In math, equivalent fractions are fractions that are of the same value when simplified or calculated. Starting with a half, the subsequent equivalent fraction would be two-fourths.
Knowing when a fraction is equivalent to another provides insight into the fraction or math problem as a whole. Three-ninths would be three parts out of the nine parts available; but if there were only three parts available and three-ninths does not apply, then finding the equivalent fraction, one-third, would help one understand how to progress through the process. Also, equivalent fractions that are simpler than the initial fraction make it easier to calculate solutions to problems.