Question

Simplify and reduce to a simple fraction:
$\frac{1}{3}\times 4\frac{2}{3}÷3\frac{1}{2}\times \frac{1}{2}$

Answer 1

Converting the mixed fraction into improper fractions

$MixedFraction=\frac{Integralpart\times Denominator+Numerator}{Denominator}$

We will use the above formula to convert the mixed fraction into improper fraction.
$\frac{1}{3}\times 4\frac{2}{3}÷3\frac{1}{2}\times \frac{1}{2}$

$=\frac{1}{3}\times \frac{4\times 3+2}{3}÷\frac{3\times 2+1}{2}\times \frac{1}{2}$

$=\frac{1}{3}\times \frac{14}{3}÷\frac{7}{2}\times \frac{1}{2}$

Applying the rule of BODMAS and simplifying further
$=\frac{1}{3}\times \frac{14}{3}÷\frac{7}{2}\times \frac{1}{2}=\frac{1}{3}\times \frac{14}{3}\times \frac{2}{7}\times \frac{1}{2}$

[Performing division first]


$=\frac{1\times 14\times 2\times 1}{3\times 3\times 7\times 2}=\frac{2}{9}$

Hence, the given expression simplifies to $\frac{2}{9}$