Arrange the following in descending order. (i) 23,421,79 (ii) 45,67,13

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Question

Arrange the following in descending order.
(i) $\frac{2}{3}, \frac{4}{21}, \frac{7}{9}$
(ii) $\frac{4}{5}, \frac{6}{7}, \frac{1}{3}$
[2 MARKS]

Options:

Answer: Option A
:
Each option: 1 Mark
Now,

\frac{7}{9}, \frac{2}{3}, \frac{4}{21}

The LCM of the denominators of the above fractions = 63

\Rightarrow \frac{7 \times 7}{9 \times 7}, \frac{2 \times 21}{3 \times 21}, \frac{4 \times 3}{21 \times 3}

\Rightarrow \frac{49}{63}, \frac{42}{63}, \frac{12}{63}

Hence, arranging in descending order we have

\frac{49}{63} > \frac{42}{63} > \frac{12}{63}

i.e.,

\frac{7}{9} > \frac{2}{3} > \frac{4}{21}

(ii) The LCM of the denominators of the given fractions = 105
Making them like fractions. We have,

\frac{1 \times 35}{3 \times 35}, \frac{4 \times 21}{5 \times 21}, \frac{6 \times 15}{7 \times 15}

\frac{35}{105}, \frac{84}{105}, \frac{90}{105}

\Rightarrow \frac{6}{7} > \frac{4}{5} > \frac{1}{3}

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