Because division and multiplication are mutually inverse operations.
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(a/b) divided by (c/d) =(a/b) x (d/c) <-- notice divisor is inverted (turned upside down) now multiply both numerators and both denominators = (ad)/(bc)
When you divide by fractions, you invert and multiply.
" ... multiply by the RECIPROCAL of the divisor.
To divide by a fraction, invert the divisor and multiply: 5/8 ÷ 5/3 = 5/8 x 3/5 = 3/8
Because that is just how it works mathematically If you divide one vulgar (or common) fraction by a second vulgar fraction, the rule is: Invert the second fraction and then multiply them together. It is too difficult to explain why this works, using typed explanation on the computer, but just accept that it works.