Use the properties of operations and rules for multiplying and dividing to solve: (−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
1. 1/6
2. 2/3
3. −2/3
4. −1/6
To solve this expression, we can simplify step by step:
(-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4)
First, we multiply the first two fractions:
(-2) × (1/5) = -2/5
Next, we divide the result by the next fraction:
(-2/5) ÷ (2/3) = (-2/5) × (3/2) = (-6/10) = -3/5
Next, we multiply the result by the next fraction:
(-3/5) × (-5/6) = (3/5) × (5/6) = (3/6) = 1/2
Finally, we divide the result by the last fraction:
(1/2) ÷ (3/4) = (1/2) × (4/3) = (4/6) = 2/3
Therefore, the simplified result is 2/3. The correct option is 2.
To solve the expression (-2)×(1/5)÷(2/3)×(-5/6)÷(3/4), we can follow the order of operations, which is parentheses, multiplication and division (from left to right).
First, let's simplify the multiplication and division from left to right:
(-2)×(1/5) = (−2/1)×(1/5) = (-2/5)
Next, we divide (-2/5) by (2/3):
(-2/5) ÷ (2/3) = (-2/5) × (3/2) = (-6/10) = (-3/5)
Finally, we multiply (-3/5) by (-5/6) and divide by (3/4):
(-3/5) × (-5/6) ÷ (3/4) = (-3/5) × (5/-6) × (4/3) = (3/1) × (-1/2) × (4/3) = (3/-2) × (4/3) = (-12/6) = -2
Therefore, the answer is 3. -2/3.