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To determine the product of the given expression \(\left(\frac{7}{8}\right)(-16)(-7)\left(-\frac{1}{14}\right)\), let's break it down step by step.

1. Simplify the constants and the signs:
   \[
   \left(\frac{7}{8}\right)(-16)(-7)\left(-\frac{1}{14}\right)
   \]

2. Combine the negative signs:
   There are three negative signs in the product, so the result will be negative:
   \[
   \text{Negative} \times \text{Negative} \times \text{Negative} = \text{Negative}
   \]

3. Simplify the product of the fractions and integers:
   \[
   \left(\frac{7}{8}\right) \left(-\frac{1}{14}\right) = \frac{7 \times (-1)}{8 \times 14} = \frac{-7}{112}
   \]

4. Now multiply this result with the integers -16 and -7:
   \[
   \frac{-7}{112} \times (-16) \times (-7)
   \]

   First, let's simplify the fraction:
   \[
   \frac{-7}{112} = \frac{-1}{16} \quad \text{(since 112 divided by 7 is 16)}
   \]

5. Now multiply the simplified fraction by -16:
   \[
   \frac{-1}{16} \times (-16) = 1
   \]

6. Finally, multiply the result by -7:
   \[
   1 \times (-7) = -7
   \]

So, the product of the given expression is \(-7\), which matches option A.

Would you like any more details or have any further questions?

Here are 5 questions you can ask:
1. How do you multiply fractions with negative numbers?
2. Can you explain the rules for multiplying multiple negative numbers?
3. How do you simplify a fraction step by step?
4. What are common mistakes to avoid when multiplying fractions?
5. How can you verify your answer when multiplying fractions and integers?

**Tip:** When dealing with multiple fractions and integers, simplify each step to avoid errors and ensure accuracy.

Learn how to calculate the product of fractions and integers, specifically (-7/8)(-16)(-7)(-1/14), with a detailed step-by-step solution. This problem involves fractions, multiplication of integers, and understanding negative numbers. Suitable for students in Grades 6-8.

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