Question

Ayesha's grandmother buys 3/4m of lace for her handkerchief.she use only 2/3 m of the lace .what length of lace is left behind?​

Answer 1

Given:

Length of lace bought = $\frac{3}{4} m$

Length of lace used = $\frac{2}{3}m$

To find:

Length of lace remaining.

Solution:

Ayesha's grandmother used $\frac{2}{3}m$ of the lace from the $\frac{3}{4} m$ of lace that she bought. To find the remaining length of the lace that was not used by her, we subtract the used up lace from the total length of the lace that she initially bought.

Remaining lace length = Original lace length - Used up lace length for handkerchief

Remaining lace length = $\frac{3}{4}-\frac{2}{3}$

The denominators of both fractions are not same because of which we cannot simply subtract the. First, the denominators should be same. For this reason, we find the LCM of the denominators. The LCM of $3$ and $4$ is $12$. So, the denominator will be 12 which will be common for both. Whatever number is multiplied with the denominator to obtain LCM, that same number is multiplied with numerator too.

In $\frac{3}{4}$, the denominator is $4$ . To make it $12$, we multiply $4$ with $3$.

$3$ is also multiplied with numerator $3$.

Similarly, for $\frac{2}{3}$. Denominator $3$ is multiplied with $4$ to obtain the LCM of $12$. The numerator $2$ is multiplied with $4$.  This is shown below:

Remaining lace length = $\frac{3}{4}*\frac{3}{3} -\frac{2}{3}*\frac{4}{4}$

Remaining lace length = $\frac{9}{12}-\frac{8}{12}$

Now, the denominators are same and we can do simple subtraction of the numerators.

Remaining lace length = $\frac{1}{12}m$

$\frac{1}{12}m$ of lace is left behind when Ayesha's grandmother has used up $\frac{2}{3}m$ of lace from $\frac{3}{4} m$ of lace she bought.