solve this (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)

Answer 1

To solve the expression \((-2) \times \left(\frac{1}{5}\right) \div \left(\frac{2}{3}\right) \times \left(-\frac{5}{6}\right) \div \left(\frac{3}{4}\right)\), we will follow the order of operations:

1. Perform the multiplications and divisions from left to right.

First, rewrite the divisions as multiplications by taking the reciprocal:

\[ (-2) \times \left(\frac{1}{5}\right) \times \left(\frac{3}{2}\right) \times \left(-\frac{5}{6}\right) \times \left(\frac{4}{3}\right) \]

Now we can rewrite the entire expression:

\[ (-2) \times \left(\frac{1}{5}\right) \times \left(\frac{3}{2}\right) \times \left(-\frac{5}{6}\right) \times \left(\frac{4}{3}\right) \]

Now, we will multiply step by step:

1. First, compute \((-2) \times \left(\frac{1}{5}\right)\): \[ (-2) \times \left(\frac{1}{5}\right) = -\frac{2}{5} \]

2. Then, multiply \(-\frac{2}{5}\) by \(\frac{3}{2}\): \[ -\frac{2}{5} \times \frac{3}{2} = -\frac{2 \times 3}{5 \times 2} = -\frac{6}{10} = -\frac{3}{5} \]

3. Next, multiply by \(-\frac{5}{6}\): \[ -\frac{3}{5} \times -\frac{5}{6} = \frac{3 \times 5}{5 \times 6} = \frac{15}{30} = \frac{1}{2} \]

4. Finally, multiply \(\frac{1}{2}\) by \(\frac{4}{3}\): \[ \frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \]

Thus, the final result of the expression is:

\[ \boxed{\frac{2}{3}} \]

Answer 2

wrong

Answer 3

Let's carefully go through the expression step by step again:

The expression we need to solve is:

\[ (-2) \times \left(\frac{1}{5}\right) \div \left(\frac{2}{3}\right) \times \left(-\frac{5}{6}\right) \div \left(\frac{3}{4}\right) \]

We can rewrite the division as multiplication by the reciprocal:

\[ (-2) \times \left(\frac{1}{5}\right) \times \left(\frac{3}{2}\right) \times \left(-\frac{5}{6}\right) \times \left(\frac{4}{3}\right) \]

Now, let's calculate this step by step:

1. Start with the first part: \[ (-2) \times \left(\frac{1}{5}\right) = -\frac{2}{5} \]

2. Multiply by \(\frac{3}{2}\): \[ -\frac{2}{5} \times \frac{3}{2} = -\frac{2 \times 3}{5 \times 2} = -\frac{6}{10} = -\frac{3}{5} \]

3. Now multiply by \(-\frac{5}{6}\): \[ -\frac{3}{5} \times -\frac{5}{6} = \frac{3 \times 5}{5 \times 6} = \frac{15}{30} = \frac{1}{2} \]

4. Finally, multiply by \(\frac{4}{3}\): \[ \frac{1}{2} \times \frac{4}{3} = \frac{1 \times 4}{2 \times 3} = \frac{4}{6} = \frac{2}{3} \]

So the final result, correctly calculated this time, still simplifies to:

\[ \boxed{\frac{2}{3}} \]

If you believe there was a misunderstanding or a specific point of confusion, please clarify, and I'll be happy to assist!

Answer 4

try and solve this (9)÷(5/4)×(7/9)×(−5)÷(7/2)

Answer 5

Let's solve the expression step by step:

\[ (9) \div \left(\frac{5}{4}\right) \times \left(\frac{7}{9}\right) \times (-5) \div \left(\frac{7}{2}\right) \]

1. Rewrite divisions as multiplications by the reciprocal:

   The expression can be rewritten as: \[ 9 \times \left(\frac{4}{5}\right) \times \left(\frac{7}{9}\right) \times (-5) \times \left(\frac{2}{7}\right) \]

2. Start evaluating from left to right:

   • First, compute \( 9 \times \frac{4}{5} \): \[ 9 \times \frac{4}{5} = \frac{36}{5} \]

   • Next, multiply by \(\frac{7}{9}\): \[ \frac{36}{5} \times \frac{7}{9} = \frac{36 \times 7}{5 \times 9} = \frac{252}{45} = \frac{28}{5} \]

   • Now, multiply by \(-5\): \[ \frac{28}{5} \times (-5) = -\frac{28 \times 5}{5} = -28 \]

   • Finally, multiply by \(\frac{2}{7}\): \[ -28 \times \frac{2}{7} = -\frac{28 \times 2}{7} = -\frac{56}{7} = -8 \]

So, the final result is:

\[ \boxed{-8} \]