NCERT Solutions for Class 6 Maths Exercise 7.4

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NCERT solutions for Maths Fractions Download as PDF

NCERT Solutions for Class 6 Maths Exercise 7.4

NCERT Solutions for Class 6 Maths Fractions

Class –VI Mathematics
(Ex. 7.4)
Question 1.Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘<’, ‘>’, ‘=’ between the fractions:

(a)

(b)

(c)

Show {tex}\frac{2}{6},\frac{4}{6},\frac{8}{6}{/tex} and {tex}\frac{6}{6}{/tex} on the number line. Put appropriate signs between the fractions given:

{tex}\frac{5}{6}\boxed{{\text{ }}}\frac{2}{6},{/tex} {tex}\frac{3}{6}\boxed{{\text{ }}}0,{/tex}

{tex}\frac{1}{6}\boxed{{\text{ }}}\frac{6}{6},{/tex} {tex}\frac{8}{6}\boxed{{\text{ }}}\frac{5}{6}{/tex}

Answer:

(a) {tex}\frac{3}{8},\frac{6}{8},\frac{4}{8},\frac{1}{8}{/tex}

Ascending order: {tex}\frac{1}{8} < \frac{3}{8} < \frac{4}{8} < \frac{6}{8}{/tex}

Descending order: {tex}\frac{6}{8} > \frac{4}{8} > \frac{3}{8} > \frac{1}{8}{/tex}

(b) {tex}\frac{8}{9},\frac{4}{9},\frac{3}{9},\frac{6}{9}{/tex}

Ascending order: {tex}\frac{3}{9} < \frac{4}{9} < \frac{6}{9} < \frac{8}{9}{/tex}

Descending order: {tex}\frac{8}{9} > \frac{6}{9} > \frac{4}{9} > \frac{3}{9}{/tex}

(c) Number line

{tex}\frac{5}{6}\boxed > \frac{2}{6}{/tex} {tex}\frac{1}{6}\boxed < \frac{6}{6}{/tex}

{tex}\frac{3}{6}\boxed > \frac{0}{6}{/tex} {tex}\frac{8}{6}\boxed > \frac{5}{6}{/tex}


Question 2.Compare the fractions and put an appropriate sign:

(a) {tex}\frac{3}{6}\boxed{{\text{ }}}\frac{5}{6}{/tex}

(b) {tex}\frac{1}{7}\boxed{{\text{ }}}\frac{1}{4}{/tex}

(c) {tex}\frac{4}{5}\boxed{{\text{ }}}\frac{5}{5}{/tex}

(d) {tex}\frac{3}{5}\boxed{{\text{ }}}\frac{3}{7}{/tex}

Answer:

(a) {tex}\frac{3}{6}\boxed < \frac{5}{6}{/tex}

(b) {tex}\frac{1}{7}\boxed < \frac{1}{4}{/tex}

(c) {tex}\frac{4}{5}\boxed < \frac{5}{5}{/tex}

(d) {tex}\frac{3}{5}\boxed > \frac{3}{7}{/tex}


NCERT Solutions for Class 6 Maths Exercise 7.4

Question 3.Make five more each pairs and put appropriate signs.

Answer:

(a) {tex}\frac{9}{{10}}\boxed > \frac{6}{{10}}{/tex}

(b) {tex}\frac{1}{3}\boxed > \frac{1}{6}{/tex}

(c) {tex}\frac{1}{8}\boxed < \frac{1}{5}{/tex}

(d) {tex}\frac{7}{8}\boxed < \frac{{11}}{8}{/tex}

(e) {tex}\frac{{11}}{{13}}\boxed > \frac{9}{{13}}{/tex}


Question 4.Look at the figures and write ‘<’ or ‘>’ between the given pairs of fractions:

(a) {tex}\frac{1}{6}\boxed{{\text{ }}}\frac{1}{3}{/tex}

(b) {tex}\frac{3}{4}\boxed{{\text{ }}}\frac{2}{6}{/tex}

(c) {tex}\frac{2}{3}\boxed{{\text{ }}}\frac{2}{4}{/tex}

(d) {tex}\frac{6}{6}\boxed{{\text{ }}}\frac{3}{3}{/tex}

(e) {tex}\frac{5}{6}\boxed{{\text{ }}}\frac{5}{5}{/tex}

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

Answer:

(a) {tex}\frac{1}{6}\boxed < \frac{1}{3}{/tex}

(b) {tex}\frac{3}{4}\boxed > \frac{2}{6}{/tex}

(c) {tex}\frac{2}{3}\boxed > \frac{2}{4}{/tex}

(d) {tex}\frac{6}{6}\boxed = \frac{3}{3}{/tex}

(e) {tex}\frac{5}{6}\boxed < \frac{5}{5}{/tex}

Five more such problems:

(a) {tex}\frac{1}{2}\boxed{{\text{ }}}\frac{3}{6}{/tex}

(b) {tex}\frac{2}{3}\boxed{{\text{ }}}\frac{3}{5}{/tex}

(c) {tex}\frac{3}{4}\boxed{{\text{ }}}\frac{4}{6}{/tex}

(d) {tex}\frac{5}{6}\boxed{{\text{ }}}\frac{2}{2}{/tex}

(e) {tex}\frac{0}{1}\boxed{{\text{ }}}\frac{0}{6}{/tex}

Sol.

