Sohini bought `4(1)/(2)` m of cloth for her kurta and `2(7)/(10)` m of cloth for her pyjamas. How much cloth did she purchase in all?

Answer

To find out how much cloth Sohini purchased in total, we need to add the lengths of cloth she bought for her kurta and her pyjamas.

**Step 1: Convert the mixed numbers to improper fractions.**

1. For the kurta:
- Sohini bought \(4 \frac{1}{2}\) m of cloth.
- To convert this to an improper fraction:
- Multiply the whole number (4) by the denominator (2): \(4 \times 2 = 8\).
- Add the numerator (1): \(8 + 1 = 9\).
- So, \(4 \frac{1}{2} = \frac{9}{2}\) m.

2. For the pyjamas:
- Sohini bought \(2 \frac{7}{10}\) m of cloth.
- To convert this to an improper fraction:
- Multiply the whole number (2) by the denominator (10): \(2 \times 10 = 20\).
- Add the numerator (7): \(20 + 7 = 27\).
- So, \(2 \frac{7}{10} = \frac{27}{10}\) m.

**Step 2: Find a common denominator to add the fractions.**

- The denominators are 2 and 10. The least common multiple (LCM) of 2 and 10 is 10.
- Convert \(\frac{9}{2}\) to have a denominator of 10:
- Multiply both the numerator and the denominator by 5:
\[ \frac{9}{2} = \frac{9 \times 5}{2 \times 5} = \frac{45}{10} \]

**Step 3: Add the two fractions.**

- Now we can add \(\frac{45}{10}\) and \(\frac{27}{10}\):
\[ \frac{45}{10} + \frac{27}{10} = \frac{45 + 27}{10} = \frac{72}{10} \]

**Step 4: Simplify the fraction if necessary.**

- \(\frac{72}{10}\) can be simplified:
- Divide both the numerator and the denominator by 2:
\[ \frac{72 \div 2}{10 \div 2} = \frac{36}{5} \]

**Step 5: Convert back to a mixed number.**

- To convert \(\frac{36}{5}\) back to a mixed number:
- Divide 36 by 5, which gives 7 with a remainder of 1.
- So, \(\frac{36}{5} = 7 \frac{1}{5}\).

**Final Answer:**
Sohini purchased \(7 \frac{1}{5}\) m of cloth in total.

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