Use the properties of operations and rules for multiplying and dividing to solve: (-2) x (1/5) divide (2/3) x (-5/6) divide (3/4)
-2/3
-1/6
2/3
1/6
To solve this expression, we will use the properties of operations and rules for multiplying and dividing fractions.
First, multiply the first two fractions: (-2) x (1/5) = -2/5.
Next, multiply the next two fractions: (2/3) x (-5/6) = -10/18, which can be simplified to -5/9 by dividing the numerator and denominator by their greatest common divisor, 2.
Finally, divide the result of the previous calculation by the last fraction: (-5/9) ÷ (3/4) = (-5/9) x (4/3) = -20/27.
So the final answer is -20/27.
To solve the expression (-2) x (1/5) ÷ (2/3) x (-5/6) ÷ (3/4), we can follow these steps:
Step 1: Simplify each multiplication operation first:
-2 x 1/5 = -2/5
Step 2: Simplify each division operation:
-2/5 ÷ 2/3 = (-2/5) x (3/2) = -6/10 = -3/5
Step 3: Simplify the remaining multiplication operation:
-3/5 x (-5/6) = (-3/5) x (5/6) = -15/30 = -1/2
Step 4: Simplify the final division operation:
-1/2 ÷ 3/4 = (-1/2) x (4/3) = -4/6 = -2/3
Therefore, the answer to the expression is -2/3.
To solve the expression: (-2) x (1/5) ÷ (2/3) x (-5/6) ÷ (3/4), we can follow the order of operations (also known as PEMDAS) to simplify the expression step by step.
Step 1: Simplify the multiplication.
Multiply the first two numbers together: (-2) x (1/5) = -2/5
Multiply the next two numbers together: (2/3) x (-5/6) = -10/18
Step 2: Simplify the division.
Divide the result from Step 1 by the next number: -2/5 ÷ -10/18
When dividing fractions, we invert the divisor (the second fraction) and multiply.
So, -2/5 ÷ -10/18 becomes -2/5 x 18/(-10).
Now, multiply the numerators (top numbers) together and the denominators (bottom numbers) together: -2 x 18 = -36 and 5 x (-10) = -50.
Therefore, the expression simplifies to: -36/(-50).
Step 3: Simplify the fraction.
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, both numbers are negative, so the GCD is positive.
The GCD of 36 and 50 is 2.
Dividing both the numerator and the denominator by 2, we get: (-36 ÷ 2) / (-50 ÷ 2) = -18/(-25).
Step 4: Simplify the negative fraction.
To simplify a negative fraction, we can divide both the numerator and the denominator by their negative signs.
Divide -18 by -1 and -25 by -1: (-18 ÷ -1) / (-25 ÷ -1) = 18/25.
Therefore, the simplified answer to the expression (-2) x (1/5) ÷ (2/3) x (-5/6) ÷ (3/4) is 18/25.