Question

Multiply:
$31\frac{1}{6}\times 31\frac{5}{6}$

Answer 1

$31\frac{1}{6}\times 31\frac{5}{6}$

Lets write these mixed fractions as addition i.e.

$31\frac{1}{6}=31+\frac{1}{6}$

Similarly,

$31\frac{5}{6}=31+\frac{5}{6}$

now we have

$=(31+\frac{1}{6})\times (31+\frac{5}{6})$

$=31(31+\frac{5}{6})+\frac{1}{6}(31+\frac{5}{6})$

$=31\times 31+31\times \frac{5}{6}+31\times \frac{1}{6}+\frac{1}{6}\times \frac{5}{6}$

$=961+31(\frac{1}{6}+\frac{5}{6})+\frac{5}{36}$

$=961+31\times \frac{6}{6}+\frac{5}{36}$

$=961+31\times 1+\frac{5}{36}$

$=961+31+\frac{5}{36}$

$=992+\frac{5}{36}$

$=992\frac{5}{36}$