Asha bought `3(1)/(4)`m of cloth and Mrinal bought `2(2)/(5)`m of cloth. How much cloth did they buy together?

Answer

To solve the problem of how much cloth Asha and Mrinal bought together, we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
Asha bought \(3 \frac{1}{4}\) meters of cloth. To convert this mixed number into an improper fraction:
- Multiply the whole number (3) by the denominator (4):
\[ 3 \times 4 = 12 \]
- Add the numerator (1) to this result:
\[ 12 + 1 = 13 \]
- Therefore, \(3 \frac{1}{4} = \frac{13}{4}\).

Now, let's convert Mrinal's cloth length of \(2 \frac{2}{5}\) meters into an improper fraction:
- Multiply the whole number (2) by the denominator (5):
\[ 2 \times 5 = 10 \]
- Add the numerator (2) to this result:
\[ 10 + 2 = 12 \]
- Therefore, \(2 \frac{2}{5} = \frac{12}{5}\).

### Step 2: Add the Improper Fractions
Now we need to add the two improper fractions:
\[ \frac{13}{4} + \frac{12}{5} \]

### Step 3: Find the Least Common Multiple (LCM)
To add these fractions, we need a common denominator. The denominators are 4 and 5. The LCM of 4 and 5 is 20.

### Step 4: Convert Each Fraction to Have the Common Denominator
Now we convert each fraction to have the denominator of 20:
- For \(\frac{13}{4}\):
\[ \frac{13}{4} = \frac{13 \times 5}{4 \times 5} = \frac{65}{20} \]
- For \(\frac{12}{5}\):
\[ \frac{12}{5} = \frac{12 \times 4}{5 \times 4} = \frac{48}{20} \]

### Step 5: Add the Converted Fractions
Now we can add the two fractions:
\[ \frac{65}{20} + \frac{48}{20} = \frac{65 + 48}{20} = \frac{113}{20} \]

### Step 6: Convert the Improper Fraction to a Mixed Number
To convert \(\frac{113}{20}\) into a mixed number:
- Divide 113 by 20. The quotient is 5 and the remainder is 13:
\[ 113 \div 20 = 5 \quad \text{(remainder 13)} \]
- Therefore, \(\frac{113}{20} = 5 \frac{13}{20}\).

### Final Answer
Asha and Mrinal bought together \(5 \frac{13}{20}\) meters of cloth.

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