Question

Rizwaan lives \[7\dfrac{3}{4}\] km away from his workshop. In the morning he covers \[2\dfrac{1}{2}\] km of his distance by foot and the remaining distance by local bus, how much distance is covered by him in the local bus?

Answer 1

Hint: We solve this problem by converting the distance of mixed fraction to proper fraction. We use the result that the conversion of mixed fraction to proper fraction is done as
\[\Rightarrow a\dfrac{b}{c}=\dfrac{\left( c\times a \right)+b}{c}\]
After converting the mixed fractions to proper fractions we use the simple formula that is adding all the individual distances of traveling in different ways equal to total distance between two points.

Complete step by step answer:
We are given that Rizwaan lives at \[7\dfrac{3}{4}\] km away from his workshop
Let us assume that the distance between Rizwaan living place and his workshop as
\[\Rightarrow D=7\dfrac{3}{4}km\]
We know that the conversion of mixed fraction to proper fraction is done as
\[\Rightarrow a\dfrac{b}{c}=\dfrac{\left( c\times a \right)+b}{c}\]
By using this conversion to above equation we get
\[\begin{align}
  & \Rightarrow D=\dfrac{\left( 7\times 4 \right)+3}{4}km \\
 & \Rightarrow D=\dfrac{31}{4}km \\
\end{align}\]
We are given that Rizwaan covers \[2\dfrac{1}{2}\] km by foot.
Let us assume that the distance covered by him by foot as
\[\Rightarrow d=2\dfrac{1}{2}km\]
Now, by converting the above mixed fraction to proper fraction we get
\[\begin{align}
  & \Rightarrow d=\dfrac{\left( 2\times 2 \right)+1}{2}km \\
 & \Rightarrow d=\dfrac{5}{2}km \\
\end{align}\]
Now, let us assume that the distance covered by Rizwaan by local bus as \['x'\]
We know that adding all the individual distances of traveling in different ways equal to total distance between two points.
Now, by using the above condition then we get
\[\begin{align}
  & \Rightarrow D=d+x \\
 & \Rightarrow x=D-d \\
\end{align}\]
Now, by substituting the required values in above equation and by subtracting by using the LCM we get
\[\begin{align}
  & \Rightarrow x=\dfrac{31}{4}-\dfrac{5}{2} \\
 & \Rightarrow x=\dfrac{31-10}{4} \\
 & \Rightarrow x=\dfrac{21}{4}km \\
\end{align}\]
Now, by converting the above proper fraction to mixed fraction we get
\[\Rightarrow x=5\dfrac{1}{4}km\]

Therefore the distance covered by Rizwaan by local train is \[5\dfrac{1}{4}km\]

Note: We can add or subtract the mixed fractions directly without converting them to proper fractions.
If the number is of the form \[a\dfrac{b}{c}\] then \['a'\] is called the real part and \[\dfrac{b}{c}\] is called fractional part.
When two mixed fractions are added or subtracted together then we can add or subtract real part separately and fractional part separately then we can combine them to get a mixed fraction.
Here we have the distance covered by Rizwaan in local bus as
\[\begin{align}
  & \Rightarrow D=d+x \\
 & \Rightarrow x=D-d \\
\end{align}\]
Now, by substituting the values in mixed fractions we get
\[\Rightarrow x=7\dfrac{3}{4}-2\dfrac{1}{2}\]
Now by subtracting real part separately and fractional part separately then we get
\[\begin{align}
  & \Rightarrow x=\left( 7-2 \right)\left( \dfrac{3}{4}-\dfrac{1}{2} \right) \\
 & \Rightarrow x=5\dfrac{1}{4} \\
\end{align}\]
Here is not a multiplication form but it is a mixed fraction form.
Therefore the distance covered by Rizwaan by local train is \[5\dfrac{1}{4}km\]