(a) {tex}\frac{1}{2}\boxed{{\text{ = }}}\frac{3}{6}{/tex}

(b) {tex}\frac{2}{3}\boxed{{\text{ > }}}\frac{3}{5}{/tex}

(c) {tex}\frac{3}{4}\boxed{{\text{ > }}}\frac{4}{6}{/tex}

(d) {tex}\frac{5}{6}\boxed{{\text{ < }}}\frac{2}{2}{/tex}

(e) {tex}\frac{0}{1}\boxed{{\text{ = }}}\frac{0}{6}{/tex}


NCERT Solutions for Class 6 Maths Exercise 7.4

Question 5.How quickly can you do this? Fill appropriate sign (<, =, >):

(a) {tex}\frac{1}{2}\boxed{{\text{ }}}\frac{1}{5}{/tex}

(b) {tex}\frac{2}{4}\boxed{{\text{ }}}\frac{3}{6}{/tex}

(c) {tex}\frac{3}{5}\boxed{{\text{ }}}\frac{2}{3}{/tex}

(d) {tex}\frac{3}{4}\boxed{{\text{ }}}\frac{2}{8}{/tex}

(e) {tex}\frac{3}{5}\boxed{{\text{ }}}\frac{6}{5}{/tex}

(f) {tex}\frac{7}{9}\boxed{{\text{ }}}\frac{3}{9}{/tex}

(g) {tex}\frac{1}{4}\boxed{{\text{ }}}\frac{2}{8}{/tex}

(h) {tex}\frac{6}{{10}}\boxed{{\text{ }}}\frac{4}{5}{/tex}

(i) {tex}\frac{3}{4}\boxed{{\text{ }}}\frac{7}{8}{/tex}

(j) {tex}\frac{6}{{10}}\boxed{{\text{ }}}\frac{4}{5}{/tex}

(k) {tex}\frac{5}{7}\boxed{{\text{ }}}\frac{{15}}{{21}}{/tex}

Answer:

(a) {tex}\frac{1}{2}\boxed{{\text{ > }}}\frac{1}{5}{/tex}

(b) {tex}\frac{2}{4}\boxed{{\text{ = }}}\frac{3}{6}{/tex}

(c) {tex}\frac{3}{5}\boxed{{\text{ < }}}\frac{2}{3}{/tex}

(d) {tex}\frac{3}{4}\boxed{{\text{ > }}}\frac{2}{8}{/tex}

(e) {tex}\frac{3}{5}\boxed{{\text{ < }}}\frac{6}{5}{/tex}

(f) {tex}\frac{7}{9}\boxed{{\text{ > }}}\frac{3}{9}{/tex}

(g) {tex}\frac{1}{4}\boxed{{\text{ = }}}\frac{2}{8}{/tex}

(h) {tex}\frac{6}{{10}}\boxed{{\text{ < }}}\frac{4}{5}{/tex}

(i) {tex}\frac{3}{4}\boxed{{\text{ < }}}\frac{7}{8}{/tex}

(j) {tex}\frac{6}{{10}}\boxed{{\text{ < }}}\frac{4}{5}{/tex}

(k) {tex}\frac{5}{7}\boxed{{\text{ = }}}\frac{{15}}{{21}}{/tex}


Question 6.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) {tex}\frac{2}{{12}}{/tex}

(b) {tex}\frac{3}{{15}}{/tex}

(c) {tex}\frac{8}{{50}}{/tex}

(d) {tex}\frac{{16}}{{100}}{/tex}

(e) {tex}\frac{{10}}{{60}}{/tex}

(f) {tex}\frac{{15}}{{75}}{/tex}

(g) {tex}\frac{{12}}{{60}}{/tex}

(h) {tex}\frac{{16}}{{96}}{/tex}

(i) {tex}\frac{{12}}{{75}}{/tex}

(j) {tex}\frac{{12}}{{72}}{/tex}

(k) {tex}\frac{3}{{18}}{/tex}

(l) {tex}\frac{4}{{25}}{/tex}

Answer:

(a) {tex}\frac{2}{12}=\frac{1}{6}{/tex}

(b) {tex}\frac{3}{15}=\frac{1}{5}{/tex}

(c) {tex}\frac{8}{50}=\frac{4}{25}{/tex}

(d) {tex}\frac{16}{100}=\frac{4}{25}{/tex}

(e) {tex}\frac{10}{60}=\frac{1}{6}{/tex}

(f) {tex}\frac{15}{75}=\frac{1}{5}{/tex}

(g) {tex}\frac{12}{60}=\frac{1}{5}{/tex}

(h) {tex}\frac{16}{96}=\frac{1}{6}{/tex}

(i) {tex}\frac{12}{75}=\frac{4}{25}{/tex}

(j) {tex}\frac{12}{72}=\frac{1}{6}{/tex}

(k) {tex}\frac{3}{18}=\frac{1}{6}{/tex}

(l) {tex}\frac{4}{25}=\frac{4}{25}{/tex}

Equivalent groups:

I group: {tex}\frac{1}{5}{/tex} [(b), (f), (g)]

II group: {tex}\frac{1}{6}{/tex} [(a), (e), (h), (j), (k)]

III group: {tex}\frac{4}{{25}}{/tex} [(c), (d), (i), (l)]


NCERT Solutions for Class 6 Maths Exercise 7.4

Question 7.Find answers to the following. Write and indicate how you solved them:

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

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

(c) Is {tex}\frac{4}{5}{/tex} equal to {tex}\frac{{16}}{{20}}{/tex} ?

