Ncert solutions mathematics class 6 Solutions for Chapter 7 fractions

Exercises in Chapter 7 fractions Grade 6

Exercise 7.1

Exercise 7.2

Exercise 7.3

Exercise 7.4

Exercise 7.5

Exercise 7.6

Questions in Exercise 7.1

Q1) Write the fraction representing the shaded portion.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

Q2) Colour the part according to the given fraction.

(i) $\frac{1}{6}$

(ii) $\frac{1}{4}$

(iii) $\frac{1}{3}$

(iv) $\frac{3}{4}$

(v) $\frac{4}{9}$

Write the fraction representing the shaded portion.

Colour the part according to the given fraction.

Identify the error, if any.

Q3) Identify the error, if any.

Q4) What fraction of a day is 8 hours?

What fraction of a day is 8 hours?

Q5) What fraction of an hour is 40 minutes?

What fraction of an hour is 40 minutes?

Q6) Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.

(a) How can Arya divide his sandwiches so that each person has an equal share?

(b) What part of a sandwich will each boy receive?

Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.

(a) How can Arya divide his sandwiches so that each person has an equal share?

(b) What part of a sandwich will each boy receive?

Q7) Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Q8) Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Q9) Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

What fraction of these circles have X’s in them?

Q10) What fraction of these circles have X’s in them?

Q11) Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?

Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts.

What fraction of her total CDs did she buy and what fraction did she receive as gifts?

Questions in Exercise 7.2

Q1) Draw number lines and locate the points on them :

(a) $\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}$ (b) $\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}$ (c) $\frac{2}{5},\ \frac{3}{5},\ \frac{8}{5},\ \frac{4}{5}$

Draw number lines and locate the points on them:

(a) 1 / 2, 1 / 4, 3 / 4, 4 / 4

(b) 1 / 8, 2 / 8, 3 / 8, 7 / 8

Q2) Express the following as mixed fractions :

(a) $\frac{20}{3}$ (b) $\frac{11}{5}$ (c) $\frac{17}{7}$ (d) $\frac{28}{5}$ (e) $\frac{19}{6}$ (f) $\frac{35}{9}$

Express the following as mixed fractions:

(a) 20 / 3

(b) 11 / 5

(d) 28 / 5

(e) 19 / 6

(f) 35 / 9

Q3) Express the following as improper fractions :

(a) $7\frac{3}{4}$ (b) $5\frac{6}{7}$ (c) $2\frac{5}{6}$ (d) $10\frac{3}{5}$ (e) $9\frac{3}{7}$ (f) $8\frac{4}{9}$

Express the following as improper fractions:

$\begin{array}{l} \text { (a) } 7 \frac{3}{4} \\ \text { (b) } 5 \frac{6}{7} \\ \text { (c) } \frac{2-}{6} \\ \text { (d) } 10 \frac{3}{5} \\ \text { (e) } 9 \frac{3}{7} \\ \text { (f) } 8 \frac{4}{9} \end{array}$

Questions in Exercise 7.3

Q1) Write the fractions. Are all these fractions equivalent?

(a)

(b)

Write the fractions. Are all these fractions equivalent?

Q2) Write the fractions and pair up the equivalent fractions from each row.

(a) ( b) (c)

(d) (e)

(i) (ii) (iii)

(iv) (v)

Write the fractions and pair up the equivalent fractions from each row.

Replace ☐ in each of the following by the correct number:

(a) 2 / 7 = 8 / ☐

(b) 5 / 8 = 10 / ☐

(d) 45 / 60 = 15 / ☐

(e) 18 / 24 = ☐ / 4

Q3) Replace $\square$ in each of the following by the correct number:

(a) $\frac{2}{7}=\frac{8}{\square}$

(b) $\frac{5}{8}=\frac{10}{\square}$

(d) $\frac{45}{60}=\frac{15}{\square}$

(e) $\frac{18}{24}=\frac{\square}{4}$

Find the equivalent fraction of 3 / 5 having

(a) denominator 20

(b) numerator 9

(d) numerator 27

Q4) Find the equivalent fraction of $\frac{3}{5}$ having:

(a) denominator 20 (b) numerator 9

Find the equivalent fraction of 36 / 48 with

(a) numerator 9

(b) denominator 4

Q5) Find the equivalent fraction of $\frac{36}{48}$ with

(a) numerator 9 (b) denominator 4

Check whether the given fractions are equivalent:

