Fractions Ex-7.3

NCERT solutions for Maths Fractions 

NCERT Solutions for Class 6 Maths Fractions

Class –VI Mathematics

(Ex. 7.3)

Question 1.Write the fractions. Are all these fractions equivalent:

(a)

(b)

Answer:

(a) $\frac{1}{2},\frac{2}{4},\frac{3}{6},\frac{4}{8}$

Yes, all of these fractions are equivalent.

(b) $\frac{4}{12},\frac{3}{9},\frac{2}{6},\frac{1}{3},\frac{6}{15}$

No, these fractions are not equivalent.

Question 2.Write the fraction and pair up the equivalent fractions to each row:

Answer:

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

(ii) $\frac{4}{8}=\frac{1}{2}$

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

(iv) $\frac{8}{12}=\frac{2}{3}$

(c) $\frac{3}{9}=\frac{1}{3}$

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

(d) $\frac{2}{8}=\frac{1}{4}$

(v) $\frac{4}{16}=\frac{1}{4}$

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

(iii) $\frac{12}{16}=\frac{3}{4}$

NCERT Solutions for Class 6 Maths Exercise 7.3

Question 3.Replace $\boxed{\,\,\,\,\,}$ in each of the following by the correct number:

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

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

(c) $\frac{3}{5} = \frac{{\boxed{{\text{ }}}}}{{20}}$

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

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

Answer:

(a) $\frac{2}{7} = \frac{{2 \times 4}}{{7 \times 4}} = \frac{8}{{\boxed{28}}}$

(b) $\frac{5}{8} = \frac{{5 \times 2}}{{8 \times 2}} = \frac{{10}}{{\boxed{16}}}$

(c) $\frac{3}{5} = \frac{{3 \times 4}}{{5 \times 4}} = \frac{{\boxed{12}}}{{20}}$

(d) $\frac{{45}}{{60}} = \frac{{45 \div 3}}{{60 \div 3}} = \frac{{15}}{{\boxed{20}}}$

(e) $\frac{{18}}{{24}} = \frac{{18 \div 6}}{{24 \div 6}} = \frac{{\boxed3}}{4}$

Question 4.Find the equivalent fraction of $\frac{3}{5}$ having:

(a) denominator 20

(b) numerator 9

(c) denominator 30

(d) numerator 27

Answer:

(a) $\frac{3}{5} = \frac{{3 \times 4}}{{5 \times 4}} = \frac{{12}}{{20}}$

(b) $\frac{3}{5} = \frac{{3 \times 3}}{{5 \times 3}} = \frac{9}{{15}}$

(c) $\frac{3}{5} = \frac{{3 \times 6}}{{5 \times 6}} = \frac{{18}}{{30}}$

(d) $\frac{3}{5} = \frac{{3 \times 9}}{{5 \times 9}} = \frac{{27}}{{45}}$

NCERT Solutions for Class 6 Maths Exercise 7.3

Question 5.Find the equivalent fraction of $\frac{{36}}{{48}}$ with:

(a) numerator 9

(b) denominator 4

Answer:

(a) $\frac{{36}}{{48}} = \frac{{36 \div 4}}{{48 \div 4}} = \frac{9}{{12}}$

(b) $\frac{{36}}{{48}} = \frac{{36 \div 12}}{{48 \div 12}} = \frac{3}{4}$

Question 6.Check whether the given fraction are equivalent:

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

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

(c)$\frac{7}{{13}},\frac{5}{{11}}$

Answer:

(a) $\frac{5}{9},\frac{{30}}{{54}}$ = $\frac{{5 \times 6}}{{9 \times 6}},\frac{{30}}{{54}}$ = $\frac{{30}}{{54}},\frac{{30}}{{54}}$

Therefore, $\frac{5}{9},\frac{{30}}{{54}}$ are equivalent.

(b) $\frac{3}{{10}},\frac{{12}}{{50}}$ = $\frac{{3 \times 5}}{{10 \times 5}},\frac{{12}}{{50}}$ = $\frac{{15}}{{50}},\frac{{12}}{{50}}$

Therefore, $\frac{3}{{10}},\frac{{12}}{{50}}$ are not equivalent.

(c) $\frac{7}{{13}},\frac{5}{{11}}$ = $\frac{{7 \times 11}}{{13 \times 11}},\frac{{5 \times 13}}{{11 \times 13}}$ = $\frac{{77}}{{143}},\frac{{65}}{{143}}$

Therefore, $\frac{7}{{13}},\frac{5}{{11}}$ are not equivalent fraction.

NCERT Solutions for Class 6 Maths Exercise 7.3

Question 7.Reduce the following fractions to simplest form:

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

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

(c) $\frac{{84}}{{98}}$

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

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

Answer:

(a) $\frac{48}{60}=\frac{2\times 2\times 2\times 2\times 3}{2\times 2\times 3\times 5}=\frac{4}{5}$

(b) $\frac{150}{60}=\frac{3\times 5\times 10}{2\times 3\times 10}=\frac{5}{2}$

(c) $\frac{84}{98}=\frac{2\times 3\times 14}{7\times 14}=\frac{6}{7}$

(d) $\frac{12}{52}=\frac{2\times 2\times 3}{2\times 2\times 13}=\frac{3}{13}$

(e) $\frac{7}{28}=\frac{7}{2\times 2\times 7}=\frac{1}{4}$

Question 8.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 is each has used up an equal fraction of her/his pencils?

Answer:

Ramesh: Total pencils = 20

Pencils used = 10

Fraction = $\frac{10}{20}=\frac{1}{2}$

Sheelu: Total pencils = 50

Pencils used = 25

Fraction = $\frac{25}{50}=\frac{1}{2}$

Jamaal: Total pencils = 80

Pencils used = 40

Fraction = $\frac{40}{80}=\frac{1}{2}$

Since, all of them used half of their pencils, therefore each one used up equal fraction of pencils.

NCERT Solutions for Class 6 Maths Exercise 7.3

Question 9. Match the equivalent fractions and write two more for each:

Answer:

(i) $\frac{250}{400}=\frac{5}{8},\frac{10}{16},\frac{15}{24}$

(d) $\frac{5}{8}$

(ii) $\frac{180}{200}=\frac{9}{10},\frac{18}{20},\frac{27}{30}$

(e) $\frac{9}{10}$

(iii) $\frac{660}{990}=\frac{2}{3},\frac{4}{6},\frac{6}{9}$

(a) $\frac{2}{3}$

(iv) $\frac{180}{360}=\frac{1}{2},\frac{2}{4},\frac{3}{6}$

(c)$\frac{1}{2}$

1. $\frac{220}{550}=\frac{2}{5},\frac{4}{10},\frac{6}{15}$

(b) $\frac{2}{5}$