Use the properties of operations and rules for multiplying and dividing to solve:
(-2) times (1 over 5) / (2 over 3) times (- 5 over 6) / (3 over 4)
A. (- 1 over 6)
B. (- 2 over 3)
C. (2 over 3)
D. (1 over 6)
To solve the expression, we can apply the rules for multiplying and dividing fractions.
First, let's simplify each multiplication individually:
(-2) times (1 over 5) becomes -2/5
(2 over 3) times (- 5 over 6) becomes (-10 over 18) or (-5 over 9)
Now, let's simplify the division:
(-2/5) divided by (-5/9) can be rewritten as (-2/5) times (9/(-5), using the reciprocal property. Multiplying the numerators and denominators gives us (-2 times 9) over (5 times -5), which simplifies to -18/(-25).
Finally, we can simplify -18/(-25) by dividing both the numerator and denominator by their greatest common factor, which is 1. This gives us 18/25.
So, the final simplified expression is 18/25.
Therefore, the answer is not provided in the options given.
To solve the expression (-2) times (1/5) / (2/3) times (-5/6) / (3/4), we can use the properties of operations and the rules for multiplying and dividing fractions.
Step 1: Start by simplifying each fraction:
(-2) times (1/5) = -2/5
(2/3) times (-5/6) = -10/18
(3/4) = 3/4
Now we have (-2/5) / (-10/18) / (3/4)
Step 2: To divide fractions, we can multiply by the reciprocal of the denominator. So, we can rewrite the expression as:
(-2/5) times (18/10) times (4/3)
Step 3: Multiply the numerators together and the denominators together:
(-2 times 18 times 4) / (5 times 10 times 3) = (-144) / (150)
Step 4: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6 in this case:
(-144) / (150) = (-24) / (25)
So, the simplified expression is (-24/25).
Therefore, the answer is D. (-24/25)
To solve the given expression, let's break it down step by step:
Step 1: Simplify the multiplication within the expression.
(-2) times (1/5) = -2/5
(2/3) times (-5/6) = -10/18, which can be simplified to -5/9
Now our expression becomes:
(-2/5) / (-5/9) / (3/4)
Step 2: Divide the fractions by multiplying by the reciprocal.
To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
(-2/5) * (9/-5) * (4/3) / (1/1)
Multiplying the numerators and denominators gives us:
(-2 * 9 * 4) / (5 * -5 * 3)
Simplifying the multiplication gives us:
(-72)/(-75)
Step 3: Simplify the final result.
To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).
In this case, the GCD of 72 and 75 is 3. Dividing both numbers by 3 gives us:
-24/(-25)
Since the numerator and denominator both have negative signs, they cancel each other out. Therefore, the final simplified result is:
24/25
So, the answer is not one of the options provided.