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For simple fractions without variables, you can simply express each fraction as a decimal number to determine equivalency. Since every fraction is actually a division problem to begin with, this is the simplest way to determine equivalency.  For instance, take our previously used 4/8. The fraction 4/8 is equivalent to saying 4 divided by 8, which 4/8 = 0.5. You can solve for the other example as well, which is 8/16 = 0.5. Regardless of the terms of a fraction, they are equivalent if the two numbers are exactly the same when expressed as a decimal. Remember that the decimal expression may go several digits before the lack of equivalence becomes apparent. As a basic example, 1/3 = 0.333 repeating while 3/10 = 0.3. By using more than one digit, we see that these two fractions are not equivalent. For more complex fractions, the division method requires additional steps. As with the multiplication method, you can 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. Most fractions should typically be expressed in their lowest terms, and you can convert fractions to their simplest terms by dividing by their greatest common factor (GCF). This step operates by the same logic of expressing equivalent fractions by converting them to have the same denominator, but this method seeks to reduce each fraction to its lowest expressible terms.  When a fraction is in its simplest terms, its numerator and denominator are both as small as they can be. Neither can be divided by the any whole number to obtain anything smaller. To convert a fraction that's not in simplest terms to an equivalent form that is, we divide the numerator and denominator by their greatest common factor. The greatest common factor (GCF) of the numerator and denominator is the largest number that divides into both to give a whole number result. So, in our 4/8 example, since 4 is the largest number that divides evenly into both 4 and 8, we would divide the numerator and denominator of our fraction by 4 to get it in simplest terms. (4 ÷ 4)/(8 ÷ 4) = 1/2. For our other example of 8/16, the GCF is 8, which also results in 1/2 as the simplest expression of the fraction.
Calculate each fraction as a decimal number. Divide the numerator and denominator of a fraction by the same number to get an equivalent fraction. Reduce the fractions to their lowest terms.