From a 9 m long cloth, two pieces of $3\frac{3}{4}$ and $4\frac{1}{2}$ long are cut. What is the length of the remaining cloth?
Express the answer as a fraction in its simplest form.

Given :

The total length of the cloth = 9 m

The length of the two pieces that are cut = $3\frac{3}{4} m\ and\ 4\frac{1}{2} m$

To find :

We have to find the length of the remaining cloth.

Solution :

The length of the remaining piece = Total length - Sum of the lengths of the two

pieces cut

$  =9-\left( 3\frac{3}{4} +4\frac{1}{2}\right)$

$=9-\left(\frac{3\times 4+3}{4} +\frac{4\times 2+1}{2}\right)$

$=9-\left(\frac{12+3}{4} +\frac{8+1}{2}\right)$

$=9-\left(\frac{15}{4} +\frac{9}{2}\right)$

$=9-\left(\frac{15\times 1+9\times 2}{4}\right)$   [ LCM of 4 and 2 is 4]

$=9-\left(\frac{15+18}{4}\right)$

$=9-\left(\frac{33}{4}\right)$

$=\frac{9}{1} -\frac{33}{4}$

$=\frac{9\times 4-33\times 1}{4}$              [ LCM of 1 and 4 is 4]

$=\frac{36-33}{4}\ =\frac{3}{4} $                    

The length of the remaining cloth is $\frac{3}{4} \ m.$ 

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Updated on: 10-Oct-2022

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