Question

Express each of the following ratios in its simplest forms:
$\left(ii\right)$ $3\frac{1}{2}:7$

Answer 1

Convert the mixed fraction into an improper fraction

An improper fraction is obtained by adding the whole part with a fractional Part of a mixed fraction.
Therefore,
$3\frac{1}{2}=3+\frac{1}{2}=\frac{3\times 2+1}{2}=\frac{6+1}{2}=\frac{7}{2}$

Find the simplest form of given ratio
$\Rightarrow 3\frac{1}{2}:7=\frac{7}{2}:\frac{7}{1}$
$=\frac{7}{2}÷\frac{7}{1}=\frac{7}{2}\times \frac{1}{7}=\frac{1}{2}$
$\Rightarrow 3\frac{1}{2}:7=1:2$
Hence, the simplest form of the ratio
$3\frac{1}{2}:7$ is $1:2$