Multiplication by 1. We bet you like the sound of that. And well you should. It's as simple as it sounds.
Mathematicians call 1 the multiplicative identity, meaning that any number multiplied by 1 gets to keep its identity. Any number multiplied by a number other than one is immediately given an alias and escorted by a U.S. Marshal to a farmhouse in Iowa as a member of the Witness Protection Program.
When we find equivalent fractions, what we're really doing is multiplying by a cleverly disguised form of 1. We're talking fake mustache, glasses, a wig made out of real human hair—the works.