Question

Question 117.
Nazima gave $2\frac{3}{4}$ L out of the $5\frac{1}{2}$ L of juice she purchased to her friends.
How many litres of juice is left with her?

Answer 1

Given that

Quantity of juice Nazima has = $5\frac{1}{2}$ L
The quantity of juice Nazima gave to her friend = $2\frac{3}{4}$ L

The quantity of juice left with Nazima + Quantity of juice she gave to her friend = Total quantity of juice Nazima had

Quantity of juice left with Nazima = Total quantity of juice Nazima had - Quantity of juice she gave to her friend

On substituting the values we get:

Juice left with her = $5\frac{1}{2}$ - $2\frac{3}{4}$ L

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

$\therefore$ Juice left with her = $\frac{5\times 2+1}{2}-\frac{2\times 4+3}{4}=\frac{11}{2}-\frac{11}{4}$ L

Now, the LCM of the denominator of the fractions $\frac{11}{2}$ and $\frac{11}{4}$ i.e. the LCM of 2 and 4 is 4.

$\therefore$ Juice left with her $=\frac{11}{2}-\frac{11}{4}=\frac{11\times 2}{2\times 2}-\frac{11}{4}=\frac{22}{4}-\frac{11}{4}=\frac{22-11}{4}=\frac{11}{4}$ 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 $\text{Quotient}\frac{\text{Remainder}}{\text{Divisor}}$.

$\left[\begin{array}{c}\because 4\left)11\right(2\\ \frac{8}{3}\end{array}\right]$

$\therefore$ Juice left with her $=2\frac{3}{4}L$
So, $2\frac{3}{4}$ L of juice is left with her.