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

(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)

3 answers

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:

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

  1. Multiply \(\frac{−2}{5}\) by \(\frac{3}{2}\):

\[ \frac{−2}{5} \times \frac{3}{2} = \frac{−2 \times 3}{5 \times 2} = \frac{−6}{10} = \frac{−3}{5} \]

  1. Now, multiply \(\frac{−3}{5}\) by \(\frac{−5}{6}\):

\[ \frac{−3}{5} \times \frac{−5}{6} = \frac{(−3) \times (−5)}{5 \times 6} = \frac{15}{30} = \frac{1}{2} \]

  1. 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:

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

is it negative or positive?

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:

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