Question

explain why multiplying the numerator and denominator of a fraction by the same number results in an equivalent fraction

Answer 1

Think:  You're treating the numerator and the denom. in precisely the same way.  In doing so you are NOT changing the value of the fraction, only the appearance.

Example:  start with 2/3.  Mult num. and den. both by 7:  14/21.

2/3 and 14/21 result in precisely the same decimal fraction, showing that the latter set of fractions is equivalent to the former set.