Use the properties of operations and rules for multiplying and dividing to solve:
(-2) x (1/5) / (2/3) x (-5/6) / (3/4)
-2/3
-1/6
2/3
1/6
To solve the expression (-2) x (1/5) / (2/3) x (-5/6) / (3/4), we can follow the order of operations (PEMDAS) and simplify step by step.
First, we multiply (-2) by (1/5):
(-2) x (1/5) = -2/5
Then, we divide (-2/5) by (2/3):
(-2/5) / (2/3) = (-2/5) * (3/2) = -6/10 = -3/5
Next, we multiply (-3/5) by (-5/6):
(-3/5) * (-5/6) = (3/5) * (5/6) = 15/30 = 1/2
Finally, we divide (1/2) by (3/4):
(1/2) / (3/4) = (1/2) * (4/3) = 4/6 = 2/3
Therefore, the simplified expression is 2/3.
To solve the given expression step-by-step, follow the order of operations (PEMDAS) and use the properties of multiplication and division:
1. Simplify multiplication and division from left to right:
(-2) x (1/5) / (2/3) x (-5/6) / (3/4)
= (-2/5) / (2/3) x (-5/6) / (3/4)
= (-2/5) x (3/2) x (-5/6) / (3/4)
= -2/5 x 3/2 x -5/6 / 3/4
2. Multiply the numerators and denominators together:
= (-2 x 3 x -5) / (5 x 2 x 6) / (3/4)
= (30) / (60) / (3/4)
3. Invert the division by multiplying by the reciprocal:
= (30) / (60) x (4/3)
= (30 x 4) / (60 x 3)
= 120 / 180
4. Simplify the fraction:
= 2/3
Therefore, the expression (-2) x (1/5) / (2/3) x (-5/6) / (3/4) simplifies to 2/3.
To solve the expression (-2) x (1/5) / (2/3) x (-5/6) / (3/4), we can follow the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication/Division (from left to right), and Addition/Subtraction (from left to right).
First, let's simplify the multiplication and division operations in the expression:
(-2) x (1/5) / (2/3) x (-5/6) / (3/4)
Multiplying -2 by 1/5 gives us: (-2) x (1/5) = -2/5
Dividing -2/5 by 2/3:
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 2/3 is 3/2. So, -2/5 ÷ 2/3 can be rewritten as (-2/5) x (3/2).
Multiplying -2/5 by 3/2 gives us: (-2/5) x (3/2) = -6/10 = -3/5
Next, let's simplify the next division operation in the expression:
-3/5 x (-5/6) / (3/4)
Dividing -3/5 by -5/6:
Again, to divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of -5/6 is -6/5. So, -3/5 ÷ -5/6 can be rewritten as (-3/5) x (-6/5).
Multiplying -3/5 by -6/5 gives us: (-3/5) x (-6/5) = 18/25
Lastly, let's simplify the final division operation in the expression:
18/25 / (3/4)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 3/4 is 4/3. So, 18/25 ÷ 3/4 can be rewritten as (18/25) x (4/3).
Multiplying 18/25 by 4/3 gives us: (18/25) x (4/3) = 72/75 = 24/25
Therefore, the final simplified expression is 24/25, which means the answer is 24/25.