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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.

Mayank walked for 3/8 km to reach the autorickshaw stand, traveled 1 3/4 km in an autorickshaw to reach the metro station, and traveled 15/6 km in the metro to reach his office. Find the total distance he traveled to reach his office. Show your work.

In this problem, Mayank travels different distances on foot, by autorickshaw, and by metro. Learn how to calculate the total distance by adding fractions, converting mixed numbers, and using a common denominator. Suitable for Grades 5-7.

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