Question
Evaluate and simplify the following complex fraction. \( \frac{\frac{2}{3}}{\frac{4}{-9}}= \) \( < \)
Ask by Hampton Reid. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified result is –3/2.
Solution
To evaluate (2/3) divided by (4/–9), follow these steps:
1. Rewrite the division as multiplication by the reciprocal:
(2/3) ÷ (4/–9) = (2/3) × (–9/4)
2. Multiply the numerators and denominators:
= (2 × –9) / (3 × 4) = –18/12
3. Simplify the fraction by dividing numerator and denominator by their greatest common divisor, 6:
–18 ÷ 6 = –3 and 12 ÷ 6 = 2
Thus, the simplified result is –3/2.
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Simplify this solution Mind Expander
To simplify the complex fraction \( \frac{\frac{2}{3}}{\frac{4}{-9}} \), you can multiply by the reciprocal of the denominator. So we compute: \[ \frac{2}{3} \div \frac{4}{-9} = \frac{2}{3} \times \frac{-9}{4} = \frac{2 \times -9}{3 \times 4} = \frac{-18}{12} \] Now, simplify \( \frac{-18}{12} \) by dividing both the numerator and denominator by their greatest common divisor, which is 6: \[ \frac{-18 \div 6}{12 \div 6} = \frac{-3}{2} \] Thus, the simplified result is: \[ \frac{2}{3} \div \frac{4}{-9} = \frac{-3}{2} \]
