Question

solve this (−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)

Answer 1

wrong

Answer 2

wrong still

Answer 3

never mind you were correct at first

Answer 4

the answer is - 5/10

Answer 5

To solve the expression \((-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \div (-\frac{3}{16}) \times (-\frac{5}{7})\), we can follow the order of operations and simplify step by step.

1. Rewrite the division as multiplication by the reciprocal:
\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \times (-\frac{16}{3}) \times (-\frac{5}{7})
\]

2. Now we can rearrange and group the terms:
\[
(-\frac{3}{5}) \times (-\frac{5}{7}) \times (\frac{5}{16}) \times (-\frac{16}{3}) \times (\frac{7}{12})
\]

3. Calculate the product of the negative and positive fractions:
- The negatives cancel out:
\[
= \frac{3}{5} \times \frac{5}{7} \times \frac{5}{16} \times \frac{16}{3} \times \frac{7}{12}
\]

4. Now multiply the fractions:
\[
= \frac{3 \times 5 \times 5 \times 16 \times 7}{5 \times 7 \times 16 \times 3 \times 12}
\]

5. Cancel out common terms in the numerator and denominator:
- The \(3\) in the numerator cancels with the \(3\) in the denominator.
- The \(5\) in the numerator cancels with one \(5\) in the denominator.
- The \(16\) in the numerator cancels with the \(16\) in the denominator.
- The \(7\) in the numerator cancels with the \(7\) in the denominator.

After cancellation, we have:
\[
= \frac{1}{12}
\]

Thus, the final result is:
\[
\boxed{\frac{1}{12}}
\]

Answer 6

Let's carefully go through the calculations step by step again for the expression

\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \div (-\frac{3}{16}) \times (-\frac{5}{7}).
\]

### Step 1: Rewrite division as multiplication
Rewrite the division as multiplication by the reciprocal:
\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \times (-\frac{16}{3}) \times (-\frac{5}{7}).
\]

### Step 2: Combine the negative signs
The product of the negative terms gives us:
\[
(-) \times (-) \times (-) = -.
\]

### Step 3: Write the full expression
Now we have:
\[
-\left( \frac{3}{5} \times \frac{5}{16} \times \frac{7}{12} \times \frac{16}{3} \times \frac{5}{7} \right).
\]

### Step 4: Multiplying the fractions together
Now multiply the fractions directly:
1. Numerator:
\[
3 \times 5 \times 7 \times 16 \times 5
\]

2. Denominator:
\[
5 \times 16 \times 12 \times 3 \times 7.
\]

The expression simplifies to:
\[
-\frac{3 \times 5 \times 7 \times 16 \times 5}{5 \times 16 \times 12 \times 3 \times 7}.
\]

### Step 5: Cancel common factors:
The \(3\), \(5\), \(7\), and \(16\) from the numerator and denominator cancel out:
- \(3\) in the numerator cancels with \(3\) in the denominator.
- One \(5\) in the numerator cancels with \(5\) in the denominator.
- \(7\) in the numerator cancels with \(7\) in the denominator.
- \(16\) in the numerator cancels with \(16\) in the denominator.

This reduces to:
\[
-\frac{5}{12}.
\]

### Final Result:
Thus, the final answer is:
\[
-\frac{5}{12}.
\]

So the correct result is:
\[
\boxed{-\frac{5}{12}}.
\]

Answer 7

Apologies for the confusion earlier. Let’s work through the calculations systematically and accurately step by step:

Given the expression:

\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \div (-\frac{3}{16}) \times (-\frac{5}{7}).
\]

### Step 1: Rewrite division as multiplication:
We rewrite the division as multiplication by the reciprocal:

\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \times \left(-\frac{16}{3}\right) \times \left(-\frac{5}{7}\right).
\]

### Step 2: Simplifying the expression:
We can multiply all the fractions together:

\[
(-\frac{3}{5}) \times (-\frac{5}{7}) \times (-\frac{5}{12}) \times (-\frac{16}{3}).
\]

### Step 3: Combine Negative Signs:
The product of the negative terms will give us a single negative sign:

Thus,

\[
= -\left(\frac{3}{5} \times \frac{5}{16} \times \frac{7}{12} \times \frac{16}{3} \times \frac{5}{7}\right).
\]

### Step 4: Arrange and Multiply the Fractions:
Now we can combine the fractions:

\[
= -\frac{3 \times 5 \times 7 \times 16 \times 5}{5 \times 16 \times 12 \times 3 \times 7}.
\]

### Step 5: Cancelling Common Factors:
Cancelling the common terms in the numerator and denominator:

1. Cancel \(3\) with \(3\).
2. Cancel \(5\) with \(5\).
3. Cancel \(16\) with \(16\).
4. Cancel \(7\) with \(7\).

After canceling, we have:

\[
= -\frac{5}{12}.
\]

### Final Answer:
Thus, the correct result is:

\[
\boxed{-\frac{5}{12}}.
\]

Let me know if you want any further explanations or steps!

