Exercise 2.4
Q 1, Ex 2.4 - Fractions and Decimals - Chapter 2 - Maths Class 7th - NCERT
Find :
(i) $12 \div \dfrac{3}{4}$
Sol :
$12 \div \dfrac{3}{4}$ $=12\times \dfrac{4}{3}$ = 16
(ii) $4\div \dfrac{5}{6}$
Sol :
$14 \div\dfrac{5}{6} $ $14\times \dfrac{6}{5}$ $=\dfrac{84}{5}$
(iii) $8\div \dfrac{7}{3}$
Sol :
$8\div \dfrac{7}{3}$ $=8\times \dfrac{3}{7}$ $=\dfrac{24}{7}$
(iv) $4\div \dfrac{8}{3}$
Sol :
$4\div \dfrac{8}{3}$ $=4\times \dfrac{3}{8}$ $=\dfrac{3}{2}$
(v) $3\div 2\dfrac{1}{3}$
Sol :
$3\div 2\dfrac{1}{3}$ $=3\div \dfrac{7}{3}$ $=3\times\dfrac{3}{7}$ $\dfrac{9}{7}$
(vi) $5\div 3\dfrac{4}{7}$
Sol :
$5\div 3\dfrac{4}{7}$ $=5\div \dfrac{25}{7}$ $=5\times \dfrac{7}{25}$ $=\dfrac{7}{5}$
Q 2, Ex 2.4 - Fractions and Decimals - Chapter 2 - Maths Class 7th - NCERT
Question 2
Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) $\dfrac{3}{7}$ (ii) $\dfrac{5}{8}$ (iii) $\dfrac{9}{7}$
(iv) $\dfrac{6}{5}$ (v) $\dfrac{12}{7}$ (vi) $\dfrac{1}{8}$
(vii) $\dfrac{1}{11}$
Sol :
Note : A proper fraction is the fraction which has its denominator greater than its numerator while improper fraction is the fraction which has its numerator greater than its denominator. Whole numbers are a collection of all positive integers including 0.
(i) $\dfrac{3}{7}$
Reciprocal $=\dfrac{7}{3}$
Therefore, it is an improper fraction.
(ii) $\dfrac{5}{8}$
Reciprocal $=\dfrac{8}{5}$
Therefore, it is an improper fraction.
(iii) $\dfrac{9}{7}$
Reciprocal $=\dfrac{7}{9}$
Therefore, it is an proper fraction.
(iv) $\dfrac{6}{5}$
Reciprocal $=\dfrac{5}{6}$
Therefore, it is an proper fraction.
(v) $\dfrac{12}{7}$
Reciprocal $=\dfrac{7}{12}$
Therefore, it is an proper fraction.
(vi) $\dfrac{1}{8}$
Reciprocal $=\dfrac{8}{1}$
Therefore, it is a whole number.
(vii) $\dfrac{1}{11}$
Reciprocal $=\dfrac{11}{1}$
Therefore, it is a whole number.
Q 3, Ex 2.4 - Fractions and Decimals - Chapter 2 - Maths Class 7th - NCERT
Question 3
Find :
(i) $\dfrac{7}{3} \div 2$ (ii) $\dfrac{4}{9} \div 5$ (iii) $\dfrac{6}{13} \div 7$ (iv) $4\dfrac{1}{3} \div 3$ (v) $3\dfrac{1}{2} \div 4$ (vi) $4\dfrac{3}{7} \div 7$
Sol :
(i) $\dfrac{7}{3} \div 2$ $=\dfrac{7}{3} \times \dfrac{1}{2}$ $=\dfrac{7}{6}$
(ii) $\dfrac{4}{9} \div 5$ $=\dfrac{4}{9} \times \dfrac{1}{5}$ $=\dfrac{4}{45}$
(iii) $\dfrac{6}{13} \div 7$ $=\dfrac{6}{13} \times \dfrac{1}{7}$ $=\dfrac{6}{91}$
(iv) $4\dfrac{1}{3} \div 3$ $=\dfrac{13}{3} \div \dfrac{3}{1}$ $=\dfrac{13}{3} \times \dfrac{1}{3}$ $=\dfrac{13}{9}$
(v) $3\dfrac{1}{2} \div 4$ $=\dfrac{7}{2} \div \dfrac{4}{1}$ $=\dfrac{7}{2} \times \dfrac{1}{4}$ $=\dfrac{7}{8}$
(vi) $4\dfrac{3}{7} \div 7$ $=\dfrac{31}{7} \div \dfrac{1}{7}$ $=\dfrac{31}{7} \times \dfrac{1}{7}$ $=\dfrac{31}{49}$
Q 4, Ex 2.4 - Fractions and Decimals - Chapter 2 - Maths Class 7th - NCERT
Find :
(i) $\dfrac{2}{5} \div \dfrac{1}{2}$ (ii) $\dfrac{4}{9} \div \dfrac{2}{3}$
(iii) $\dfrac{3}{7} \div \dfrac{8}{7}$ (iv) $2\dfrac{1}{3} \div \dfrac{3}{5}$
(v) $3\dfrac{1}{2} \div \dfrac{8}{3}$ (vi) $\dfrac{2}{5} \div 1\dfrac{1}{2}$
(vii) $3\dfrac{1}{5} \div 1\dfrac{2}{3}$ (viii) $2\dfrac{1}{5} \div 1\dfrac{1}{5}$
Sol :
(i) $\dfrac{2}{5} \div \dfrac{1}{2}$ $=\dfrac{2}{5} \times \dfrac{2}{1}$ $=\dfrac{4}{5}$
(ii) $\dfrac{4}{9} \div \dfrac{2}{3}$ $=\dfrac{4}{9} \times \dfrac{3}{2}$ $=\dfrac{2}{3}$
(iii) $\dfrac{3}{7} \div \dfrac{8}{7}$ $=\dfrac{3}{7} \times \dfrac{7}{8}$ $=\dfrac{3}{8}$
(iv) $2\dfrac{1}{3} \div \dfrac{3}{5}$ $=\dfrac{7}{3} \div \dfrac{3}{5}$ $=\dfrac{7}{3} \times \dfrac{5}{3}$ $=\dfrac{35}{9}$
(v) $3\dfrac{1}{2} \div \dfrac{8}{3}$ $=\dfrac{7}{2} \div \dfrac{8}{3}$ $=\dfrac{7}{2} \times \dfrac{3}{8}$ $=\dfrac{21}{16}$
(vi) $\dfrac{2}{5} \div 1\dfrac{1}{2}$ $=\dfrac{2}{5} \div \dfrac{3}{2}$ $=\dfrac{2}{5} \times \dfrac{2}{3}$ $=\dfrac{4}{15}$
(vii) $3\dfrac{1}{5} \div 1\dfrac{2}{3}$ $=\dfrac{16}{5} \div \dfrac{5}{3}$ $=\dfrac{16}{5} \times \dfrac{3}{5}$ $=\dfrac{48}{25}$
(viii) $2\dfrac{1}{5} \div 1\dfrac{1}{5}$ $=\dfrac{11}{5} \div \dfrac{6}{5}$ $=\dfrac{11}{5} \times \dfrac{5}{6}$ $=\dfrac{11}{6}$
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