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
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.
To solve the expression (-2) x (1/5) divided by (2/3) x (-5/6) divided by (3/4), we need to follow the order of operations and use the rules for multiplying and dividing fractions.
Step 1: Simplify each individual multiplication or division operation.
(-2) x (1/5) = -2/5
(2/3) x (-5/6) = -10/18 (simplify by dividing both the numerator and denominator by their greatest common divisor, which is 2)
(3/4) = 3/4 (no simplification needed)
Step 2: Multiply the simplified fractions from Step 1 together.
(-2/5) divided by (-10/18) divided by (3/4) can be written as (-2/5) * (18/-10) * (4/3)
Step 3: Multiply the numerators together and the denominators together.
(-2 * 18 * 4) / (5 * -10 * 3)
Step 4: Simplify the resulting fraction.
-144 / -150
Step 5: Reduce the fraction to its simplest form.
The greatest common divisor of -144 and -150 is 6. Divide both the numerator and denominator by 6.
-144/6 = -24
-150/6 = -25
The simplified fraction is -24/-25, which is equivalent to 24/25.
Therefore, the answer is option A - 24/25.