(a) 5 / 9, 30 / 54

(b) 3 / 10, 12 / 50

Q6) Check whether the given fractions are equivalent :

(a) $\frac{5}{9},\ \frac{30.}{54}$

(b) $\frac{3}{10},\ \frac{12}{50}$

Q7) Reduce the following fractions to simplest form :

(a) $\frac{48}{60}$

(b) $\frac{150}{60}$

(d) $\frac{12}{52}$

(e) $\frac{7}{28}$

Reduce the following fractions to simplest form:

(a) 48 / 60

(b) 150 / 60

(d) 12 / 52

(e) 7 / 28

Q8) Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months,

Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

Match the equivalent fractions and write two more for each.

(i) 250 / 400—– (a) 2 / 3

(ii) 180 / 200——– (b) 2 / 5

(iii) 660 / 990——– (c) 1 / 2

(iv) 180 / 360 ——-(d) 5 / 8

(v) 220 / 550———- (e) 9 / 10

Q9) Match the equivalent fractions and write two more for each.

(i) $\frac{250}{400}$ (ii) $\frac{180}{200}$ (iii) $\frac{660}{990}$ (iv) $\frac{180}{360}$ (v) $\frac{220}{550}$

(a) $\frac{2}{3}$ (b) $\frac{2}{5}$ (c) $\frac{1}{2}$ (d) $\frac{5}{8}$ (e) $\frac{9}{10}$

Questions in Exercise 7.4

Q1) Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘<’, ‘=’, ‘>’ between the fractions:

(a)

(b)

(c) Show $\frac{2}{6},\ \frac{4}{6},\ \frac{8}{6}\ and\ \frac{6}{6}$ on number line. Put appropriate sign between the fraction given:

$\frac{5}{6}$ $\square$ $\frac{2}{6}$ , $\frac{3}{6}\square0$ , $\frac{1}{6}\square\ \frac{6}{6}$ , $\frac{8}{6}\square\ \frac{5}{6}$

Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘’ between the fractions:

5 / 6 ☐ 2 / 6, 3 / 6 ☐ 0, 1 / 6 ☐ 6 / 6, 8 / 6 ☐ 5 / 6

Compare the fractions and put an appropriate sign.

(a) 3 / 6 ☐ 5 / 6

(b) 1 / 7 ☐ 1 / 4

(d) 3 / 5 ☐ 3 / 7

Q2) Compare the fractions and put an appropriate sign.

(a) $\frac{3}{6}\ \square\ \frac{5}{6}$ (b) $\frac{1}{7}\ \square\ \frac{1}{4}$ (c) $\frac{4}{5}\ \square\ \frac{5}{5}$ (d) $\frac{3}{5}\ \square\ \frac{3}{7}$

Q3) Make five more such pairs and put appropriate signs.

Make five more such pairs and put appropriate signs.

Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

(a) 1 / 6 ☐ 1 / 3

(b) 3 / 4 ☐ 2 / 6

(d) 6 / 6 ☐ 3 / 3

(e) 5 / 6 ☐ 5 / 5

Q4) Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

(a) $\frac{1}{6}\ \square\ \frac{1}{3}$ (b) $\frac{3}{4}\ \square\ \frac{2}{6}$ (c) $\frac{2}{3}\ \square\ \frac{2}{4}$ (d) $\frac{6}{6}\ \square\ \frac{3}{3}$ (e) $\frac{5}{6}\ \square\ \frac{5}{5}$

Make five more such problems and solve them with your friends.

Q5) How quickly can you do this? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)

(a) $\frac{1}{2}\square\ \frac{1}{5}$

(b) $\frac{2}{4}\square\ \frac{3}{6}$

(d) $\frac{3}{4}\square\ \frac{2}{8}$

(e) $\frac{3}{5}\square\ \frac{6}{5}$

(f) $\frac{7}{9}\square\ \frac{3}{9}$

(g) $\frac{1}{4}\square\ \frac{2}{8}$

(h) $\frac{6}{10}\square\ \frac{4}{5}$

(i) $\frac{3}{4}\square\ \frac{7}{8}$

(j) $\frac{6}{10}\square\ \frac{3}{5}$

(k) $\frac{5}{7}\square\ \frac{15}{21}$

How quickly can you do this? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)

