Ex.2.3 Q4 fractions-and-decimals Solutions-Ncert Maths Class 7

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Question

Which is greater?

(i) \(\begin{align} \frac{2}{7}{\text{ of }}\frac{3}{4}{\text{ or }}\frac{3}{5}{\text{ of }}\frac{5}{8}\end{align} \)

ii) \(\begin{align} \frac{1}{2}{\text{ of }}\frac{6}{7}{\text{ or }}\frac{2}{3}{\text{ of }}\frac{3}{7}\end{align} \)

Text Solution

What is known?

Fractions.

What is unknown?

Which is greater.

Reasoning:

Convert the fractions into like fractions then compare by numerator.

Steps:

(i) \(\begin{align} \frac{2}{7}{\text{ of }}\frac{3}{4}{\text{ or }}\frac{3}{5}{\text{ of }}\frac{5}{8}\end{align} \)

\[\begin{align}&= \frac{2}{7} \times \frac{3}{4} = \frac{3}{{14}}\\&= \frac{3}{5} \times \frac{5}{8} = \frac{3}{8}\end{align}\]

Converting these fractions into like fraction, we get

\[\begin{align}\frac{3}{{14}} &= \frac{{3 \times 4}}{{14 \times 4}} = \frac{{12}}{{56}}\\\frac{3}{8} &= \frac{{3 \times 7}}{{8 \times 7}} = \frac{{21}}{{56}}\end{align}\]

Since,

\[\begin{align}\frac{{21}}{{56}} > \frac{{12}}{{56}}\\\frac{3}{8} > \frac{3}{{14}}\end{align}\]

Thus \(\begin{align} \frac{3}{5}{\rm{ of }}\frac{5}{8}\end{align} \) is greater.

ii) \(\begin{align} \frac{1}{2}{\text{ of }}\frac{6}{7}{\text{ or }}\frac{2}{3}{\text{ of }}\frac{3}{7}\end{align} \)

\[\begin{align}&= \frac{1}{2} \times \frac{6}{7} = \frac{3}{7}\\&= \frac{2}{3} \times \frac{3}{7} = \frac{2}{7}
\end{align}\]

On comparing, we get

\[\frac{3}{7} > \frac{2}{7}\]

Thus, \(\begin{align} \frac{1}{2}{\rm{ of }}\frac{6}{7}\end{align} \) is greater.

  
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