While coming back home from his school. Kishan covered `4(3)/(4) "km"` by rickshaw and `1(1)/(2) "km"` on foot. What is the distance of his house from the school?

Answer

To find the total distance Kishan covered from school to his house, we need to add the distances he traveled by rickshaw and on foot. Let's break it down step by step.

### Step 1: Convert mixed numbers to improper fractions
1. **Distance by rickshaw:**
- Kishan traveled \(4 \frac{3}{4}\) km.
- To convert this to an improper fraction:
\[ 4 \frac{3}{4} = \frac{(4 \times 4) + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4} \text{ km} \]

2. **Distance on foot:**
- Kishan traveled \(1 \frac{1}{2}\) km.
- To convert this to an improper fraction:
\[ 1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2} \text{ km} \]

### Step 2: Find a common denominator
To add the two fractions, we need a common denominator. The denominators are 4 and 2. The least common multiple (LCM) of 4 and 2 is 4.

### Step 3: Convert the second fraction to have the common denominator
- The distance on foot \(\frac{3}{2}\) needs to be converted:
\[ \frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4} \]

### Step 4: Add the two fractions
Now we can add the distances:
\[ \frac{19}{4} + \frac{6}{4} = \frac{19 + 6}{4} = \frac{25}{4} \]

### Step 5: Convert the improper fraction to a mixed number
To convert \(\frac{25}{4}\) back to a mixed number:
- Divide 25 by 4:
- 25 divided by 4 is 6 with a remainder of 1.
- Thus, we can express it as:
\[ \frac{25}{4} = 6 \frac{1}{4} \text{ km} \]

### Conclusion
The total distance of Kishan's house from the school is \(6 \frac{1}{4}\) km.

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