(a) 1 / 2 ☐ 1 / 5

(b) 2 / 4 ☐ 3 / 6

(d) 3 / 4 ☐ 2 / 8

(e) 3 / 5 ☐ 6 / 5

(f) 7 / 9 ☐ 3 / 9

(g) 1 / 4 ☐ 2 / 8

(h) 6 / 10 ☐ 4 / 5

(i) 3 / 4 ☐ 7 / 8

(j) 6 / 10 ☐ 3 / 5

(k) 5 / 7 ☐ 15 / 21

The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

(a) 2 / 12

(b) 3 / 15

(d) 16 / 100

(e) 10 / 60

(f) 15 / 75

(g) 12 / 60

(h) 16 / 96

(i) 12 / 75

(j) 12 / 72

(k) 3 / 18

(l) 4 / 25

Q6) The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

(a) $\frac{2}{12}$ (b) $\frac{3}{15}$ (c) $\frac{8}{50}$ (d) $\frac{16}{100}$ (e) $\frac{10}{60}$

(f) $\frac{15}{75}$ (g) $\frac{12}{60}$ (h) $\frac{16}{96}$ (i) $\frac{12}{75}$ (j) $\frac{12}{72}$ (k) $\frac{3}{18}$ (l) $\frac{4}{25}$

Q7) Find answers to the following. Write and indicate how you solved them.

(a) Is $\frac{5}{9}$ equal to $\frac{4}{5}$ ?

(b) Is $\frac{9}{16}$ equal to $\frac{5}{9}$ ?

(d) Is $\frac{1}{5}$ equal to $\frac{4}{30}$ ?

Find answers to the following. Write and indicate how you solved them.

(a) Is 5 / 9 equal to 4 / 5

(b) Is 9 / 16 equal to 5 / 9

(d) Is 1 / 15 equal to 4 / 30

Ila read 25 pages of a book containing 100 pages. Lalita read 2 / 5 of the same book. Who read less?

Q8) Ila read 25 pages of a book containing 100 pages. Lalita read $\frac{2}{5}$ of the same book. Who read less?

Rafiq exercised for 3 / 6 of an hour, while Rohit exercised for 3 / 4 of an hour. Who exercised for a longer time?

Q9) Rafiq exercised for $\frac{3}{6}$ of an hour, while Rohit exercised for $\frac{3}{4}$ of an hour. Who exercised for a longer time?

In a class A of 25 students, 20 passed with 60% or more marks; in another class B of 30 students, 24 passed with 60% or more marks. In which class was a greater fraction of students getting with 60% or more marks?

Q10) In a class A of 25 students, 20 passed with 60% or more marks; in another class B of 30 students, 24 passed with 60% or more marks. In which class was a greater fraction of students getting with 60% or more marks?

Questions in Exercise 7.5

Solve

(a) 2 / 3 + 1 / 7

(b) 3 / 10 + 7 / 15

(d) 5 / 7 + 1 / 3

(e) 2 / 5 + 1 / 6

(f) 4 / 5 + 2 / 3

(g) 3 / 4 – 1 / 3

(h) 5 / 6 – 1 / 3

(i) 2 / 3 + 3 / 4 + 1 / 2

(j) 1/ 2 + 1 / 3 + 1 / 6

(k) $\begin{array}{l} 1 \frac{1}{3}+3 \frac{2}{3} \\ 4 \frac{2}{3}+3 \frac{1}{4} \end{array}$ (l)

(m) 16 / 5 – 7 / 5

(n) 4 / 3 – 1 / 2

Q1) Write these fractions appropriately as additions or subtractions :

(a)

(b)

(c)

Write these fractions appropriately as additions or subtractions:

Solve:

(a) 1 / 18 + 1 / 18

(b) 8 / 15 + 3 / 15

(d) 1 / 22 + 21 / 22

(e) 12 / 15 – 7 / 15

(f) 5 / 8 + 3 / 8

(g) 1 – 2 / 3 (1 = 3 / 3)

(h) 1 / 4 + 0 / 4

(i) 3 – 12 / 5

Q2) Solve :

(a) $\frac{1}{18}+\frac{1}{18}$ (b) $\frac{8}{15}+\frac{3}{15}$ (c) $\frac{7}{7}-\frac{5}{7}$ (d) $\frac{1}{22}+\frac{21}{22}$ (e) $\frac{12}{15}-\frac{7}{15}$ (f) $\frac{5}{8}+\frac{3}{8}$ (g) $1-\frac{2}{3}\ \left(1=\frac{3}{3}\right)$ (h) $\frac{1}{4}+\frac{0}{4}$ (i) $3-\frac{12}{5}$

Q3) Shubham painted $\frac{2}{3}$ of the wall space in his room. His sister Madhavi helped and painted $\frac{1}{3}$ of the wall space. How much did they paint together?

