Question

Rita has bought a carpet of size 4m x 6 1/3m. but her room size is 3 1/4m x 5 3/4m What fraction of area should be cut off to fit the carpet wall-to-wall (completely) in the room​

Answer 1

Given,

Area of carpet $\[ = 4m \times 6\frac{1}{3}m\]$

Room area $\[ = 3\frac{1}{4}m \times 5\frac{3}{4}m\]$

Solution,

Calculate the area of carpet,

$\[ = 4 \times 6\frac{1}{3}\]$

$\[ = 4 \times \frac{{19}}{3}\]$

$\[ = \frac{{76}}{3}{m^2}\]$

Calculate room area,

$\[ = 3\frac{1}{4} \times 5\frac{3}{4}\]$

$\[ = \frac{{13}}{4} \times \frac{{23}}{4}{m^2}\]$

$\[ = \frac{{299}}{{16}}{m^2}\]$

Calculate the fraction of area cut from the room to fit the carpet.

$\[ = \frac{{-299}}{{16}} + \frac{{76}}{3}\]$

$\[ = \frac{{-299 \times 3 + 76 \times 16}}{{48}}\]$

$\[ = \frac{{1216 - 897}}{{48}}\]$

$\[ = \frac{{319}}{{48}}{m^2}\]$

Hence the fraction of area should be cut is $\[\frac{{319}}{{48}}{m^2}\]$.