Question

Katty rode her bicycle $7{\displaystyle \frac{1}{2}}$ km on yesterday and $4{\displaystyle \frac{3}{8}}$ km on today. Find the distance travelled by her altogether on both the days.

Answer 1

Hint:
First convert the mixed fractions into improper fraction by first multiplying the fraction’s denominator into the whole number and then adding the obtained number to the numerator. Then add the distance travelled by her on yesterday and today to get the total distance travelled by Katty.

Complete step by step solution:
The distance travelled by Katty on yesterday=$7{\displaystyle \frac{1}{2}}$ km
And the distance travelled by Katty on today=$4{\displaystyle \frac{3}{8}}$ km
We have to find the distance travelled by her altogether.
Here the distances are given in mixed fraction so first we have to convert them into improper fraction.
First we convert $7{\displaystyle \frac{1}{2}}$ into improper fraction-
To convert a mixed fraction into proper fraction first we first multiply the fraction’s denominator into the whole number written beside it.
So on multiplying we get, $2\times 7=14$
Now we add this obtained number to the numerator. So on addition we get,
$\Rightarrow 14+1=15$
Then we write this result on the top of the denominator. So we can write-
$\Rightarrow 7{\displaystyle \frac{1}{2}}={\displaystyle \frac{14}{2}}$ --- (i)
Then covert $4{\displaystyle \frac{3}{8}}$ into improper fraction-
To convert a mixed fraction into proper fraction first we first multiply the fraction’s denominator into the whole number written beside it.
So on multiplying we get,$8\times 4=32$
Now we add this obtained number to the numerator. So on addition we get,
$$\Rightarrow 32+3=35$$
Then we write this result on the top of the denominator. So we can write-
$\Rightarrow 4{\displaystyle \frac{3}{8}}={\displaystyle \frac{35}{3}}$ -- (ii)
Now the total distance travelled by Katty will be the sum of the distance travelled by her on yesterday and today. We can write it as-
Total distance travelled=distance travelled on yesterday + distance travelled on today
On putting the values we get,
Total distance travelled=$7{\displaystyle \frac{1}{2}}+4{\displaystyle \frac{3}{8}}$
Then from eq. (i) and (ii) we can write-
Total distance travelled=${\displaystyle \frac{14}{2}}+{\displaystyle \frac{35}{8}}$
On talking LCM we get,
Total distance travelled=${\displaystyle \frac{56+70}{8}}={\displaystyle \frac{126}{8}}$
Then on solving we get,

Hence, total distance travelled=$15.75$ Km

Note:
Note: Here we can also convert the mixed fraction into improper fraction by writing the given fraction as-
$7{\displaystyle \frac{1}{2}}=7+{\displaystyle \frac{1}{2}}$
$4{\displaystyle \frac{8}{3}}=4+{\displaystyle \frac{8}{3}}$
Then take LCM of the denominators and solve to get the improper fraction.
$7{\displaystyle \frac{1}{2}}={\displaystyle \frac{14+1}{2}}={\displaystyle \frac{15}{2}}$
$4{\displaystyle \frac{3}{8}}={\displaystyle \frac{32+3}{8}}={\displaystyle \frac{35}{8}}$
Here the student may get confused about proper and improper fraction so remember that in the improper fraction the denominator is smaller than the numerator. In the proper fraction the number in the numerator is smaller than the denominator.