The problem in the image states that Mayank traveled in three stages to reach his office:

1. Walked $\frac{3}{8}$ km to reach the autorickshaw stand.
2. Took an autorickshaw and traveled $1 \frac{3}{4}$ km.
3. Took the metro and traveled $\frac{15}{6}$ km to reach his office.

We are tasked with finding the total distance Mayank traveled. Let's break this down step-by-step.

1. First Distance (Walked):
   Mayank walked $\frac{3}{8}$ km.

2. Second Distance (Autorickshaw):
   Mayank traveled $1 \frac{3}{4}$ km in an autorickshaw.
   This can be converted into an improper fraction: $1 \frac{3}{4} = \frac{7}{4} \text{ km}.$

3. Third Distance (Metro):
   Mayank traveled $\frac{15}{6}$ km in the metro. Simplifying this: $\frac{15}{6} = 2.5 \text{ km}.$

Now, to find the total distance traveled, we sum these three distances: $\text{Total distance} = \frac{3}{8} + \frac{7}{4} + 2.5.$ To add these fractions, we first convert everything into a common format. Let's convert $2.5$ into a fraction: $2.5 = \frac{5}{2}.$

Now, the total distance is: $\text{Total distance} = \frac{3}{8} + \frac{7}{4} + \frac{5}{2}.$ We need a common denominator for these fractions, which would be 8:

• $\frac{3}{8}$ remains $\frac{3}{8}$.
• $\frac{7}{4}$ becomes $\frac{14}{8}$.
• $\frac{5}{2}$ becomes $\frac{20}{8}$.

Now, adding these: $\text{Total distance} = \frac{3}{8} + \frac{14}{8} + \frac{20}{8} = \frac{37}{8}.$ Converting $\frac{37}{8}$ into a mixed number: $\frac{37}{8} = 4 \frac{5}{8} \text{ km}.$

Thus, the total distance Mayank traveled is 4 $\frac{5}{8}$ km.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How do you convert improper fractions to mixed numbers?
2. What is the importance of finding a common denominator when adding fractions?
3. How can you simplify a fraction like $\frac{15}{6}$ quickly?
4. What are some methods to solve real-world problems using fractions?
5. How would the total distance change if any of the given distances increased?

Tip: When dealing with mixed numbers, converting them into improper fractions first often makes the calculations easier.