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Reducing Fractions, a la Shmoop. You may not be aware of it, but we have a

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serious fraction problem in this country. Every year, thousands of fractions are carelessly

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discarded. They make their way into our food and water

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supplies… … and pollute our air.

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So please – do your part to reduce, reuse and recycle fractions.

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Well… reduce them, anyway. Okay, so reducing fractions may not save the

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environment, but it will make your life easier. But how do we reduce a fraction?

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In this sense, “reduce” is simply another word for “simplify.”

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Say we are given the fraction twenty-four thirty-sixths.

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Hopefully we’re not following a recipe, because we might want to buy ourselves a new

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cookbook. Basically, we want to find the “equivalent

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fraction” with the smallest numbers, so it’s easier for us to wrap our head around

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it. Equivalent fractions are fractions that are

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exactly equal to one another. For example, three-fourths and six-eighths

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are equivalent fractions. If we give you three-fourths of a dollar,

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we’d be giving you seventy-five cents. If we give you six-eighths of a dollar, we’d

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still be giving you seventy-five cents. Just don’t spend it all in one place

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Well, back to our original fraction – twenty-four thirty-sixths.

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If we divide both our numerator and denominator in half, we get twelve-eighteenths.

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Because we are doing the same thing to the top and bottom, we wind up with an equivalent

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fraction. Chop it in half again, and we get six-ninths.

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We can no longer divide evenly by two, but we CAN divide by three…

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Now that both our numerator and denominator are prime numbers, our reducing days are behind

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us.

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Looks like the most reduced version of our original fraction is two-thirds.

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If you had realized from the beginning that the greatest common factor of 24 and 36 is

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12…

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…you could have saved yourself a couple of steps.

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But you’ll get the hang of it the more you practice.

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And we know you’ll practice plenty, because the world’s fractions are counting on you.

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Give a hoot. Don’t pollute. Reduce a fraction today.

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