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)
First, let's simplify the expression step by step using the properties of operations and rules for multiplying and dividing.
(-2) x (1/5) divided by (2/3) x (5/6) divided by (3/4)
To simplify this expression, we'll begin by multiplying the numerators and multiplying the denominators.
(-2) x (1/5) = -2/5
(2/3) x (5/6) = (2x5)/(3x6) = 10/18
Now, let's divide the products:
(-2/5) divided by (10/18) divided by (3/4)
To divide fractions, we need to multiply by the reciprocal of the second fraction.
(-2/5) ÷ (10/18) = (-2/5) x (18/10) = (-36/50)
Now, let's divide by the third fraction:
(-36/50) divided by (3/4)
To divide fractions, we multiply by the reciprocal of the divisor.
(-36/50) ÷ (3/4) = (-36/50) x (4/3) = (-144/150) = -48/50
Finally, we can simplify the result by dividing the numerator and denominator by their greatest common divisor, which is 2.
-48/50 = (-48 ÷ 2) / (50 ÷ 2) = -24/25
So, the simplified form of the expression is -24/25.
To solve the expression (-2) x (1/5) divided by (2/3) x (5/6) divided by (3/4), let's break it down step by step.
Step 1: Simplify each multiplication operation separately.
(-2) x (1/5) = -2/5
(2/3) x (5/6) = 10/18
Step 2: Simplify each division operation separately.
(-2/5) divided by (10/18) = (-2/5) x (18/10)
= -36/50
= -18/25
Step 3: Simplify the final division operation.
(-18/25) divided by (3/4) = (-18/25) x (4/3)
= -72/75
= -24/25
Therefore, (-2) x (1/5)) divided by (2/3) x (5/6) divided by (3/4) simplifies to -24/25.
To solve the expression (-2) x (1/5)) divided by (2/3) x (5/6) divided by (3/4), we can follow the order of operations, which states that multiplication and division should be performed from left to right.
First, let's simplify the multiplication:
(-2) x (1/5) = -2/5
Now, let's simplify the division:
(-2/5) divided by (2/3) = (-2/5) x (3/2) = -6/10 = -3/5
Next, simplify the other division:
(-3/5) divided by (5/6) = (-3/5) x (6/5) = -18/25
Lastly, divide by (3/4):
(-18/25) divided by (3/4) = (-18/25) x (4/3) = -72/75 = -24/25
Therefore, the value of the expression is -24/25.