Question

Ramesh and anil are classmates. They cycle 2 3/10km and 3 7/9km respectively everyday to reach their school. Who travels more and by how many kilometres

Answer 1

Given: Distance covered by Ramesh to reach school = $2\frac{3}{10}$ km

          Distance covered by Anil to reach school = $3\frac{7}{9}$ km

To find: Who covers more distance and by how many kilometers

Solution:

The given fractions are in mixed form. To apply any operation, first we need to change them to Improper fractions

$2\frac{3}{10}$ = (10 × 2 + 3)/10 = $\frac{23}{10}$ km

$3\frac{7}{9}$ = (9 ×3 + 7)/9 = $\frac{34}{9}$ km

Now, to compare the fraction, we need to make denominators of both the fractions equal. To do that, we will find the L.C.M. of the denominators and will multiply the fractions with required numbers to make their denominators equal to the L.C.M.

L.C.M. of 10 and 9 = 90

$\frac{23}{10}$ × $\frac{9}{9}$ = $\frac{207}{90}$

$\frac{34}{9}$ × $\frac{10}{10}$ = $\frac{340}{90}$

On comparing the numerators, we got to know

   $\frac{207}{90}$ < $\frac{340}{90}$

Hence, Anil covers more distance compared to Ramesh

To know, by how much, we need to subtract the distance covered by Ramesh from the distance covered by Anil

i.e., $\frac{340}{90}$ - $\frac{207}{90}$ = $\frac{340 - 207}{90}$ = $\frac{133}{90}$

Anil covers $\frac{133}{90}$ km more than Ramesh to reach school everyday.