Find `2(1)/(5)xx3(2)/(7)`.

Answer

To solve the problem \(2\frac{1}{5} \times 3\frac{2}{7}\), we will follow these steps:

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

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, \(2\frac{1}{5} = \frac{11}{5}\)

For \(3\frac{2}{7}\):
- Multiply the whole number (3) by the denominator (7): \(3 \times 7 = 21\)
- Add the numerator (2): \(21 + 2 = 23\)
- So, \(3\frac{2}{7} = \frac{23}{7}\)

### Step 2: Multiply the Improper Fractions
Now we can multiply the two improper fractions:
\[ \frac{11}{5} \times \frac{23}{7} = \frac{11 \times 23}{5 \times 7} \]

### Step 3: Calculate the Numerator and Denominator
Calculate the numerator:
\[ 11 \times 23 = 253 \]
Calculate the denominator:
\[ 5 \times 7 = 35 \]

So, we have:
\[ \frac{253}{35} \]

### Step 4: Convert the Improper Fraction to a Mixed Number
Now, we will convert \(\frac{253}{35}\) back to a mixed number:
- Divide the numerator (253) by the denominator (35):
\[ 253 \div 35 = 7 \quad \text{(the whole number part)} \]
- Calculate the remainder:
\[ 253 - (35 \times 7) = 253 - 245 = 8 \]
So, we can express this as:
\[ 7 \frac{8}{35} \]

### Final Answer
Thus, the final answer is:
\[ 2\frac{1}{5} \times 3\frac{2}{7} = 7\frac{8}{35} \]

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