If you have memorized the rule "divide fractions by flipping and multiplying" without knowing why, check it here. Division originally asks "how many times does it fit?" Use the bars to count how many 1/2 pieces fit into one cake, and see why multiplying by the reciprocal always gives the same answer.
The original meaning of division: 6÷2 asks, "How many times does 2 fit into 6?" The answer is 3. Fractions work the same way. 3/4 ÷ 1/8 asks, "How many times does 1/8 fit into 3/4?"
Why does multiplying by the reciprocal give the answer? If we rewrite both fractions with the same denominator, 3/4=6/8 and 1/8=1/8. When the denominators are the same, division is the same as dividing the numerators, so 6/8 ÷ 1/8 = 6÷1 = 6. When you write this process as a formula, it turns out to be exactly the same calculation as "the first fraction × the reciprocal of the second fraction" — so instead of finding a common denominator every time, we use multiplying by the reciprocal as a shortcut.