# 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) $\frac{4}{25}$

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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

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

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

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

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