Excercise 2.4 Fractions and Decimals - NCERT Solutions Class 7

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Chapter 2 Ex.2.4 Question 1

 Find:

(i) \(\begin{align} 12 \div \frac{3}{4}\end{align} \)

(ii) \(\begin{align} 14 \div \frac{5}{6}\end{align} \)

(iii) \(\begin{align} 8 \div \frac{7}{3}\end{align} \)

(iv) \(\begin{align} 4 \div \frac{8}{3}\end{align} \)

(v) \(\begin{align} 3 \div 2\frac{1}{3}\end{align} \)

(vi) \(\begin{align} 5 \div 3\frac{4}{7}\end{align} \)

Solution

Video Solution

What is known?

Expression.

What is unknown?

Value of the expression.

Reasoning:

To divide fractions take the reciprocal of the divisor and multiply it with dividend.

Steps:

(i) \(\begin{align} 12 \div \frac{3}{4}\end{align} \)

\[\begin{align}&= \frac{{12}}{1} \times \frac{4}{3}\\&= 4 \times 4\\& = 16\end{align}\]

(ii) \(\begin{align} 14 \div \frac{5}{6}\end{align} \)

\[\begin{align}&= \frac{{14}}{1} \times \frac{6}{5}\\&= \frac{{84}}{5}\;({\text{improper fraction}})\end{align}\]

Converting into mixed fraction,

we get \(\begin{align}= 16\frac{4}{5} \end{align}\)

(iii) \(\begin{align} 8 \div \frac{7}{3}\end{align} \)

\[\begin{align}&= \frac{8}{1} \times \frac{3}{7}\\&= \frac{{24}}{7}\;{\text{(improper fraction)}}\end{align}\]

Converting into mixed fraction,

we get \(\begin{align} = 3\frac{3}{7} \end{align}\)

(iv) \(\begin{align} 4 \div \frac{8}{3}\end{align} \)

\[\begin{align}&= \frac{4}{1} \times \frac{3}{8}\\&= \frac{{12}}{8} \;{\text{(improper fraction)}}\end{align}\]

Converting into mixed fraction,

we get \(\begin{align} = 1\frac{1}{2}\end{align}\)

(v) \(\begin{align} 3 \div 2\frac{1}{3}\end{align} \)

\[\begin{align}&= 3 \div \frac{7}{3}\\&= \frac{3}{1} \times \frac{3}{7}\\&= \frac{9}{7}\;({\text{improper fraction}})\end{align}\]

Converting into mixed fraction,

we get \(\begin{align} = 1\frac{2}{7} \end{align}\)

(vi) \(\begin{align} 5 \div 3\frac{4}{7}\end{align} \)

\[\begin{align}&= 5 \div \frac{{25}}{7}\\&= \frac{5}{1} \times \frac{7}{{25}}\\&= \frac{7}{5}\;({\text{improper fraction}})\end{align}\]

Converting into mixed fraction,

we get \(\begin{align} = 1\frac{2}{5} \end{align}\)

Chapter 2 Ex.2.4 Question 2

Find the reciprocals of the following fractions. Classify the reciprocals as proper fractions, improper fractions, and whole numbers.

i) \(\begin{align} \frac{3}{7}\end{align} \)

ii) \(\begin{align} \frac{5}{8}\end{align} \)

iii) \(\begin{align} \frac{9}{7}\end{align} \)

iv) \(\begin{align} \frac{6}{5}\end{align} \)

v) \(\begin{align} \frac{{12}}{7}\end{align} \)

vi) \(\begin{align} \frac{1}{8}\end{align} \)

vii) \(\begin{align} \frac{1}{{11}}\end{align} \)

Solution

Video Solution

What is known?

Fractions.

What is unknown?

Reciprocal of given fraction.

Reasoning:

Reciprocal means interchanging numerator with denominator.

Steps:

(1) Proper fraction: -In proper fractions numerator is less than the denominator.

(2) Improper fraction: - In improper fractions numerator is greater than the denominator.

