Question

Use the properties of operations and rules for multiplying and dividing to solve:


(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)

Answer 1

is it negative or positive?

Answer 2

To solve the expression \((−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)\), we will follow the order of operations and rewrite it in a more manageable form.

First, we'll convert the division into multiplication by taking the reciprocal:

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

Now we can multiply all the terms together. Let's group them for clarity:

\[
= (−2) \times (1/5) \times (3/2) \times (−5/6) \times (4/3)
\]

Now we can multiply step-by-step. Let's deal with the fractions first.

1. Multiply the numerator and denominator of the first two terms:

\[
(−2) \times (1/5) = \frac{−2}{5}
\]

2. 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. Now, multiply \(\frac{−3}{5}\) 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 value of the expression \((−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)\) is:

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

Answer 3

To determine whether the final result is negative or positive, let's review the multiplications step-by-step, particularly focusing on the signs of the products.

1. The first term is \(-2\) (negative).
2. The second term is \( \frac{1}{5} \) (positive).
- Multiplying a negative by a positive gives a negative:
\[
-2 \times \frac{1}{5} = \frac{-2}{5}
\]

3. The third term is \( \frac{2}{3} \) (positive).
- Multiplying a negative \(\frac{-2}{5}\) by a positive \(\frac{3}{2}\) gives:
\[
\frac{-2}{5} \times \frac{3}{2} = \frac{-6}{10} = \frac{-3}{5} \text{ (negative)}
\]

4. The fourth term is \( \frac{-5}{6} \) (negative).
- Multiplying two negatives gives a positive:
\[
\frac{-3}{5} \times \frac{-5}{6} = \frac{15}{30} = \frac{1}{2} \text{ (positive)}
\]

5. The fifth term is \( \frac{4}{3} \) (positive).
- Multiplying a positive by a positive gives:
\[
\frac{1}{2} \times \frac{4}{3} = \frac{4}{6} = \frac{2}{3} \text{ (positive)}
\]

So, the final result of the calculation is \(\frac{2}{3}\), which is positive.

Thus, the final answer is:

\[
\frac{2}{3} \text{ (positive)}
\]