Answer 8

I apologize for any confusion caused during our discussion. Let's summarize the correct steps correctly again for clarity:

The original expression is:

\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \div (-\frac{3}{16}) \times (-\frac{5}{7}).
\]

### Steps for Solution:

1. **Rewrite the Division:**
Instead of division, we use multiplication by the reciprocal:
\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \times (-\frac{16}{3}) \times (-\frac{5}{7}).
\]

2. **Combine the Negative Signs:**
The negatives cancel out to give a positive overall sign:
\[
\left(\frac{3}{5} \times \frac{5}{16} \times \frac{7}{12} \times \frac{16}{3} \times \frac{5}{7}\right).
\]

3. **Multiply the Fractions:**
Combining the fractions:
\[
= \frac{(3) \times (5) \times (7) \times (16) \times (5)}{(5) \times (16) \times (12) \times (3) \times (7)}.
\]

4. **Cancel Common Factors:**
- The \(3\) cancels with \(3\).
- The \(5\) cancels with \(5\).
- The \(16\) cancels with \(16\).
- The \(7\) cancels with \(7\).

After cancellations:

\[
= \frac{1 \cdot 1 \cdot 1 \cdot 1 \cdot 5}{1 \cdot 1 \cdot 12 \cdot 1 \cdot 1} = \frac{5}{12}.
\]

So, the final positive result is:

\[
\boxed{\frac{5}{12}}.
\]

Thank you for your understanding, and if there’s anything else you'd like to clarify or discuss further, please feel free to ask!

Answer 9

I apologize for my previous responses, and let's carefully work through the expression one more time to confirm the calculations.

The expression given is:

\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \div (-\frac{3}{16}) \times (-\frac{5}{7}).
\]

### Step-by-step Calculation:

1. **Rewrite Division as Multiplication:**
Changing the division to multiplication by the reciprocal:
\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \times (-\frac{16}{3}) \times (-\frac{5}{7}).
\]

2. **Combine the negatives:**
The three negative signs will yield one negative overall:
\[
-\left(\frac{3}{5} \times \frac{5}{16} \times \frac{7}{12} \times \frac{16}{3} \times \frac{5}{7}\right).
\]

3. **Multiply the fractions:**
The numerator and denominator can be multiplied:
\[
= -\frac{(3 \times 5 \times 7 \times 16 \times 5)}{(5 \times 16 \times 12 \times 3 \times 7)}.
\]

4. **Cancel out common terms:**
- The \(3\) cancels with \(3\).
- One \(5\) in the numerator cancels with \(5\) in the denominator.
- The \(16\) cancels with \(16\).
- The \(7\) cancels with \(7\).

This simplifies the fraction to:
\[
= -\frac{5}{12}.
\]

**However**: Let's confirm everything again without missing any steps to ensure your stated result \(-\frac{5}{10}\):

### Finding a Common Error:

Let's recompute it one more time stepwise:

### Final verification:
Starting from the original problem:
\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \div (-\frac{3}{16}) \times (-\frac{5}{7}).
\]

1. **Convert the division into multiplication**:
\[
(-\frac{3}{5}) \times (\frac{5}{16}) \times (\frac{7}{12}) \times (-\frac{16}{3}) \times (-\frac{5}{7}).
\]

2. **Combine the negatives**:
Since we have three negations the final result will remain negative:
\[
-\left(\frac{3 \cdot 5 \cdot 5 \cdot 16 \cdot 7}{5 \cdot 16 \cdot 12 \cdot 3 \cdot 7}\right).
\]

3. **Cancel multiplying through**:
Each term can cancel:
- \(3\) cancels with \(3\)
- One \(5\) is left in the numerator.
- \(16\) cancels out.
- \(7\) cancels out.

After finding valid cancellations, we find the workings:
\[
= -\frac{5}{12}.
\]

### Conclusion
The answer still appears to be \(-\frac{5}{12}\).

If there was a misunderstanding regarding the expression or the steps that led to your answer of \(-\frac{5}{10}\), please clarify, and I'd be happy to assist further. Thank you for your patience!