(3) Whole number: - It is a collection of positive integers including \(0\).

i) \(\begin{align} \frac{3}{7}\end{align} \)

Reciprocal of \(\begin{align} \frac{3}{7}\end{align} \) is \(\begin{align} \frac{7}{3}\end{align}\) (Improper fraction)

ii) \(\begin{align} \frac{5}{8}\end{align} \)

Reciprocal of \(\begin{align} \frac{5}{8}\end{align} \) is \(\begin{align} \frac{8}{5}\end{align}\) (Improper fraction)

iii) \(\begin{align} \frac{9}{7}\end{align} \)

Reciprocal of \(\begin{align} \frac{9}{7}\end{align} \) is \(\begin{align} \frac{7}{9}\end{align}\) (Proper fraction)

iv) \(\begin{align} \frac{6}{5}\end{align} \)

Reciprocal of \(\begin{align} \frac{6}{5}\end{align} \) is \(\begin{align} \frac{5}{6}\end{align}\) (Proper fraction)

v) \(\begin{align} \frac{{12}}{7}\end{align} \)

Reciprocal of \(\begin{align} \frac{{12}}{7}\end{align} \) is \(\begin{align} \frac{7}{{12}}\end{align}\) (Proper fraction)

vi) \(\begin{align} \frac{1}{8}\end{align} \)

Reciprocal of \(\begin{align} \frac{1}{8}\end{align} \) is \(\begin{align} \frac{8}{1} = 8\end{align}\) (Whole number)

vii) \(\begin{align} \frac{1}{{11}}\end{align} \)

Reciprocal of \(\begin{align} \frac{1}{{11}}\end{align} \) is \(\begin{align} \frac{{11}}{1} = 11\end{align}\) (Whole number)

Chapter 2 Ex.2.4 Question 3

 Find:

(i) \(\begin{align} \frac{7}{3} \div 2\end{align} \)

(ii) \(\begin{align} \frac{4}{9} \div 5 \end{align} \)

(iii) \(\begin{align} \frac{6}{{13}} \div 7\end{align} \)

(iv) \(\begin{align} 4\frac{1}{3} \div 3\end{align} \)

(v) \(\begin{align} 3\frac{1}{2} \div 4\end{align} \)

(vi) \(\begin{align} 4\frac{3}{7} \div 7\end{align} \)

Solution

Video Solution

What is known?

Expression.

What is unknown?

Value of the expression.

Reasoning:

To divide fractions take the reciprocal of the divisor and multiply it with dividend.

Steps:

(i) \(\begin{align} \frac{7}{3} \div 2\end{align} \)

\[\begin{align}&= \frac{7}{3} \times \frac{1}{2}\\&= \frac{7}{6}\;({\text{improper fraction}})\end{align}\]

Converting into mixed fraction,

we get \(\begin{align} = 1\frac{1}{6} \end{align}\)

(ii) \(\begin{align} \frac{4}{9} \div 5 \end{align} \)

\[\begin{align}&= \frac{4}{9} \times \frac{1}{5}\\&= \frac{4}{{45}}\end{align}\]

(iii) \(\begin{align} \frac{6}{{13}} \div 7\end{align} \)

\[\begin{align}& = \frac{6}{{13}} \times \frac{1}{7}\\ &= \frac{6}{{91}}\end{align}\]

(iv) \(\begin{align} 4\frac{1}{3} \div 3\end{align} \)

\[\begin{align}&= \frac{{13}}{3} \times \frac{1}{3}\\&= \frac{{13}}{9}\;({\text{improper fraction}})
\end{align}\]

Converting into mixed fraction,

we get \(\begin{align} = 1\frac{4}{9} \end{align}\)

(v) \(\begin{align} 3\frac{1}{2} \div 4\end{align} \)

\[\begin{align}&= \frac{7}{2} \times \frac{1}{4}\\&= \frac{7}{8}\end{align}\]

(vi) \(\begin{align} 4\frac{3}{7} \div 7\end{align} \)

\[\begin{align}&= 4\frac{3}{7} \times \frac{1}{7}\\&= \frac{{31}}{7} \times \frac{1}{7}\\&= \frac{{31}}{{49}}\end{align}\]

