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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)

−1/6

2/3

−2/3

1/6

1 answer

To solve the expression \((−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)\), we will follow the order of operations and simplify step by step.

  1. First, let's rewrite the division as multiplication by the reciprocal: \[ (−2)×(1/5)×(3/2)×(−5/6)×(4/3) \]

  2. Now, combine the multiplications: \[ = (−2)×(1/5)×(3/2)×(−5/6)×(4/3) \]

  3. We can multiply the fractions and constants together one step at a time. Start with \((−2) × (1/5)\): \[ = (−2/5) \]

  4. Next, multiply \((−2/5)\) by \((3/2)\): \[ = (−2/5) × (3/2) = (−2 × 3) / (5 × 2) = (−6/10) = (−3/5) \]

  5. Now, multiply \((−3/5)\) by \((−5/6)\): \[ = (−3/5) × (−5/6) = (3 × 5) / (5 × 6) = (15/30) = (1/2) \]

  6. Finally, multiply \((1/2)\) by \((4/3)\): \[ = (1/2) × (4/3) = (1 × 4) / (2 × 3) = 4/6 = (2/3) \]

So, the final answer is: \[ \boxed{2/3} \]