Use the properties of operations and rules for multiplying and dividing to solve: (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4) (1 point) Responses −16 negative Start Fraction 1 over 6 End Fraction 16 Start Fraction

Answer 1

To solve the expression, we need to simplify each step using the properties of operations and rules for multiplying and dividing.

First, let's simplify the multiplication: (-2) × (1/5) = -2/5.
Next, let's simplify the division: -2/5 ÷ (2/3) = -2/5 × (3/2) = -6/10.
Then, let's simplify the next multiplication: -6/10 × (-5/6) = (-6*-5)/(10*6) = 30/60.
Finally, let's simplify the last division: 30/60 ÷ (3/4) = 30/60 × (4/3) = 120/180.

To further simplify the expression, we can find the greatest common divisor (GCD) of 120 and 180, which is 60. Dividing both numerator and denominator by 60, we get:

120/180 = (120 ÷ 60) / (180 ÷ 60) = 2/3.

Therefore, the final result is 2/3.