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Study Guide

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It would be shocking to find we have a common ancestor with a friendâ€”even more so if it's an enemy. Numerators and denominators know how we feel. If both the numerator and denominator of a fraction have a common factor (i.e. if they can both be divided by the same number), we can find an equivalent fraction with smaller numbers. This is called **reducing** or **simplifying** the fraction. To find a reduced fraction, we divide both the numerator and denominator by their common ancestor, er, factor.

It's fastest to use the greatest common factor of the numerator and denominator. If we don't happen to know the GCF, it's perfectly fine to reduce a fraction over and over until it can't be reduced any further.

For example, let's reduce this fraction:

We know for sure that 24 and 36 are both divisible by 2, so we can divide the top and bottom by 2.

Boom; we've got an equivalent fraction. But the numerator and denominator can still both be divided by 2, so let's reduce again.

Finally, we can divide the top and bottom by 3.

And that's it. There aren't any more common factors between 2 and 3, so we can't reduce it any further.

In the example above, if we had spotted right away that the GCF of the numerator and denominator is 12, we could have solved this in one step by dividing the top and bottom by 12.

Fractions in answers should pretty much always be reduced. In other words, if we get a fraction for our final answer in a problem, we should always reduce that thing as much as we can.

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