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]

Answer 1

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,

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

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

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