(b) 2/5 − 4/15

Ans: Given 2/5 − 4/15

Here LCM of 5 and 15 is 15. Fractional unit for both fractions should be 1/15

then 2×3/5×3 − 4×1/15×1

= 6/15 − 4/15

= 6−4/15

= 2/15

(c) 5/6 − 4/9

Ans: Given 5/6 − 4/9

Hence LCM of 6 and 9 is 18. Fractional unit for both fractions should be 1/18 Then

(d) 2/3 − 1/2

Ans: Given 2/3 − 1/2

Here LCM of 3 and 2 is 6. Fractional unit for both fractions should be 1/6

2. Subtract as indicated:

(a) 13/4 from 10/3

Ans: The denominators of the given fractions are 3 and 4. The LCM of 3 and 4 is 12.

Then 13/4 = 13×3/4×3 = 39/12, 10/3 = 10×4/3×4 = 40/12

Therefore, 10/3 − 13/4 = 40/12 − 39/12 = 1/12

(b) 18/5 from 23/3

Ans: The denominators of the given fractions are 3 and 5.

The LCM of 3 and 5 is 15.

Then, 23/3 = 23×5/3×5 = 115/15, 18/5 = 18×3/5×3 = 54/15

Therefore, 23/3 − 18/5 = 115/15 − 54/15 = 61/15 = 4 1/15

(c) 29/7 from 45/7

Ans: The denominators are same.

Therefore, 45/7 − 29/7 = 16/7 = 2 2/7

3. Solve the following problems:

(a) Jaya’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?

Ans: (a) Total distance between school and home = 7/10 km

Distance travelled in Auto = 1/2 km.

∴ Distance she walks daily to reach the school

(b) Jeevika takes 10/3 minutes to take a complete round of the park and her friend Namit takes 13/4 minutes to do the same. Who takes less time and by how much?

Ans: Time taken by Jeevika = 10/3 minutes

and time taken by Narnit = 13/4 minutes

Now, 10/3 × 4/4 = 40/12 and 13/4 × 3/3 = 39/12

Clearly, 10/3 > 13/4

∴ Jeevika takes less ti me by (10/3 − 13/4) minutes

= (40/12 − 39/12) minutes

= 1/12 minutes.