`(2)/(3)` of `(5)/(4)` of `(6)/(7)` of 2170 = ?

Options

A. 1050
B. 1550
C. 1005
D. 1555

Answer

To solve the problem `(2)/(3)` of `(5)/(4)` of `(6)/(7)` of 2170, we will follow these steps:

1. **Understand the expression**: The expression means we need to multiply the fractions together and then multiply the result by 2170.

2. **Multiply the fractions**:
- First, we multiply the fractions:
\[ \frac{2}{3} \times \frac{5}{4} \times \frac{6}{7} \]

3. **Calculate the product of the numerators and the denominators**:
- Multiply the numerators:
\[ 2 \times 5 \times 6 = 60 \]
- Multiply the denominators:
\[ 3 \times 4 \times 7 = 84 \]
- So, we have:
\[ \frac{60}{84} \]

4. **Simplify the fraction**:
- To simplify \(\frac{60}{84}\), we find the greatest common divisor (GCD) of 60 and 84, which is 12.
- Dividing both the numerator and the denominator by 12:
\[ \frac{60 \div 12}{84 \div 12} = \frac{5}{7} \]

5. **Multiply by 2170**:
- Now, we multiply \(\frac{5}{7}\) by 2170:
\[ \frac{5}{7} \times 2170 \]
- This can be calculated as:
\[ = \frac{5 \times 2170}{7} = \frac{10850}{7} \]

6. **Perform the division**:
- Now, we divide 10850 by 7:
\[ 10850 \div 7 = 1550 \]

Thus, the final answer is:
\[ \boxed{1550} \]