Question

Express the following ratios in their simplest form.

$2\frac{1}{15}:3\frac{1}{5}$

Answer 1

We know that mixed fraction can be written as:

$a\frac{b}{c}=\frac{a\times c+b}{c}$and $\frac{a}{b}:\frac{c}{d}=a\times d:c\times b$

So, as we have given,

$2\frac{1}{15}=\frac{2\times 15+1}{15}$

$=\frac{31}{15}$

$3\frac{1}{5}=\frac{3\times 5+1}{5}$

$=\frac{16}{5}$

So the ratio becomes:$\frac{31}{15}:\frac{16}{5}$

Using the concept$\frac{a}{b}:\frac{c}{d}=a\times d:c\times b$ we get,

$\frac{31}{15}:\frac{16}{5}=31\times 5:16\times 15$

$=\frac{31\times 5}{16\times 15}=\frac{31\times 5}{16\times 5\times 3}$

$=\frac{31}{16\times 3}=\frac{31}{48}$

Hence, the simplest form of the given ratio is $31:48$.