The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.
(a) $ \frac{2}{12} $
(b) $ \frac{3}{15} $
(c) $ \frac{8}{50} $
(d) $ \frac{16}{100} $
(e) $ \frac{10}{60} $
(f) $ \frac{15}{75} $
(g) $ \frac{12}{60} $
(h) $ \frac{16}{96} $
(i) $ \frac{12}{75} $
(j) $ \frac{12}{72} $
(k) $ \frac{3}{18} $
(l) $ \frac{4}{25} $

AcademicMathematicsNCERTClass 6

To do:

We have to change the given fractions to their simplest form.

Solution:

(a) $\frac{2}{12}=\frac{2\times1}{2\times6}$

$=\frac{1}{6}$

Therefore,

The simplest form of \( \frac{2}{12} \) is $\frac{1}{6}$.

(b) $\frac{3}{15}=\frac{3\times1}{3\times5}$

$=\frac{1}{5}$

Therefore,

The simplest form of \( \frac{3}{15} \) is $\frac{1}{5}$.

(c) $\frac{8}{50}=\frac{2\times4}{2\times25}$

$=\frac{4}{25}$

Therefore,

The simplest form of \( \frac{8}{50} \) is $\frac{4}{25}$.

(d) $\frac{16}{100}=\frac{4\times4}{4\times25}$

$=\frac{4}{25}$

Therefore,

The simplest form of \( \frac{16}{100} \) is $\frac{4}{25}$.

(e) $\frac{10}{60}=\frac{10\times1}{10\times6}$

$=\frac{1}{6}$

Therefore,

The simplest form of \( \frac{10}{60} \) is $\frac{1}{6}$.

(f) $\frac{15}{75}=\frac{15\times1}{15\times5}$

$=\frac{1}{5}$

Therefore,

The simplest form of \( \frac{15}{75} \) is $\frac{1}{5}$.

(g) $\frac{12}{60}=\frac{12\times1}{12\times5}$

$=\frac{1}{5}$

Therefore,

The simplest form of \( \frac{12}{60} \) is $\frac{1}{5}$.

(h) $\frac{16}{96}=\frac{16\times1}{16\times6}$

$=\frac{1}{6}$

Therefore,

The simplest form of \( \frac{16}{96} \) is $\frac{1}{6}$.

(i) $\frac{12}{75}=\frac{3\times4}{3\times25}$

$=\frac{4}{25}$

Therefore,

The simplest form of \( \frac{12}{75} \) is $\frac{4}{25}$.

(j) $\frac{12}{72}=\frac{12\times1}{12\times6}$

$=\frac{1}{6}$

Therefore,

The simplest form of \( \frac{12}{72} \) is $\frac{1}{6}$.

(k) $\frac{3}{18}=\frac{3\times1}{3\times6}$

$=\frac{1}{6}$

Therefore,

The simplest form of \( \frac{3}{18} \) is $\frac{1}{6}$.

(l) $\frac{4}{25}$

4 and 25 are co-prime numbers.

This implies,

The simplest form of \( \frac{4}{25} \) is $\frac{4}{25}$.

Therefore,

The three groups of equivalent fractions are 

$\frac{1}{6} = (a), (e), (h), (j), (k)$

$\frac{1}{5} = (b), (f), (g)$

$\frac{4}{25} = (c), (d), (i), (l)$

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

Advertisements