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((-5)/(6) divide (-2)/(3))=?...

`((-5)/(6) divide (-2)/(3))=?`

A

`(-5)/(4)`

B

`(5)/(4)`

C

`(-4)/(5)`

D

`(4)/(5)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem \((-5/6) \div (-2/3)\), we can follow these steps: ### Step 1: Write the division as multiplication by the reciprocal When dividing fractions, we can multiply by the reciprocal of the second fraction. Thus, we rewrite the expression: \[ (-5/6) \div (-2/3) = (-5/6) \times (-3/2) \] ### Step 2: Multiply the numerators and denominators Now, we multiply the numerators together and the denominators together: \[ (-5) \times (-3) = 15 \] \[ 6 \times 2 = 12 \] So, we have: \[ (-5/6) \times (-3/2) = \frac{15}{12} \] ### Step 3: Simplify the fraction Next, we simplify the fraction \(\frac{15}{12}\). Both the numerator and the denominator can be divided by their greatest common divisor (GCD), which is 3: \[ \frac{15 \div 3}{12 \div 3} = \frac{5}{4} \] ### Final Answer Therefore, the final answer is: \[ \frac{5}{4} \] ---
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