Chapter 2 Ex.2.4 Question 4

Find:

i) \(\begin{align} \frac{2}{5} \div \frac{1}{2}\end{align} \)

ii) \(\begin{align} \frac{4}{9} \div \frac{2}{3}\end{align} \)

iii) \(\begin{align} \frac{3}{7} \div \frac{8}{7}\end{align} \)

iv) \(\begin{align} 2\frac{1}{3} \div \frac{3}{5}\end{align} \)

v) \(\begin{align} 3\frac{1}{2} \div \frac{8}{3}\end{align} \)

vi) \(\begin{align} \frac{2}{5} \div 1\frac{1}{2}\end{align} \)

vii) \(\begin{align} 3\frac{1}{5} \div 1\frac{2}{3}\end{align} \)

viii) \(\begin{align} 2\frac{1}{5} \div 1\frac{1}{5}\end{align} \)

Solution

Video Solution

Steps:

i) \(\begin{align} \frac{2}{5} \div \frac{1}{2}\end{align} \)

\[\begin{align}&= \frac{2}{5} \times \frac{2}{1}\\&= \frac{{2 \times 2}}{{5 \times 1}}\\ &= \frac{4}{5}\end{align}\]

ii) \(\begin{align} \frac{4}{9} \div \frac{2}{3}\end{align} \)

\[\begin{align}&= \frac{4}{9} \times \frac{3}{2}\\&= \frac{{4 \times 3}}{{9 \times 2}}\\&= \frac{{2 \times 1}}{{3 \times 1}}\\&= \frac{2}{3}\end{align}\]

iii) \(\begin{align} \frac{3}{7} \div \frac{8}{7}\end{align} \)

\[\begin{align}&= \frac{3}{7} \times \frac{7}{8}\\&= \frac{{3 \times 7}}{{7 \times 8}}\\&= \frac{3}{8}\end{align}\]

iv) \(\begin{align} 2\frac{1}{3} \div \frac{3}{5}\end{align} \)

\[\begin{align}&= 2\frac{1}{3} \times \frac{5}{3}\\&= \frac{7}{3} \times \frac{5}{3}\\&= \frac{{7 \times 5}}{{3 \times 3}}\\&= \frac{{35}}{9}\;{\text{ (improper fraction) }}\end{align}\]

Converting \(\begin{align} \frac{{35}}{9}\end{align} \) into mixed fraction,

we get \(\begin{align} = 3\frac{8}{9} \end{align}\)

v) \(\begin{align} 3\frac{1}{2} \div \frac{8}{3}\end{align} \)

\[\begin{align}&= 3\frac{1}{2} \times \frac{3}{8}\\&= \frac{7}{2} \times \frac{3}{8}\\&= \frac{{7 \times 3}}{{2 \times 8}}\\&= \frac{{21}}{{16}}\;({\text{improper fraction}})\end{align}\]

Converting \(\begin{align} \frac{{21}}{{16}}\end{align} \) into mixed fraction,

we get \(\begin{align}= 1\frac{5}{{16}} \end{align}\)

vi) \(\begin{align} \frac{2}{5} \div 1\frac{1}{2}\end{align} \)

\[\begin{align}&= \frac{2}{5} \div \frac{3}{2}\\&= \frac{2}{5} \times \frac{2}{3}\\&= \frac{4}{{15}}\end{align}\]

vii) \(\begin{align} 3\frac{1}{5} \div 1\frac{2}{3}\end{align} \)

\[\begin{align}&= \frac{{16}}{5} \div \frac{5}{3}\\&= \frac{{16}}{5} \times \frac{3}{5}\\&= \frac{{48}}{{25}}\;{\text{ (improper fraction) }}\end{align}\]

Converting \(\begin{align} \frac{{48}}{{25}}\end{align} \) into mixed fraction,

we get \(\begin{align} = 1\frac{{23}}{{25}} \end{align}\)

viii) \(\begin{align} 2\frac{1}{5} \div 1\frac{1}{5}\end{align} \)

\[\begin{align}&= \frac{{11}}{5} \div \frac{6}{5}\\&= \frac{{11}}{5} \times \frac{5}{6}\\&= \frac{{11}}{6}\;{\text{ (improper fraction) }}\end{align}\]

Converting \(\begin{align} \frac{{11}}{6}\end{align} \) into mixed fraction,

we get \( \begin{align} = 1\frac{5}{6} \end{align}\)

  
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