List the factors of the numerator and denominator of the first fraction, then divide them by the largest factor that both possess. For an example, let the first fraction be 2/8. The numerator's factors are 1 and 2; the denominator's factors are 1, 2, 4 and 8; and the largest factor that both possess is 2. Dividing 2 by 2 results in 1 and dividing 8 by 2 results in 4. The reduced fraction is 1/4.
List the factors of the second fraction's numerator and denominator, then divide them by the largest factor that both possess. For this example, the second fraction is 3/12. The numerator's factors are 1 and 3; the denominator's factors are 1, 2, 3, 4, 6 and 12; and the largest factor for both is 3. Dividing 3 by 3 results in 1 and dividing 12 by 3 results in 4. The reduced fraction is 1/4.
Compare the two reduced fractions. If they are equal, then the two original fractions are equivalent --- 1/4 and 1/4 are equal, so the fractions 2/8 and 3/12 are equivalent.
Multiply one fraction's numerator with the other's denominator. For an example, the fractions are 9/10 and 28/30. Multiplying 9 by 30 results in 270.
Multiply the other fraction's numerator with the first fraction's denominator. For this example, 28 multiplied by 10 equals 280.
Compare the two cross products. Equal cross products mean equivalent fractions, and unequal ones mean the fractions are not equivalent. Concluding this example, 270 is not equal to 280, so the fractions are not equivalent.