Question

Vedant walks $\dfrac{7}{{10}}$km from his home to the bus stop. He boards a bus at the bus stop and travels $\dfrac{3}{5}$km to his school. What is the total distance in
(a)Meters
(b)Kilometres

Answer 1

Hint: This problem is related to Fractional Addition. In the fractional addition, it is required to find out Least Common Multiple (LCM) among the denominators and then add the fractions.

Complete step-by-step answer:
As we know that Vedant walks from home to bus stop and the distance is given in km as
$ = \dfrac{7}{{10}}$………………………………. (1)
And travels by bus to go to his school is given in km as
$ = \dfrac{3}{5}$ ………………………………. (2)
Therefore, the total distance travelled will be equal to addition of expression (1) and (2) as
Total distance $ = \dfrac{7}{{10}} + \dfrac{3}{5}$
Now, taking the LCM of both the denominators, we will get 10. Now adding these fractions as
Below,
 $
   = \dfrac{7}{{10}} + \dfrac{3}{5} \\
   = \dfrac{{7 + 3 \times 2}}{{10}} \\
   = \dfrac{{7 + 6}}{{10}} \\
   = \dfrac{{13}}{{10}} \\
 $
Therefore, the total distance in km is = $\dfrac{{13}}{{10}}$ ……………………….. (3)
Case 1: Total distance in meters (m)
As we know that
1 km = 1000 m
Therefore, total distance in meters from expression (3) will be
$
   = \dfrac{{13}}{{10}} \times 1000 \\
   = 13 \times 100 \\
   = 1300{\text{ m}} \\
 $
The answer to the case (1) = 1300 m
Case 2: Total distance in kilometres (km)
It is already calculated, hence the total distance in km = $\dfrac{{13}}{{10}}$km

Note: To solve such problems, one must have knowledge of how to calculate LCM. Calculation of LCM can be understood with the following example:
Say, we have to find out LCM for 5, 8, and 10 then, following are the steps,
List down the multiples of given numbers and find the lowest common number in all of them. That number will be the LCM.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
Multiples of 8: 8, 16, 24, 32, 40, 48, 56
Multiples of 10: 10, 20, 30, 40, 50, 60
Now, the number 40 is the LCM of 5, 8 and 10.