To solve the equation \( \frac{7}{3} \div \frac{2}{3} \) and determine its relationship to \( \frac{1}{2} \), follow these steps:
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Dividing by a fraction is the same as multiplying by its reciprocal. So, we have: \[ \frac{7}{3} \div \frac{2}{3} = \frac{7}{3} \times \frac{3}{2} \]
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Now, perform the multiplication: \[ \frac{7 \times 3}{3 \times 2} = \frac{21}{6} \]
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Simplifying \( \frac{21}{6} \): \[ \frac{21}{6} = \frac{7}{2} \quad \text{(after dividing both the numerator and denominator by 3)} \]
Now, comparing \( \frac{7}{2} \) with \( \frac{1}{2} \):
To express \( \frac{7}{2} \) in relation to \( \frac{1}{2} \): \[ \frac{7}{2} = 7 \times \frac{1}{2} \]
Thus, \[ \frac{7}{3} \div \frac{2}{3} = \frac{7}{2} = 7 \times \frac{1}{2} \]
Therefore, the answer is: \[ \frac{7}{3} \div \frac{2}{3} = \frac{7}{2} \quad \text{which equals } 7 \times \frac{1}{2} \]