Subjects algebra

Negative Fraction Sign 928308

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1. The problem is understanding how the fraction $-\frac{3}{2}$ can become positive. 2. The sign of a fraction depends on the signs of the numerator and denominator. 3. If both numerator and denominator are negative, the fraction becomes positive because a negative divided by a negative is positive. 4. For example, if you multiply numerator and denominator by $-1$, you get: $$-\frac{3}{2} = \frac{-3 \times -1}{2 \times -1} = \frac{3}{-2}$$ 5. But $\frac{3}{-2}$ is still negative, so to make it positive both must be negative: $$-\frac{3}{2} = \frac{-3}{2}$$ is negative, but $$\frac{-3}{-2} = \frac{3}{2}$$ is positive. 6. So, $-\frac{3}{2}$ becomes positive only if both numerator and denominator are negative, which cancels the negatives.