The product of 3 and `4(2/5)` is:

Options

A. `17(2/5)`
B. `24/5`
C. `13(1/5)`
D. `13(5/3)`

Answer

To find the product of 3 and \(4\frac{2}{5}\), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction.
The mixed number \(4\frac{2}{5}\) can be converted into an improper fraction. To do this, we multiply the whole number (4) by the denominator (5) and then add the numerator (2).

\[ 4\frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5} \]

### Step 2: Set up the multiplication.
Now we need to multiply 3 by the improper fraction we just found. We can express 3 as a fraction by writing it as \(\frac{3}{1}\).

\[ 3 \times 4\frac{2}{5} = \frac{3}{1} \times \frac{22}{5} \]

### Step 3: Multiply the fractions.
To multiply two fractions, we multiply the numerators together and the denominators together.

\[ \frac{3 \times 22}{1 \times 5} = \frac{66}{5} \]

### Step 4: Simplify if necessary.
The fraction \(\frac{66}{5}\) is already in its simplest form, but we can convert it back to a mixed number if needed.

\[ \frac{66}{5} = 13\frac{1}{5} \]

### Final Answer:
The product of 3 and \(4\frac{2}{5}\) is \(\frac{66}{5}\) or \(13\frac{1}{5}\).

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