Question

Simplify and reduce to a simple fraction:
$\frac{2}{3}\times 1\frac{1}{4}÷\frac{3}{7}of2\frac{5}{8}$

Answer 1

Converting the mixed fraction into improper fraction

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

We will use the above formula to convert the mixed fraction into improper fraction.

$\frac{2}{3}\times 1\frac{1}{4}÷\frac{3}{7}of2\frac{5}{8}$

$=\frac{2}{3}\times \frac{1\times 4+1}{4}÷\frac{3}{7}of\frac{2\times 8+5}{8}$

$=\frac{2}{3}\times \frac{5}{4}÷\frac{3}{7}of\frac{21}{8}$

Applying the rule of BODMAS and simplifying further

$\frac{2}{3}\times \frac{5}{4}÷\frac{3}{7}of\frac{21}{8}=\frac{2}{3}\times 54÷\frac{3}{7}\times \frac{21}{8}$
[Changing ‘of’ into the sign of multiplication]

$=\frac{2}{3}\times \frac{5}{4}÷\frac{9}{8}$
[Performing division first]

$=\frac{2}{3}\times \frac{5}{4}\times \frac{8}{9}$

$=\frac{2\times 5\times 8}{3\times 4\times 9}=\frac{20}{27}$

Hence, the given expression simplifies to $\frac{20}{27}$