4/6 : 12/3

To solve the proportion \( \frac{4}{6} : \frac{12}{3} \), you can first simplify each fraction.

1. Simplify \( \frac{4}{6} \): \[ \frac{4}{6} = \frac{2}{3} \quad (\text{dividing both numerator and denominator by 2}) \]

2. Simplify \( \frac{12}{3} \): \[ \frac{12}{3} = 4 \quad (\text{dividing both numerator and denominator by 3}) \]

Now, you can rewrite the ratio: \[ \frac{2}{3} : 4 \]

To express this in a more manageable form, you can convert it into a fraction: \[ \frac{2/3}{4} = \frac{2}{3} \cdot \frac{1}{4} = \frac{2}{12} = \frac{1}{6} \]

So, the ratio \( \frac{4}{6} : \frac{12}{3} \) simplified is \( \frac{1}{6} \).