use the properties of operations and rules for multiplying and dividing to solve

(-2) x (1/5) divided by (2/3) x (-5/6) divided by (3/4)

A -1/6

B 2/3

C 1/6

B -2/3

1 answer

To solve the expression (-2) x (1/5) divided by (2/3) x (-5/6) divided by (3/4), we can simplify each multiplication and division step by following the properties of operations and the rules for multiplying and dividing fractions.

First, let's simplify the first multiplication:

(-2) x (1/5) = -2/1 x 1/5 = -2/5

Next, let's simplify the second multiplication:

(2/3) x (-5/6) = (2 x -5) / (3 x 6) = -10/18

Now, let's simplify the division by multiplying by the reciprocal of the divisor:

-2/5 divided by -10/18 = -2/5 x 18/(-10) = -2/5 x -9/5 = (2 x 9) / (5 x 5) = 18/25

Finally, let's simplify the last division:

(18/25) divided by (3/4) = (18/25) x (4/3) = (18 x 4) / (25 x 3) = 72/75

Now, we can simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 3:

72/75 = (24 x 3) / (25 x 3) = 24/25

Therefore, the result of the expression (-2) x (1/5) divided by (2/3) x (-5/6) divided by (3/4) is 24/25.

So, the correct option is not among the given options.