Ritin had `21/(5)` litres of lemonade of which he distributed `13/(4)` litres. How much lemonade is left with him?

Answer

To find out how much lemonade Ritin has left after distributing some of it, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amounts:**
- Ritin initially had \( \frac{21}{5} \) litres of lemonade.
- He distributed \( \frac{13}{4} \) litres of lemonade.

2. **Set Up the Subtraction:**
- To find out how much lemonade is left, we need to subtract the amount distributed from the initial amount:
\[ \text{Lemonade left} = \frac{21}{5} - \frac{13}{4} \]

3. **Find the Least Common Multiple (LCM):**
- The denominators are 5 and 4. The LCM of 5 and 4 is 20.

4. **Convert Each Fraction:**
- Convert \( \frac{21}{5} \) to a fraction with a denominator of 20:
\[ \frac{21}{5} = \frac{21 \times 4}{5 \times 4} = \frac{84}{20} \]
- Convert \( \frac{13}{4} \) to a fraction with a denominator of 20:
\[ \frac{13}{4} = \frac{13 \times 5}{4 \times 5} = \frac{65}{20} \]

5. **Perform the Subtraction:**
- Now we can subtract the two fractions:
\[ \frac{84}{20} - \frac{65}{20} = \frac{84 - 65}{20} = \frac{19}{20} \]

6. **Conclusion:**
- The amount of lemonade left with Ritin is \( \frac{19}{20} \) litres.

### Final Answer:
Ritin has \( \frac{19}{20} \) litres of lemonade left.

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