Question

Mrs. Soni bought $7\dfrac{1}{2}$ litres of milk. Out of this milk, $5\dfrac{3}{4}$ litres was consumed. How much milk is left with her.
$\begin{align}
  & \left( A \right)\,1\dfrac{3}{4} \\
 & \left( B \right)1\dfrac{4}{7} \\
 & \left( C \right)1\dfrac{5}{\begin{align}
  & 2 \\
\end{align}} \\
 & \left( D \right)1\dfrac{2}{5} \\
\end{align}$

Answer 1

Hint:In this type of question, at first convert the given mixed fraction into an improper fraction, so we are able to calculate it. Second, Apply mathematical operation according to the requirement of the question i.e We have to subtract consumed milk from total quantity of milk. Hence ,we get a total quantity of milk left with her.

Complete step-by-step answer:
The given numbers are in mixed fraction , to calculate we should convert it in improper fraction.
Then
$7\dfrac{1}{2}$=$\dfrac{15}{2}$
$5\dfrac{3}{4}$=$\dfrac{23}{4}$
Now according to the question, Mrs. Soni bought $7\dfrac{1}{2}$=$\dfrac{15}{2}$ litres of milk.
And they were given $5\dfrac{3}{4}$=$\dfrac{23}{4}$ litres of milk consumed.
We have to find how much milk is left with her.
For this we should subtract the amount of consumed milk from the amount of whole milk.
Therefore amount of left milk $=\dfrac{15}{2}-\dfrac{23}{4}$
Now to calculate above numbers first we have to take the LCM of the denominator.
LCM of $2$ and $4$ will be $4$

Then multiply the first number to LCM and same with the second number.
Amount of left milk= $\dfrac{\dfrac{15}{2}-\dfrac{23}{4}}{4}$
                                    $\begin{align}
  & =\dfrac{30-23}{4} \\
 & =\dfrac{7}{4} \\
\end{align}$
Because in question the options numbers are in mixed fraction, so we should convert improper fraction $\dfrac{7}{4}$ into mixed form.
$\dfrac{7}{4}=1\dfrac{3}{4}$
Therefore the amount of milk left with Mrs. Soni is $1\dfrac{3}{4}$liters.

So, the correct answer is “Option A”.

Note:In such type of questions, where we have to calculate fraction, we can also the concept of common denominator like in the above question we have two fraction numbers with different denominators. To subtract them we can change it into common denominator by multiplying and dividing the fraction with same number $\dfrac{15}{2}=\dfrac{15\times 2}{2\times 2}=\dfrac{30}{4}$.Now both numbers have the same denominator and perform arithmetic operation.