If you mean multiplying numerator and denominator by different numbers, the result is then a different ratio. If you mean variously multiplying the numerator and denominator by the same number on different occasions, the result is unchanged.
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you multiply first then you divide
Whatever you multiply or divide the numerator by, you must do the same to the denominator. If you multiply or divide the numerator and denominator by different numbers, you change the value of the fraction and turn it into a different number. After that, nothing is "equivalent" any more ... you're working with a changed number.
" ... multiply by the RECIPROCAL of the divisor.
multiply them and divide by two