Fractions Ex-7.4

NCERT solutions for Maths Fractions 

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

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

$\frac{1}{6}\boxed{{\text{ }}}\frac{6}{6},$ $\frac{8}{6}\boxed{{\text{ }}}\frac{5}{6}$

Answer:

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

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

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

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

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

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

(c) Number line

$\frac{5}{6}\boxed > \frac{2}{6}$ $\frac{1}{6}\boxed < \frac{6}{6}$

$\frac{3}{6}\boxed > \frac{0}{6}$ $\frac{8}{6}\boxed > \frac{5}{6}$

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

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

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

(c) $\frac{4}{5}\boxed{{\text{ }}}\frac{5}{5}$

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

Answer:

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

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

(c) $\frac{4}{5}\boxed < \frac{5}{5}$

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

NCERT Solutions for Class 6 Maths Exercise 7.4

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

Answer:

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

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

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

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

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

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

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

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

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

(d) $\frac{6}{6}\boxed{{\text{ }}}\frac{3}{3}$

(e) $\frac{5}{6}\boxed{{\text{ }}}\frac{5}{5}$

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

Answer:

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

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

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

(d) $\frac{6}{6}\boxed = \frac{3}{3}$

(e) $\frac{5}{6}\boxed < \frac{5}{5}$

Five more such problems:

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

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

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

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

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

Sol.

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

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

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

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

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

NCERT Solutions for Class 6 Maths Exercise 7.4

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

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

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

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

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

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

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

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

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

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

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

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

Answer:

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

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

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

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

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

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

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

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

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

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

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

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) $\frac{2}{{12}}$

(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) $\frac{4}{{25}}$

Answer:

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

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

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

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

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

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

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

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

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

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

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

(l) $\frac{4}{25}=\frac{4}{25}$

Equivalent groups:

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

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

III group: $\frac{4}{{25}}$ [(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 $\frac{5}{9}$ equal to $\frac{4}{5}$ ?

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

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

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

Answer:

(a)$\frac{5}{9}$ and $\frac{4}{5}$

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

Since, $\frac{{25}}{{45}} \ne \frac{{36}}{{45}}$

Therefore, $\frac{5}{9} \ne \frac{4}{5}$

(b) $\frac{9}{{16}}$ and $\frac{5}{9}$

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

Since, $\frac{{81}}{{144}} \ne \frac{{80}}{{144}}$

Therefore, $\frac{9}{{16}} \ne \frac{5}{9}$

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

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

Since, $\frac{{80}}{{100}} = \frac{{80}}{{100}}$

Therefore, $\frac{4}{5} = \frac{{16}}{{20}}$

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

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

Since, $\frac{4}{{30}} = \frac{4}{{30}}$ Therefore,

$\frac{1}{{15}} = \frac{4}{{30}}$

NCERT Solutions for Class 6 Maths Exercise 7.4

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

Answer:

Ila read 25 pages out of 100 pages.

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

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

Since $\frac{1}{4} < \frac{2}{5}$

Therefore, Ila read less.

Question 9.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?

Answer:

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

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

Since $\frac{3}{4} > \frac{3}{6}$

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., $\frac{{20}}{{25}}$ = $\frac{4}{5}$

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

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