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((-5)/(9) divide (2)/(3))=?...

`((-5)/(9) divide (2)/(3))=?`

A

`(-5)/(2)`

B

`(-5)/(6)`

C

`(-10)/(27)`

D

`(-6)/(5)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem \((-5/9) \div (2/3)\), we will follow these steps: ### Step 1: Write the division as multiplication When dividing by a fraction, we can multiply by its reciprocal. The reciprocal of a fraction is obtained by swapping its numerator and denominator. \[ (-5/9) \div (2/3) = (-5/9) \times (3/2) \] ### Step 2: Multiply the fractions Now, we multiply the numerators together and the denominators together. \[ (-5 \times 3) / (9 \times 2) \] Calculating the numerator: \[ -5 \times 3 = -15 \] Calculating the denominator: \[ 9 \times 2 = 18 \] So we have: \[ (-5/9) \div (2/3) = -15/18 \] ### Step 3: Simplify the fraction Now we need to simplify \(-15/18\). We can find the greatest common divisor (GCD) of 15 and 18, which is 3. Dividing both the numerator and the denominator by their GCD: \[ -15 \div 3 = -5 \] \[ 18 \div 3 = 6 \] Thus, we have: \[ -15/18 = -5/6 \] ### Final Answer \[ (-5/9) \div (2/3) = -5/6 \] ---
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