Question

Question 116.
Sunil purchased $12\frac{1}{2}$ L of juice on Monday and $14\frac{3}{4}$ L of juice on Tuesday. How many litres of juice did he purchase together in two days?

Answer 1

Given that

Amount of juice purchased by Sunil on Monday = $12\frac{1}{2}$ L
Amount of juice purchased by Sunil on Tuesday = $14\frac{3}{4}$ L

Amount of juice purchased by Sunil together in the two days = Amount of juice purchased by him on Monday + Amount of juice purchased by him on Tuesday

On substituting the values we get:
Total juice purchased = $12\frac{1}{2}$+$14\frac{3}{4}$ L
Total juice purchased = $\frac{12\times 2+1}{2}$+$\frac{14\times 4+3}{4}$ L

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

Total juice purchased = $\frac{25}{2}+\frac{59}{4}$ L

The LCM of the denominator of the fractions $\frac{25}{2}$, $\frac{59}{4}$ i.e. LCM of 2 and 4 is 4.
$\therefore$ Total juice purchased = $\frac{25\times 2}{2\times 2}+\frac{59\times 1}{4\times 1}$ L

Total juice purchased = $\frac{50}{4}+\frac{59}{4}=\frac{50+59}{4}=\frac{109}{4}$ L

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 $\text{Quotient}\frac{\text{Remainder}}{\text{Divisor}}$.

$\left[\begin{array}{c}\because 4\left)109\right(27\\ \frac{8}{29}\\ \frac{28}{1}\end{array}\right]$

$\therefore$ Total juice purchased = $27\frac{1}{4}L$
So, he purchased $27\frac{1}{4}$ L of juice in two days.