What is the multiplication of `2 (1)/(5) and 5 (1)/(2)` ?

Options

A. `2 (1)/(5)`
B. `12 (1)/(10)`
C. `(5)/(11)`
D. `- (5)/(11)`

Answer

To solve the multiplication of \(2 \frac{1}{5}\) and \(5 \frac{1}{2}\), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

1. For \(2 \frac{1}{5}\):
- Multiply the whole number (2) by the denominator (5): \(2 \times 5 = 10\).
- Add the numerator (1): \(10 + 1 = 11\).
- So, \(2 \frac{1}{5} = \frac{11}{5}\).

2. For \(5 \frac{1}{2}\):
- Multiply the whole number (5) by the denominator (2): \(5 \times 2 = 10\).
- Add the numerator (1): \(10 + 1 = 11\).
- So, \(5 \frac{1}{2} = \frac{11}{2}\).

### Step 2: Multiply the Improper Fractions
Now, we will multiply the two improper fractions:

\[ \frac{11}{5} \times \frac{11}{2} \]

To multiply fractions, we multiply the numerators together and the denominators together:

\[ \text{Numerator: } 11 \times 11 = 121 \]
\[ \text{Denominator: } 5 \times 2 = 10 \]

So, we have:

\[ \frac{121}{10} \]

### Step 3: Convert Improper Fraction to Mixed Number
Now, we need to convert \(\frac{121}{10}\) into a mixed number.

1. Divide the numerator (121) by the denominator (10):
- \(121 \div 10 = 12\) remainder \(1\).
- This means \(121 = 10 \times 12 + 1\).

2. Write it as a mixed number:
- The whole number part is \(12\) and the remainder is \(1\), so we write it as:
\[ 12 \frac{1}{10} \]

### Final Answer
Thus, the multiplication of \(2 \frac{1}{5}\) and \(5 \frac{1}{2}\) is:

\[ 12 \frac{1}{10} \]

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