Question

Jaidev takes $2{\displaystyle \frac{1}{5}}$ minutes to walk across the school ground. Rahul takes ${\displaystyle \frac{7}{4}}$ minutes to do the same. Who takes less time by what fraction?

Answer 1

Hint – In order to solve this question we have to convert mixed fraction into improper fraction and after that we have to make the denominator the same and then by using simple subtraction we will get our required answer.

Complete step-by-step answer:
In this question , it is given that –
Time taken by Jaidev –
=$2{\displaystyle \frac{1}{5}}$ min or ${\displaystyle \frac{11}{5}}$ min ( by converting mixed fraction into improper fraction )
Time taken by Rahul –
= ${\displaystyle \frac{7}{4}}$ min
Now in order to solve the question we need to make the denominator the same as it will help to determine the bigger problem.
$\Rightarrow {\displaystyle \frac{11}{5}}$ min ( Multiply Jaidev’s time by ${\displaystyle \frac{4}{4}}$)
= ${\displaystyle \frac{11}{5}}\times {\displaystyle \frac{4}{4}}$
= ${\displaystyle \frac{44}{20}}$ min
Now, for Rahul’s time –
= ${\displaystyle \frac{7}{4}}$ min.
${\displaystyle \frac{7}{4}}\times {\displaystyle \frac{5}{5}}$ ( Multiply Rahul’s time by ${\displaystyle \frac{5}{5}}$ )
= ${\displaystyle \frac{35}{20}}$
Now, we can easily determine that Rahul takes less time compared to Jaidev as we know that denominators are the same then the fraction with the higher value in the numerator will be larger. So by subtracting Rahul’s time by Jaidev time we will get –
$={\displaystyle \frac{44}{20}}\text{ - }{\displaystyle \frac{35}{20}}$ (Jaidev’s time – Rahul’s time )
= ${\displaystyle \frac{9}{20}}$ min
$\therefore$ We can say that Rahul took less time to walk across the ground by ${\displaystyle \frac{9}{20}}$ min (fraction).

Note- Whenever we face such types of problems , we have to first convert mixed fraction into improper fraction and then multiply the fraction with similar numerator and denominator to make the denominator same for both the given values rather than subtracting the fraction one by one. It helps us to determine the bigger fraction easily and will make our job simple .