# 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 $\frac{4}{30}$ ?

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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 $\frac{4}{30}$.

Updated on 10-Oct-2022 13:33:00