(d) Is {tex}\frac{1}{{15}}{/tex} equal to {tex}\frac{4}{{30}}{/tex} ?

Answer:

(a){tex}\frac{5}{9}{/tex} and {tex}\frac{4}{5}{/tex}

{tex} \Rightarrow {/tex} {tex}\frac{{5 \times 5}}{{9 \times 5}} = \frac{{25}}{{45}}{/tex} and {tex}\frac{{4 \times 9}}{{5 \times 9}} = \frac{{36}}{{45}}{/tex} [{tex}\because {/tex} L.C.M. of 9 and 5 is 45]

Since, {tex}\frac{{25}}{{45}} \ne \frac{{36}}{{45}}{/tex}

Therefore, {tex}\frac{5}{9} \ne \frac{4}{5}{/tex}

(b) {tex}\frac{9}{{16}}{/tex} and {tex}\frac{5}{9}{/tex}

{tex} \Rightarrow {/tex}{tex}\frac{{9 \times 9}}{{16 \times 9}} = \frac{{81}}{{144}}{/tex} and {tex}\frac{{5 \times 16}}{{9 \times 16}} = \frac{{80}}{{144}}{/tex} [{tex}\because {/tex} L.C.M. of 16 and 9 is 144]

Since, {tex}\frac{{81}}{{144}} \ne \frac{{80}}{{144}}{/tex}

Therefore, {tex}\frac{9}{{16}} \ne \frac{5}{9}{/tex}

(c) {tex}\frac{4}{5}{/tex} and {tex}\frac{{16}}{{20}}{/tex}

{tex} \Rightarrow {/tex}{tex}\frac{{4 \times 20}}{{5 \times 20}} = \frac{{80}}{{100}}{/tex} and {tex}\frac{{16 \times 5}}{{20 \times 5}} = \frac{{80}}{{100}}{/tex} [{tex}\because {/tex} L.C.M. of 5 and 20 is 100]

Since, {tex}\frac{{80}}{{100}} = \frac{{80}}{{100}}{/tex}

Therefore, {tex}\frac{4}{5} = \frac{{16}}{{20}}{/tex}

(d) {tex}\frac{1}{{15}}{/tex} and {tex}\frac{4}{{30}}{/tex}

{tex}\Rightarrow {/tex}{tex}\frac{{1 \times 2}}{{15 \times 2}} = \frac{2}{{30}}{/tex} and {tex}\frac{{4 \times 1}}{{30 \times 1}} = \frac{4}{{30}}{/tex} [{tex}\because {/tex} L.C.M. of 15 and 30 is 30]

Since, {tex}\frac{4}{{30}} = \frac{4}{{30}}{/tex} Therefore,

{tex}\frac{1}{{15}} = \frac{4}{{30}}{/tex}


NCERT Solutions for Class 6 Maths Exercise 7.4

Question 8.Ila read 25 pages of a book containing 100 pages. Lalita read {tex}\frac{2}{5}{/tex} of the same book. Who read less?

Answer:

Ila read 25 pages out of 100 pages.

Fraction of reading the pages = {tex}\frac{{25}}{{100}} = \frac{1}{4}th{/tex} part of book

Lalita read {tex}\frac{2}{5}th{/tex} part of book = {tex}\frac{{40}}{{100}}{/tex} pages

Since {tex}\frac{1}{4} < \frac{2}{5}{/tex}

Therefore, Ila read less.


Question 9.Rafiq exercised for {tex}\frac{3}{6}{/tex} of an hour, while Rohit exercised for {tex}\frac{3}{4}{/tex} of an hour. Who exercised for a longer time?

Answer:

Rafiq exercised {tex}\frac{3}{6}{/tex} of an hour.

Rohit exercised {tex}\frac{3}{4}{/tex} of an hour.

Since {tex}\frac{3}{4} > \frac{3}{6}{/tex}

Therefore, Rohit exercised for a longer time.


NCERT Solutions for Class 6 Maths Exercise 7.4

Question 10.In a class A of 25 students, 20 passed in first class; in another class B of 30 students, 24 passed in first class. In which class was a greater fraction of students getting first class?

Answer:

In class A, 20 passed out of 25, i.e., {tex}\frac{{20}}{{25}}{/tex} = {tex}\frac{4}{5}{/tex}

In class B, 24 passed out of 30, i.e., {tex}\frac{{24}}{{30}}{/tex} = {tex}\frac{4}{5}{/tex}

Hence, each class have same fraction of student getting first class.

NCERT Solutions for Class 6 Maths Exercise 7.4

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