Question
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)
(-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)
Answers
GPT 3.5
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.
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.