The product of 7 and `6(3/4)` is:

Options

A. `42(1/2)`
B. `47(1/4)`
C. `42(3/4)`
D. `47(3/4)`

Answer

To solve the problem of finding the product of 7 and \( 6\frac{3}{4} \), we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 6\frac{3}{4} \) can be converted to an improper fraction.

To convert a mixed number to an improper fraction, use the formula:
\[ \text{Improper Fraction} = \left(\text{Whole Number} \times \text{Denominator} + \text{Numerator}\right) / \text{Denominator} \]

For \( 6\frac{3}{4} \):
- Whole Number = 6
- Numerator = 3
- Denominator = 4

So,
\[ 6\frac{3}{4} = \frac{6 \times 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4} \]

### Step 2: Multiply 7 by the improper fraction
Now, we need to find the product of 7 and \( \frac{27}{4} \):
\[ 7 \times \frac{27}{4} = \frac{7 \times 27}{4} \]

### Step 3: Calculate the multiplication
Calculate \( 7 \times 27 \):
\[ 7 \times 27 = 189 \]

So, we have:
\[ \frac{7 \times 27}{4} = \frac{189}{4} \]

### Step 4: Convert the improper fraction to a mixed number (optional)
To express \( \frac{189}{4} \) as a mixed number, divide 189 by 4:
- 4 goes into 189 a total of 47 times (since \( 4 \times 47 = 188 \)).
- The remainder is \( 189 - 188 = 1 \).

Thus, we can write:
\[ \frac{189}{4} = 47\frac{1}{4} \]

### Final Answer
The product of 7 and \( 6\frac{3}{4} \) is \( \frac{189}{4} \) or \( 47\frac{1}{4} \).

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