A tailor used `(31)/(4)m` of satin cloth and `(23)/(5)m` of velvet cloth to make curtains. Find the total length of the cloth used.

Answer

To find the total length of cloth used by the tailor, we need to add the lengths of satin cloth and velvet cloth together. Let's break this down step by step.

### Step 1: Write down the lengths of cloth used
The lengths of cloth used are:
- Satin cloth: \( \frac{31}{4} \) meters
- Velvet cloth: \( \frac{23}{5} \) meters

### Step 2: Find a common denominator
To add the two fractions, we need a common denominator. The denominators are 4 and 5. The least common multiple (LCM) of 4 and 5 is 20.

### Step 3: Convert each fraction to have the common denominator
Now we convert each fraction:
- For \( \frac{31}{4} \):
\[ \frac{31}{4} = \frac{31 \times 5}{4 \times 5} = \frac{155}{20} \]
- For \( \frac{23}{5} \):
\[ \frac{23}{5} = \frac{23 \times 4}{5 \times 4} = \frac{92}{20} \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ \frac{155}{20} + \frac{92}{20} = \frac{155 + 92}{20} = \frac{247}{20} \]

### Step 5: Convert the improper fraction to a mixed number
To convert \( \frac{247}{20} \) to a mixed number:
- Divide 247 by 20:
- 20 goes into 247 a total of 12 times (since \( 20 \times 12 = 240 \)).
- The remainder is \( 247 - 240 = 7 \).

Thus, we can express \( \frac{247}{20} \) as:
\[ 12 \frac{7}{20} \]

### Step 6: Convert to decimal (optional)
To convert \( \frac{247}{20} \) to a decimal:
\[ 247 \div 20 = 12.35 \]

### Final Answer
The total length of cloth used by the tailor is:
\[ 12 \frac{7}{20} \text{ meters or } 12.35 \text{ meters} \]

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