Question

The length of a rope is $12$$\frac{1}{2}$$m$$.$ if $3\frac{1}{2}$$m$ is cut out$,$ find the length of the remaining rope

Answer 1

Step 1 : write the given data

Total length of rope $=$ $12$$\frac{1}{2}$$m$ $=$ $\frac{25}{2}$$m$

$($$12$$\frac{1}{2}$$=$$\frac{(12\times 2)+1}{2}$$=$$\frac{24+1}{2}$ $=$$\frac{25}{2}$$)$

Length cut off $=$$3\frac{1}{2}$$m$ $=$$\frac{7}{2}$$m$

$($$3\frac{1}{2}$ $=$ $\frac{(3\times 2)+1}{2}$ $=$$\frac{6+1}{2}$ $=$$\frac{7}{2}$$)$

Step 2 : Find the length of remaining rope

Length of remaining rope $=$Total length of rope $-$Length cut off

$=$$\frac{25}{2}$$-$$\frac{7}{2}$

The bottom numbers are same, so subtract the numerators and put the answer over the denominator

$\frac{25}{2}$$-$$\frac{7}{2}$ $=$$\frac{25-7}{2}$ $=$$\frac{18}{2}$ $=$$9$

Hence$,$ Length of the remaining rope is $9$$m$.