Use the properties of operations and rules for multiplying and dividing signed numbers to solve: (-2/3) x (-3) divided by (-6/11) x (3/4)
To solve the expression (-2/3) x (-3) divided by (-6/11) x (3/4), we can simplify each term separately and then divide the results.
First, let's simplify (-2/3) x (-3):
When multiplying two negative numbers, the result is positive. So (-2/3) x (-3) becomes (2/3) x 3 which simplifies to 2.
Next, let's simplify (-6/11) x (3/4):
When multiplying a negative number and a positive number, the result is negative. So (-6/11) x (3/4) becomes -(6/11) x (3/4). To simplify further, we multiply the numerators together and the denominators together to get (-6 x 3) / (11 x 4) = -18/44. (Note that we can simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which in this case is 2. So, -18/44 simplifies to -9/22.)
Now, we can divide the results: 2 divided by (-9/22)
To divide by a fraction, we multiply by its reciprocal. So, 2 divided by (-9/22) is the same as 2 multiplied by (-22/9). Multiplying the numerators together and the denominators together gives us (2 x -22) / (1 x 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 can follow the order of operations and apply the rules for multiplying and dividing signed numbers.
Step 1: Simplify the multiplication on the numerator.
(-2/3) x (-3) = (2/3) x 3 = 2
Step 2: Simplify the multiplication on the denominator.
(-6/11) x (3/4) = (-6/11) x (3/4) = -18/44 = -9/22
Step 3: Divide the numerator by the denominator.
2 ÷ (-9/22)
To divide by a fraction, we multiply by its reciprocal:
2 x (22/-9) = -44/9
So, the solution is -44/9.
To solve (-2/3) x (-3) divided by (-6/11) x (3/4), we can apply the properties of operations and rules for multiplying and dividing signed numbers. Let's break it down step by step:
Step 1: Simplify the multiplication first, remembering the rule that states multiplying two negative numbers results in a positive number:
(-2/3) x (-3) = (2/3) x (3)
Now, we have (2/3) multiplied by (3), and the 3's cancel out:
(2/3) x (3) = 2
Step 2: Simplify the division:
(-6/11) x (3/4) = (-6/11) / (4/3)
To divide fractions, we take the reciprocal of the second fraction and multiply:
(-6/11) / (4/3) = (-6/11) x (3/4)
Now, we have (-6/11) multiplied by (3/4):
(-6/11) x (3/4) = (-6 x 3) / (11 x 4)
(-6 x 3) = -18, and (11 x 4) = 44:
(-6/11) x (3/4) = -18/44
The fraction -18/44 can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 2:
-18/44 = -9/22
Step 3: Divide the results of step 1 by step 2:
2 / (-9/22)
To divide by a fraction, we multiply by its reciprocal:
2 / (-9/22) = 2 x (-22/9)
Now, multiplying:
2 x (-22/9) = -44/9
The fraction -44/9 cannot be simplified further, so it is the final result.
Therefore, (-2/3) x (-3) divided by (-6/11) x (3/4) equals -44/9.