Question

Vedant walks $\dfrac{7}{{10}}$ km from his home to the bus stop. He boards a bus and travels $\dfrac{3}{5}$km to his school. What is the total distance (a) meters (b) kilometres travelled by vedant?

Answer 1

Hint: This problem comes under fraction. We need to find the distance of his home to school. For that first we need to add the distance between his home and bus stop and bus stop to school. The question is in the form of fraction so we need to solve in fraction addition and complete step by step explanation and we also convert the fraction into kilometres and meters.

Complete step-by-step answer:
It is given that in the question,
The distance vedant walks from his home to bus stop he boards $ = \dfrac{7}{{10}}$
The distance vedant walks from bus boarding to his school$ = \dfrac{3}{5}$
Now, we need to add the distance vedant walks from his home to his school
$ \Rightarrow \dfrac{7}{{10}} + \dfrac{3}{5}$
By taking the least common multiple for both the denominator \[10\] and \[5\].
\[
  2{\text{ }}\left| \!{\underline {\,
  {10,5} \,}} \right. \\
  5{\text{ }}\left| \!{\underline {\,
  {5,1} \,}} \right. \\
  {\text{ }}\left| \!{\underline {\,
  {1,1} \,}} \right. \\
 \]
Least common multiple \[ = 2 \times 5 = 10\]
\[\therefore \]The Least common multiple of \[10\] and \[5\] is $ = 10$
Now adding both the fraction, we get
$ \Rightarrow \dfrac{7}{{10}} + \dfrac{3}{5}$
Now, convert the denominator to \[10\] and in numerator multiply the same number which was multiplied in denominator
\[ \Rightarrow \dfrac{{7 \times 1}}{{10 \times 1}} + \dfrac{{3 \times 2}}{{5 \times 2}}\]
Multiplying the terms we get,
\[ \Rightarrow \dfrac{7}{{10}} + \dfrac{6}{{10}}\]
Now, the denominator is same adding the numerator we get,
\[ \Rightarrow \dfrac{{7 + 6}}{{10}}\]
Adding the terms we get,
\[ \Rightarrow \dfrac{{13}}{{10}}\]
Thus the total distance vedant walked from his home to his school is \[ = \dfrac{{13}}{{10}}km\]
Now (a) convert the fraction into meters
\[ \Rightarrow 1km = 1000m\]
\[ \Rightarrow \dfrac{{13}}{{10}}km = \dfrac{{13}}{{10}} \times 1000m = 1.3km\]
$ \Rightarrow 1300m$
Now (b) Convert into km
$ \Rightarrow 1 m = \dfrac{1}{{1000}}km$
$ \Rightarrow 1300m = \dfrac{{1300}}{{1000}}km$
$ \Rightarrow 1.3km$
Thus, we find the total distance the vedant walked from his home to his school in meters and kilometers.

Note: This kind of problem is basic addition and the problem is theoretical so we need to observe the question clearly and also we want to convert the units as mentioned in the question. This question is mainly on fraction and measurements concepts.