Question

Question 112

Rita has bought a carpet of size $4m\times 6\frac{2}{3}m$. But her room size is $3\frac{1}{3}m\times 5\frac{1}{3}$, what fraction of the area should be cut - off to fit wall to wall carpet into the room?

Answer 1

Given carpet size
$=4m\times 6\frac{2}{3}m=4\times \frac{(6\times 3)+2}{3}=4\times \frac{(18+2)}{3}=4\times \frac{20}{3}=\frac{4}{1}\times \frac{20}{3}=\frac{80}{3}=\frac{80}{3}{m}^2\because Roomsize=3\frac{1}{3},\times 5\frac{1}{3}m=\frac{(3\times 3)+1}{3}\times \frac{(5\times 3)+1}{3}=\frac{(9+1)}{3}\times \frac{(15+1)}{3}=\frac{10}{3}\times \frac{16}{3}=\frac{16}{9}{m}^2$
$\therefore$ Difference between the area of carpet and room sizes = size fo the carpet- Size of the room
$=\frac{80}{3}=\frac{160}{9}=\frac{240-160}{9}=\frac{80}{9}{m}^2$
In fraction
$\frac{\text{Area that will be cut-off}}{\text{Original area}}=\frac{\left(\frac{80}{9}\right)}{\left(\frac{80}{3}\right)}=\frac{80}{9}\times \frac{3}{80}=\frac{1}{3}$