Question

Question 119.
Nasir travelled $3\frac{1}{2}$ km in a bus and then walked $1\frac{1}{8}$ km to reach a town.
How much did he travel to reach the town?

Answer 1

Given that

The distance traveled by Nasir in a bus = $3\frac{1}{2}$ km
The distance walked by Nasir to reach the town = $1\frac{1}{8}$ km

Total distance traveled by Nasir to reach the town = The distance traveled by Nasir in a bus + The distance walked by Nasir to reach the town

On substituting the values we get:

Total distance traveled by Nasir to reach the town = $3\frac{1}{2}$+$1\frac{1}{8}$ km

We can express a mixed fraction as an improper fraction as $\frac{(\text{Whole}\times \text{Denominator})+\text{Numerator}}{\text{Denominator}}$.

$\therefore$ Total distance traveled by Nasir to reach the town = $\frac{3\times 2+1}{2}+\frac{1\times 8+1}{8}=\frac{7}{2}+\frac{9}{8}$ km

Now, the LCM of the denominator of the fractions $\frac{7}{2}$ and $\frac{9}{8}$ i.e. the LCM of 2 and 8 is 8.

$\therefore$ Total distance traveled by Nasir to reach the town = $\frac{7}{2}+\frac{9}{8}=\frac{7\times 4}{2\times 4}+\frac{9\times 1}{8\times 1}=\frac{28}{8}+\frac{9}{8}$ km

Total distance traveled by Nasir to reach the town = $\frac{28}{8}+\frac{9}{8}=\frac{28+9}{8}=\frac{37}{8}$ km

We can express an improper fraction as a mixed fraction by dividing the numerator by denominator to obtain the quotient and the remainder.

Then the mixed fraction will be written as $\text{Quotient}\frac{\text{Remainder}}{\text{Divisor}}$.

$\left[\begin{array}{c}\because 8\left)37\right(4\\ \frac{32}{5}\end{array}\right]$

Total distance traveled by Nasir to reach the town = $4\frac{5}{8}$ km
So, total distance travelled by Nasir to reach the town is $4\frac{5}{8}km.$