Question

Rita has bought a carpet of size 4 m × `6 2/3` m. But her room size is `3 1/3` m × `5 1/3` m. What fraction of area should be cut off to fit wall to wall carpet into the room?

Answer 1

Given, carpet size = 4 m × `6 2/3` m

= `4 xx ((6 xx 3) + 2)/3`

= `4 xx ((18 + 2))/3`

= `4 xx 20/3`

= `4/1 xx 20/3`

= `80/3`

= `80/3` m²

∵ Room size = `3 1/3` m × `5 1/3` m

= `((3 xx 3) + 1)/3 xx ((5 xx 3) + 1)/3`

= `((9 + 1))/3 xx ((15 + 1))/3`

= `10/3 xx 16/3`

= `160/9` m²

∴ Difference between the area of carpet and room sizes = Size of the carpet – Size of the room

= `80/3 - 160/9`

= `(240 - 160)/9`  .....[∵ LCM of 3 and 9 = 9]

= `80/9` m² 

In fraction, `"Area that will be cut-off"/"Original area"`

= `((80/9))/((80/3))`

= `80/9 xx 3/80`

= `1/3`

Hence, `1/3` of area should be cut-off.