Question

Rafiq exercised for $\dfrac{3}{6}$ of an hour, while Rohit exercised for $\dfrac{3}{4}$ of an hour. Who exercised for a longer time?

Answer 1

Hint: To find the who of the two given people exercised more, we need to bring them to the same units. We can choose hours or minutes. We will take the hourly approach. We are given two proper fractions. Thus, we will convert those fractions into decimals. This conversion will be with the help of long division. After division, whichever decimal has more overall value will be larger and thus that person will have exercised for a longer time.

Complete step-by-step solution:
It is given that Rafiq exercised for $\dfrac{3}{6}$ of an hour, while Rohit exercised for $\dfrac{3}{4}$ of an hour.
First, we will find the time taken by Rafiq.
To find the time, we need to find a decimal value of $\dfrac{3}{6}$ with the help of long division.
Since 3 is less than 6, we will first write 0 in the quotient and add a decimal after it. Also, add a zero to the dividend. Thus, the dividend will be 30.
$6\overset{0.}{\overline{\left){30}\right.}}$
Now, we know that 30 is 5 times 6. Therefore, the long division is as follows:
$6\overset{0.5}{\overline{\left){\begin{align}
  & \ \ 30 \\
 & -30 \\
 & \overline{\ \ \ \ 0} \\
\end{align}}\right.}}$
Therefore, Rafiq exercised for 0.5 hours.
Now, we will find the time for which Rohit exercised.
To find the time, we need to find a decimal value of $\dfrac{3}{4}$ with the help of long division.
Since 3 is less than 4, we will first write 0 in the quotient and add a decimal after it. Also, add a zero to the dividend Thus, the dividend will be 30.
$4\overset{0.}{\overline{\left){30}\right.}}$
We know that 8 times 4 is 32 and 7 times 4 is 28. Thus, we will write 7 in the quotient and subtract 28 from the denominator.
$4\overset{0.7}{\overline{\left){\begin{align}
  & \ \ 30 \\
 & -28 \\
 & \overline{\ \ \ \ 2} \\
\end{align}}\right.}}$
Now, we shall write a zero after 2, since the quotient already has a decimal. The dividend now is 20. We know that 20 is 5 times 4.
$4\overset{0.75}{\overline{\left){\begin{align}
  & \ \ 30 \\
 & -28 \\
 & \overline{\begin{align}
  & \ \ \ \ 20 \\
 & \ \ -20 \\
 & \overline{\ \ \ \ \ \ 0} \\
\end{align}} \\
\end{align}}\right.}}$
Therefore, Rohit exercised for 0.75 hours.
Hence, we can say that Rohit exercised more than Rafiq.

Note: The other approach is minute approach. We know that every hour has 60 mins. Therefore, to find the time in a minute, we shall multiply $\dfrac{3}{6}$ by 60 and $\dfrac{3}{4}$ by 60. 60 is divisible by both 6 and 4. Thus, Rafiq exercised for 30 mins whereas Rohit exercised for 45 mins.