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

To solve the expression (-2)x(1/5) ÷ (2/3)x(-5/6) ÷ (3/4), we will simplify the expression step by step using the properties of operations and the rules for multiplying and dividing.

First, let's simplify the numerator and denominator separately:

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

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

Now, let's divide the numerator (-2/5) by the denominator (-10/18):

(-2/5) ÷ (-10/18)

When dividing fractions, we invert the divisor (the second fraction) and multiply:

(-2/5) x (18/-10)

Next, we simplify the fraction:

-2/5 x 18/-10 = -36/(-50)

To reduce this fraction, we can simplify both the numerator and denominator by dividing by their greatest common divisor, which is 2:

-36/(-50) = (-36÷2)/(-50÷2) = -18/(-25)

Finally, the expression becomes -18/(-25) ÷ (3/4):

When dividing fractions, we invert the divisor (the second fraction) and multiply:

-18/(-25) x (4/3)

Next, we simplify the fraction:

-18/(-25) x 4/3 = 72/(-75)

To reduce this fraction, we can simplify both the numerator and denominator by dividing by their greatest common divisor, which is 3:

72/(-75) = (72÷3)/(-75÷3) = 24/(-25) = -24/25

Therefore, (-2)x(1/5) ÷ (2/3)x(-5/6) ÷ (3/4) simplifies to -24/25.