Question & Answer
QUESTION

Ritu bought $5\dfrac{1}{2}l$ of milk and her sister bought $4\dfrac{3}{4}l$ of milk. Who bought less milk and by what quantity?

ANSWER Verified Verified
Hint: Change the given mixed fractions to the simple form of fraction. And compare the fractions by making the denominators the same quantity by how much less can be calculated by the difference of the quantity from higher to lower.

Complete step-by-step answer:
As it is given that Ritu has bought $5\dfrac{1}{2}l$ milk and her sister bought $4\dfrac{3}{4}l$ milk and hence, we need to determine the person who bought less milk and by how much. As the given volumes of the milk are in the form of mixed fraction, as we can’t compare two mixed fractions, so we need to convert them in simple form. As we know any mixed fraction $a\dfrac{c}{d}$ can be written in simple fraction as $\dfrac{a\times d+c}{d}$ .
So, using the above relation, we can get volumes of the milk for both Ritu and her sister as Volume of milk bought by Ritu $=5\dfrac{1}{2}=\dfrac{5\times 2+1}{2}=\dfrac{11}{2}$ and
Volume of milk bought by her sister $=4\dfrac{3}{4}=\dfrac{4\times 4\times 3}{4}=\dfrac{19}{4}$ .
So, in the form of a simple fraction, Ritu and her sister have bought $\dfrac{11}{2}l,\dfrac{19}{4}l$ milk. Now, we cannot compare them because of their denominators as they are not the same. So, we have to mark denominators equal for comparison. So, we need to find LCM of denominator and hence, multiply it to the numerators. It can be done in following way;
As LCM of 2 and 4 = 4, for the fraction $\dfrac{11}{2}$ , we have to divide LCM by ‘2’ and hence multiply it to 11. So, we get a fraction as $\dfrac{11}{2},\dfrac{19}{4}$ . LCM of denominator (2, 4) is 4.
So, we can rewrite the fractions, by replacing numerator by the product of given numerator and the number calculated by dividing LCM by the given denominator and denominators of each are replaced by their LCM. Hence, we get fractions as
$\begin{align}
  & \dfrac{11\times 2}{4},\dfrac{19\times 1}{4} \\
 & \dfrac{22}{4},\dfrac{19}{4} \\
\end{align}$
Now, we can compare both the fraction as now their denominators are the same. So, we get $\dfrac{22}{4}>\dfrac{19}{4}$ . Hence milk bought by Ritu is higher in quantity than her sister. Now, we can get the quantity by which the volume of milk bought by Ritu is higher than her sister, by the difference of the amounts of the volume of milk bought by them. So, we get
$\dfrac{22}{4}-\dfrac{19}{4}=\dfrac{22-19}{4}=\dfrac{3}{4}l$
It means Ritu’s sister has bought less milk than Ritu by quantity of $\dfrac{3}{4}l$ .

Note: One may compare the fractions $\dfrac{11}{2},\dfrac{19}{4}$ by multiplying and dividing the first fraction by ‘4’ and second fraction by ‘2’ as well i.e. with the denominators of each other. So we get
$\dfrac{44}{8},\dfrac{38}{8}$ . Hence it can be another approach without calculating the LCM of both. For comparison of two fraction, their denominators should be same, one may go wrong if he or she given $\dfrac{19}{4}$ as higher fraction than $\dfrac{11}{2}$ because denominator and numerator of $\dfrac{19}{4}$ are higher than $\dfrac{11}{2}$ but it is wrong, because $\dfrac{11}{2}$ is greater than $\dfrac{19}{4}$ . So, don’t confuse and take care that the denominator of fractions should be the same for comparison of the fraction.