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) options
2 3/4
-2 3/4
81/99
-81/99
To solve the expression (-2/3) x (-3) ÷ (-6/11) x (3/4), let's simplify each individual multiplication and division step.
(-2/3) x (-3) = 2/3 x 3 = 6/3 = 2
(-6/11) x (3/4) = -18/44 = -9/22
Now, we have 2 ÷ (-9/22). Dividing is the same as multiplying by the reciprocal, so this becomes: 2 x (-22/9) = -44/9.
Therefore, the final answer is -44/9, which is equivalent to -4 8/9 or -4.888... rounded to the nearest tenth.
Thus, the correct option is -4 8/9.
whitch one a b c or d
The correct option is d) -4 8/9.
To solve the expression (-2/3) x (-3) ÷ (-6/11) x (3/4), we can simplify the calculation step by step using the properties of operations and rules for multiplying and dividing signed numbers.
Step 1: Multiply the numerator and denominator of each fraction separately.
(-2/3) x (-3) = 6/3 = 2
(-6/11) x (3/4) = (-18)/(44) = -9/22
Step 2: Divide the resulting fractions.
(2) ÷ (-9/22)
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
(2) x (22/(-9)) = (44)/(-9) = -(44/9) = -4 8/9
Therefore, the option that correctly solves the expression is -4 8/9.
To solve this problem using the properties of operations and rules for multiplying and dividing signed numbers, we will follow these steps:
Step 1: Simplify the expression
Start by simplifying each of the fractions before performing any operations.
(-2/3) x (-3) can be simplified as follows:
-2/3 x -3 = 6/3 = 2
(-6/11) x (3/4) can be simplified as follows:
-6/11 x 3/4 = -18/44 = -9/22
So, the expression becomes:
2 divided by (-9/22)
Step 2: Divide the fractions
To divide two fractions, multiply the first fraction by the reciprocal of the second fraction.
2 divided by (-9/22) is the same as multiplying 2 by the reciprocal of (-9/22). The reciprocal of (-9/22) is (-22/9).
So, 2 x (-22/9) = -44/9
Step 3: Simplify the result
The fraction -44/9 can be simplified further by finding the greatest common divisor (GCD). The GCD of 44 and 9 is 1.
Divide both the numerator and denominator by the GCD:
-44/9 = (-44 ÷ 1) / (9 ÷ 1) = -44/9
Therefore, the final answer to the expression (-2/3) x (-3) divided by (-6/11) x (3/4) is -44/9, which is option (C) -81/99 when simplified.