(-2/3) x (-3) divided by (-6/11) x (3/4)
To divide these fractions, you simply multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of (-6/11) x (3/4) is (4/3) x (-11/6).
So, the expression (-2/3) x (-3) divided by (-6/11) x (3/4) simplifies to:
(-2/3) x (-3) x (4/3) x (-11/6)
Multiplying the numerators and denominators, we get:
(-2 x -3 x 4 x -11) / (3 x 3 x 6 x 6)
This simplifies to:
(24 x 11) / (54 x 6)
Multiplying the numbers, we get:
264 / 324
Finally, we simplify the fraction if possible by dividing both the numerator and denominator by their greatest common divisor, which is 12:
22 / 27
Therefore, the answer is 22/27.
To solve the expression (-2/3) x (-3) divided by (-6/11) x (3/4), follow these steps:
Step 1: Simplify both numerator and denominator separately.
Numerator: (-2/3) x (-3) = 2
Denominator: (-6/11) x (3/4) = -18/44
Step 2: Divide the numerator by the denominator.
2 / (-18/44)
Step 3: Invert the denominator and multiply.
2 x (44/-18)
Step 4: Simplify the fraction.
2 x (-22/9) = -44/9
Therefore, the expression (-2/3) x (-3) divided by (-6/11) x (3/4) simplifies to -44/9.
To solve the expression (-2/3) x (-3) divided by (-6/11) x (3/4), we need to follow the order of operations, which is parentheses, exponents, multiplication/division (from left to right), and addition/subtraction (from left to right). Here's how you can solve this step by step:
Step 1: Simplify the multiplication within the parentheses:
-2/3 x -3 = 2/1 = 2
Step 2: Simplify the multiplication outside the parentheses:
(-6/11) x (3/4) = -18/44 = -9/22
Step 3: Divide the value obtained in Step 1 by the value obtained in Step 2:
2 ÷ (-9/22)
To divide by a fraction, we invert and multiply, which means we take the reciprocal of the second fraction and multiply it by the first fraction:
2 ÷ (-9/22) = 2 x (-22/9)
Now, multiply the numerators (2 x -22) to get -44 and multiply the denominators (1 x 9) to get 9:
-44/9
Therefore, the answer to the expression (-2/3) x (-3) divided by (-6/11) x (3/4) is -44/9.