use the properties of operations and rules for multiplying and dividing to solve
(-2) x (1/5) divided by (2/3) x(-5/6) divided by (3/4)
A 2/3
B -2/3
C -1/6
D 1/6
To solve this expression, we can follow the order of operations, which is parentheses, multiplication/division (from left to right), and then addition/subtraction (from left to right). Let's simplify the expression step by step:
(-2) x (1/5) divided by (2/3) x (-5/6) divided by (3/4)
First, let's simplify the multiplication/division within each fraction:
(-2) x (1/5) = -2/5
(2/3) x (-5/6) = -10/18 = -5/9
(3/4) = 3/4
Now, let's perform the division of the fractions:
(-2/5) divided by (-5/9) divided by (3/4)
Dividing fractions is the same as multiplying by the reciprocal of the second fraction. Let's simplify each division step-wise:
(-2/5) divided by (-5/9) = (-2/5) x (-9/5) = 18/25
18/25 divided by (3/4) = 18/25 x (4/3) = 72/75 = 24/25
Therefore, the final answer is 24/25, which can also be simplified to 6/25.
Answer: D) 1/6
To solve (-2) x (1/5) divided by (2/3) x (-5/6) divided by (3/4), let's simplify the expression step-by-step:
Step 1: Multiply the numerators and the denominators for each pair of fractions separately.
Numerator 1 = (-2) x (1/5) = -2/5
Denominator 1 = (2/3) x (-5/6) = -10/18
Step 2: Divide the first result by the second result.
(-2/5) ÷ (-10/18) = (-2/5) x (18/-10)
Simplifying the multiplication, we get (-2/5) x (-9/5) = 18/25
Step 3: Repeat steps 1 and 2 with the next fraction: 18/25 divided by (3/4).
Numerator 2 = 18/25
Denominator 2 = 3/4
18/25 ÷ (3/4) = (18/25) x (4/3)
Multiplying the fractions, we get (72/75) or (24/25)
Therefore, the solution to the expression (-2) x (1/5) divided by (2/3) x (-5/6) divided by (3/4) is 24/25, which is option answer D.
To solve the expression (-2) x (1/5) ÷ (2/3) x(-5/6) ÷ (3/4), we need to apply the properties of operations and rules for multiplying and dividing.
Step 1: Start by multiplying the numerator and denominator of each fraction separately, following the rule that multiplying two fractions means multiplying their numerators and denominators.
(-2) x (1/5) = -2/5
(2/3) x (-5/6) = -10/18
Step 2: Simplify the resulting fractions if possible. In this case, both fractions can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2.
-2/5 can be simplified to -1/2
-10/18 can be simplified to -5/9
Step 3: Rewrite the expression with the simplified fractions.
So, the expression now becomes:
(-1/2) ÷ (-5/9) ÷ (3/4)
Step 4: Remember that dividing by a fraction is the same as multiplying by its reciprocal. So, to divide by a fraction, we can multiply by its reciprocal.
Therefore:
(-1/2) ÷ (-5/9) ÷ (3/4) is equivalent to (-1/2) x (9/-5) x (4/3)
Step 5: Multiply the numerators and denominators:
(-1 x 9 x 4) / (2 x -5 x 3)
(-36) / (-30)
Step 6: Simplify the resulting fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6.
(-36) / (-30) can be simplified to 6/5
Therefore, the answer to the expression (-2) x (1/5) ÷ (2/3) x(-5/6) ÷ (3/4) is 6/5.
Hence, the correct option is D) 1/6.