https://file.aiquickdraw.com/mathbot/file/17268876048870yki4nsd.jpg

The problem in the image is:

**Mayank walked for \( \frac{3}{8} \) km to reach the autorickshaw stand, travelled \( \frac{3}{4} \) km in an autorickshaw to reach the metro station and travelled \( \frac{15}{6} \) km in the metro to reach his office. Find the total distance he travelled to reach his office. Show your work.**

### Solution:

To find the total distance Mayank travelled, we need to sum the distances he travelled by walking, in the autorickshaw, and in the metro.

#### Step 1: Distance walked
- Mayank walked \( \frac{3}{8} \) km.

#### Step 2: Distance travelled in the autorickshaw
- Mayank travelled \( \frac{3}{4} \) km in the autorickshaw.

#### Step 3: Distance travelled in the metro
- Mayank travelled \( \frac{15}{6} \) km in the metro.
- Simplify \( \frac{15}{6} \) to \( 2.5 \) km.

#### Step 4: Total distance
Now, we sum the distances:
\[
\text{Total distance} = \frac{3}{8} + \frac{3}{4} + 2.5
\]
We first convert everything to a common denominator (8) to add the fractions:
\[
\frac{3}{4} = \frac{6}{8}
\]
So, the total distance is:
\[
\frac{3}{8} + \frac{6}{8} + 2.5
\]
Now, add the fractions:
\[
\frac{3 + 6}{8} = \frac{9}{8}
\]
Convert \( \frac{9}{8} \) to a decimal:
\[
\frac{9}{8} = 1.125
\]
Finally, add 2.5:
\[
1.125 + 2.5 = 3.625
\]
Thus, the total distance Mayank travelled is **3.625 km**.

Let me know if you have any questions or need further explanation.

---

### Additional Questions:
1. How can you convert improper fractions to decimals?
2. What is the best way to find a common denominator when adding fractions?
3. Why do we simplify fractions like \( \frac{15}{6} \)?
4. How can you verify the correctness of a sum involving fractions?
5. Can you express \( 3.625 \) as a mixed fraction?

### Tip:
Always simplify fractions before adding or subtracting to make the calculations easier!

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

Learn how to find the total distance travelled by adding fractional distances. This example involves walking 3/8 km, travelling 3/4 km by autorickshaw, and covering 15/6 km by metro. Includes steps on simplifying fractions and converting to decimals.

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