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To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
1/2 ÷ 2/3 = 1/2 * 3/2
Next, multiply the numerators together (1 * 3 = 3) and multiply the denominators together (2 * 2 = 4):
1/2 * 3/2 = 3/4
Therefore, the simplified answer is 3/4.