Find answers to the following. Write and indicate how you solved them.
(a) Is $ \frac{5}{9} $ equal to $ \frac{4}{5} $ ?
(b) Is $ \frac{9}{16} $ equal to $ \frac{5}{9} $ ?
(c) Is $ \frac{4}{5} $ equal to $ \frac{16}{20} $ ?
(d) Is $ \frac{1}{15} $ equal to $ \frac{4}{30} $ ?

To do:

We have to find whether the given statements are true.

Solution:

(a) To check whether \( \frac{5}{9} \) is equal to \( \frac{4}{5} \), we have to convert them to like fractions.

LCM of denominators 9 and 5 is 45.

This implies,

$\frac{5}{9}\times\frac{5}{5}=\frac{25}{45}$

$\frac{4}{5}\times\frac{9}{9}=\frac{36}{45}$

$25 ≠ 36$

This implies,

$\frac{36}{45} ≠ \frac{25}{45}$

Therefore,\( \frac{5}{9} \) is not equal to \( \frac{4}{5} \).

(b) To check whether \( \frac{9}{16} \) is equal to \( \frac{5}{9} \), we have to convert them to like fractions.

LCM of denominators 16 and 9 is 144.

This implies,

$\frac{9}{16}\times\frac{9}{9}=\frac{81}{144}$

$\frac{2}{9}\times\frac{16}{16}=\frac{32}{144}$

$81 ≠ 32$

This implies,

$\frac{81}{144} ≠ \frac{32}{144}$

Therefore,\( \frac{9}{16} \) is not equal to \( \frac{5}{9} \).

(c) To check whether \( \frac{4}{5} \) is equal to \( \frac{16}{20} \), we have to convert them to like fractions.

LCM of denominators 5 and 20 is 20.

This implies,

$\frac{16}{20}=\frac{4\times4}{4\times5}$

$=\frac{4}{5}$

Here,

Numerators are same ($4 = 4$)

Therefore,\( \frac{4}{5} \) is equal to \( \frac{16}{20} \).

(d) To check whether \( \frac{1}{15} \) is equal to \( \frac{4}{30} \), we have to convert them to like fractions.

LCM of denominators 15 and 30 is 30.

This implies,

$\frac{4}{30}=\frac{2\times2}{2\times15}$

$=\frac{2}{15}$

Here,

$2 > 1$

This implies,

$\frac{2}{15}>\frac{1}{15}$

Therefore,\( \frac{1}{15} \) is not equal to \( \frac{4}{30} \).

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Updated on: 10-Oct-2022

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