Ex 2.1 Q2 Fractions and Decimals Solution - NCERT Maths class 7

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Question

 Arrange the following in descending order: -

(i)\(\begin{align}\,\,\frac{2}{9},\frac{2}{3},\frac{8}{21}\end{align}\)

(ii)\(\begin{align}\,\,\frac{1}{5},\frac{3}{7},\frac{7}{10}\end{align}\)

Text Solution

What is Known?

Unlike fractions

What is unknown?

Descending order of the given fractions.

Reasoning:

Convert the given fractions into like fractions so the all of them have the same denominator. Now the fractions can be easily arranged into descending order by comparing their numerators.

Steps:

i)\(\begin{align}\,\,\frac{2}{9},\frac{2}{3},\frac{8}{21}\end{align}\)

Converting them into like fractions, we get

\(\begin{align} \,\,\,\,\,\,\,\frac{2\times 7}{9\times 7},\frac{2\times 21}{3\times 21},\frac{8\times 3}{21\times 3} \\ \Rightarrow \frac{14}{63},\frac{42}{63},\frac{24}{63} \\ \end{align}\)

Arranging in descending order

\(\begin{align}\Rightarrow \frac{42}{63}>\frac{24}{63}>\frac{14}{63}\end{align}\)

Therefore,\(\begin{align}\frac{2}{3}>\frac{8}{21}>\frac{2}{9}\end{align}\)

ii)\(\begin{align}\,\,\frac{1}{5},\frac{3}{7},\frac{7}{10}\end{align}\)

(converting them into like fractions, we get)

\(\begin{align} \,\,\,\,\frac{1\times 14}{5\times 14},\frac{3\times 10}{7\times 10},\frac{7\times 7}{10\times 7} \\ \Rightarrow \frac{14}{70},\frac{30}{70},\frac{49}{70} \\ \end{align}\)

Arranging in descending order

                      \(\begin{align}\Rightarrow \frac{49}{70}>\frac{30}{70}>\frac{14}{70}\end{align}\)

Therefore, \(\begin{align}\frac{2}{3}>\frac{8}{21}>\frac{2}{9}\end{align}\)

  
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