Question

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)

Answer 1

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.