Sudhir and Mukesh have a lawn each of equal area. Sudhir mowed `2/(7)` of his lawn amd Mukesh mowed `9/(10)` of his. How much did they mow together?

Answer

To solve the problem of how much Sudhir and Mukesh mowed together, we need to add the fractions representing the portions of their lawns that they mowed.

### Step-by-Step Solution:

1. **Identify the fractions:**
- Sudhir mowed \( \frac{2}{7} \) of his lawn.
- Mukesh mowed \( \frac{9}{10} \) of his lawn.

2. **Add the fractions:**
To add the fractions \( \frac{2}{7} \) and \( \frac{9}{10} \), we need a common denominator.

3. **Find the least common multiple (LCM) of the denominators:**
- The denominators are 7 and 10.
- The LCM of 7 and 10 is 70.

4. **Convert each fraction to have the common denominator:**
- For \( \frac{2}{7} \):
\[ \frac{2}{7} = \frac{2 \times 10}{7 \times 10} = \frac{20}{70} \]
- For \( \frac{9}{10} \):
\[ \frac{9}{10} = \frac{9 \times 7}{10 \times 7} = \frac{63}{70} \]

5. **Add the converted fractions:**
\[ \frac{20}{70} + \frac{63}{70} = \frac{20 + 63}{70} = \frac{83}{70} \]

6. **Convert the improper fraction to a mixed number:**
- Divide 83 by 70:
- 70 goes into 83 once (1 time).
- Remainder: \( 83 - 70 = 13 \).
- Thus, \( \frac{83}{70} = 1 \frac{13}{70} \).

### Final Answer:
Sudhir and Mukesh mowed together \( \frac{83}{70} \) or \( 1 \frac{13}{70} \) of their lawns.

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