Ex.2.4 Q4 fractions-and-decimals Solutions-Ncert Maths Class 7

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Question

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

Text 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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