Question

Question 121.
Neelam's father needs $1\frac{3}{4}$ m of cloth for the skirt of Neelam's new dress and $\frac{1}{2}$ m for the scarf. How much cloth must he buy in all?

Answer 1

Given that

The length of the cloth required for Neelam's skirt = $1\frac{3}{4}$ m
The length of th cloth required for her scarf = $\frac{1}{2}$ m

The total length of cloth required = length of cloth required for the skirt + length of cloth required for the scarf
On substituting the values we get:

Total cloth required = $1\frac{3}{4}$+$\frac{1}{2}$ m

We can express a mixed fraction as an improper fraction as $\frac{(\text{Whole}\times \text{Denominator})\text{+ Numerator}}{\text{Denominator}}$.

Total cloth required =$\frac{1\times 4+3}{4}+\frac{1}{2}=\frac{7}{4}+\frac{1}{2}$ m

Now, the LCM of the denominator of the fractions $\frac{7}{4}$ and $\frac{1}{2}$ i.e. the LCM of 4 and 2 is 4.
$\therefore$ Total cloth required =$\frac{7}{4}+\frac{1\times 2}{2\times 2}=\frac{7}{4}+\frac{2}{4}$ m
$\therefore$ Total cloth required =$\frac{7}{4}+\frac{2}{4}=\frac{7+2}{4}=\frac{9}{4}m$

We can express an improper fraction as a mixed fraction by dividing the numerator by denominator to obtain the quotient and the remainder.

Then the mixed fraction will be written as $\text{Quotient}\frac{\text{Remainder}}{\text{Divisor}}$.

$\left[\begin{array}{c}\because 4\left)9\right(2\\ \frac{8}{1}\end{array}\right]$

Total cloth required =$2\frac{1}{4}m$
So, he must buy $2\frac{1}{4}$ m of cloth.