Shubham painted 2 / 3 of the wall space in his room. His sister Madhavi helped and painted 1 / 3 of the wall space. How much did they paint together?

Q4) Fill in the missing fractions.

(a) $\frac{7}{10}-\ \square\ =\frac{3}{10}$ (b) $\square\ -\ \frac{3}{21}=\frac{5}{21}$

Fill in the missing fractions.

(a) 7 / 10 – ▯ = 3 / 10

(b) ▯ – 3 / 21 = 5 / 21

(d) ▯ + 5 / 27 = 12 / 27

Q5) Javed was given $\frac{5}{7}$ of a basket of oranges. What fraction of oranges was left in the basket?

Javed was given 5 / 7 of a basket of oranges. What fraction of oranges was left in the basket?

Questions in Exercise 7.6

Q1) Solve:

(a) $\frac{2}{3}+\frac{1}{7}$ (b) $\frac{3}{10}+\frac{7}{15}$ (c) $\frac{4}{9}+\frac{2}{7}$ (d) $\frac{5}{7}+\frac{1}{3}$

(e) $\frac{2}{5}+\frac{1}{6}$ (f) $\frac{4}{5}+\frac{2}{3}$ (g) $\frac{3}{4}-\frac{1}{3}$ (h) $\frac{5}{6}-\frac{1}{3}$

(i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$ (j) $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$ (k) $1\frac{1}{3}+3\frac{2}{3}$

(l) $4\frac{2}{3}+3\frac{1}{4}$ (m) $\frac{16}{5}-\frac{7}{5}$ (n) $\frac{4}{3}-\frac{1}{2}$

Q2) Sarita bought $\frac{2}{5}$ metre of ribbon and Lalita $\frac{3}{4}$ metre of ribbon. What is the total length of the ribbon they bought?

Sarita bought 2 / 5 metre of ribbon and Lalita 3 /4 metre of ribbon. What is the total length of the ribbon they bought?

Naina was given $1\frac{1}{2}$ piece of cake and Najma was given $1\frac{1}{3}$ piece of cake. Find the total amount of cake was given to both of them.

Q3) Naina was given 1 $\frac{1}{2}$ piece of cake and Najma was given 1 $\frac{1}{3}$ piece of cake. Find the total amount of cake was given to both of them.

Q4) Fill in the boxes :

(a) $\square-\frac{5}{8}=\frac{1}{4}$ (b) $\square-\frac{1}{5}=\frac{1}{2}$ (c) $\frac{1}{2}-\square=\frac{1}{6}$

Fill in the boxes:

(a) ▯ – 5 / 8 = 1 / 4

(b) ▯ – 1 / 5 = 1 / 2

Q5) Complete the addition-subtraction box.

(a)

(b)

Complete the addition and subtraction box.

Q6) A piece of wire $\frac{7}{8}$ metre long broke into two pieces. One piece was $\frac{1}{4}$ metre long. How long is the other piece?

piece of wire 7 / 8 metre long broke into two pieces. One piece was 1 / 4 metre long. How long is the other piece?

Nandini’s house is 9 / 10 km from her school. She walked some distance and then took a bus for 1 / 2 km to reach the school. How far did she walk?

Q7) Nandini’s house is $\frac{9}{10}$ km from her school. She walked some distance and then took a bus for $\frac{1}{2}$ km to reach the school. How far did she walk?

Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is 5 / 6 th full and Samuel’s shelf is 2/ 5 th full. Whose bookshelf is more full? By what fraction?

Q8) Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is $\frac{5}{6}$ th full and Samuel’s shelf is $\frac{2}{5}$ th full. Whose bookshelf is more full? By what fraction?

Jaidev takes $2\frac{1}{5}$ minutes to walk across the school ground. Rahul takes 7 / 4 minutes to do the same. Who takes less time and by what fraction?

Q9) Jaidev takes $2\frac{1}{5}$ minutes to walk across the school ground. Rahul takes $\frac{7}{4}$ minutes to do the same. Who takes less time and by what fraction?