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Two fractions that are different but equivalent have, by definition, numerators and denominators that are multiples of each other. In other words, multiplying the numerator and denominator of a fraction by the same number will produce an equivalent fraction. Though the numbers in the new fraction will be different, the fractions will have the same value. For instance, if we take the fraction 4/8 and multiply both the numerator and denominator by 2, we get (42)/(82) = 8/16. These two fractions are equivalent. (42)/(82) is essentially the same as 4/8 2/2 Remember that when multiplying two fractions, we multiply across, meaning numerator to numerator and denominator to denominator. Notice that 2/2 equals 1 when you carry out the division. Thus, it's easy to see why 4/8 and 8/16 are equivalent since multiplying 4/8 (2/2) = 4/8 still. The same way it's fair to say that 4/8 = 8/16. Any given fraction has an infinite number of equivalent fractions. You can multiply the numerator and denominator by any whole number, no matter how large or small to obtain an equivalent fraction. Like multiplication, division can also be used to find a new fraction that's equivalent to your starting fraction. Simply divide the numerator and the denominator of a fraction by the same number to obtain an equivalent fraction. There is one caveat to this process--the resulting fraction must have whole numbers in both the numerator and denominator to be valid. For instance, let's look at 4/8 again. If, instead of multiplying, we divide both the numerator and denominator by 2, we get (4 2)/(8 2) = 2/4. 2 and 4 are both whole numbers, so this equivalent fraction is valid.
Multiply the numerator and denominator by the same number. Divide the numerator and denominator by the same number.