Check whether the following fractions an equivalent or not.
a. $ \frac{18}{45} $ and $ \frac{28}{70} $
b. $ \frac{10}{13} $ and $ \frac{60}{65} $
c. $ \frac{16}{14} $ and $ \frac{32}{28} $

Given:

Given fractions are

a. \( \frac{18}{45} \) and \( \frac{28}{70} \)
b. \( \frac{10}{13} \) and \( \frac{60}{65} \)
c. \( \frac{16}{14} \) and \( \frac{32}{28} \)

To do:

We have to check whether the given fractions are equivalent.

Solution:

To check whether the given fractions are equivalent we have to simplify them to the simplest fractions.

(a) $\frac{18}{45}=\frac{9\times2}{9\times5}$

$=\frac{2}{5}$

$\frac{28}{70}=\frac{14\times2}{14\times5}$

$=\frac{2}{5}$

Therefore, \( \frac{18}{45}, \frac{28}{70} \) are equivalent fractions.

(b) $\frac{10}{13}=\frac{10\times1}{13\times1}$

$=\frac{10}{13}$

$\frac{60}{65}=\frac{5\times12}{5\times13}$

$=\frac{12}{13}$

$\frac{10}{13}≠\frac{60}{65}$

Therefore, \( \frac{10}{13}, \frac{60}{65} \) are not equivalent fractions.

(c) $\frac{16}{14}=\frac{2\times8}{2\times7}$

$=\frac{8}{7}$

$\frac{32}{28}=\frac{4\times8}{4\times7}$

$=\frac{8}{7}$

Therefore, \( \frac{16}{14}, \frac{32}{28} \) are equivalent fractions.

Tutorialspoint

Updated on: 10-Oct-2022

54 Views

Kickstart Your Career

Get certified by completing the course

Get Started