Simplify: `3 4/7xx2 2/5xx1 3/4`

Options

A. `25`
B. `35`
C. `15`
D. `5`

Answer

To simplify the expression \(3 \frac{4}{7} \times 2 \frac{2}{5} \times 1 \frac{3}{4}\), we can follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert each mixed number into an improper fraction.

1. **Convert \(3 \frac{4}{7}\)**:
\[ 3 \frac{4}{7} = \frac{(3 \times 7) + 4}{7} = \frac{21 + 4}{7} = \frac{25}{7} \]

2. **Convert \(2 \frac{2}{5}\)**:
\[ 2 \frac{2}{5} = \frac{(2 \times 5) + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5} \]

3. **Convert \(1 \frac{3}{4}\)**:
\[ 1 \frac{3}{4} = \frac{(1 \times 4) + 3}{4} = \frac{4 + 3}{4} = \frac{7}{4} \]

### Step 2: Multiply the Improper Fractions
Now we can multiply the improper fractions together:
\[ \frac{25}{7} \times \frac{12}{5} \times \frac{7}{4} \]

### Step 3: Multiply the Numerators and Denominators
Multiply the numerators together and the denominators together:
\[ \text{Numerator: } 25 \times 12 \times 7 \]
\[ \text{Denominator: } 7 \times 5 \times 4 \]

Calculating the numerator:
\[ 25 \times 12 = 300 \]
\[ 300 \times 7 = 2100 \]

Calculating the denominator:
\[ 7 \times 5 = 35 \]
\[ 35 \times 4 = 140 \]

So we have:
\[ \frac{2100}{140} \]

### Step 4: Simplify the Fraction
Now we simplify \(\frac{2100}{140}\):
\[ \frac{2100 \div 140}{140 \div 140} = \frac{15}{1} = 15 \]

### Final Answer
The simplified result of \(3 \frac{4}{7} \times 2 \frac{2}{5} \times 1 \frac{3}{4}\) is \(15\).

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