ShmoopTube

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Adding & Subtracting Fractions, a la Shmoop.

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Have you ever known someone who wants to be just like you? [Girl hugging her sister]

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Maybe the kid who lives next door, or your little kid brother.

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Or your stalker? [man stalking another man with binoculars]

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Maybe they noticed your sweet new plaid pants… … and decided to wear the same pair.

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They do whatever they can to be similar… …because they want to be friends. [man looking through binoculars at men playing golf]

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In a creepy sort of way.

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Adding fractions sort of works the same way. If the denominator is different…

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…one - or both - of the fractions attempt to have the same bottom.

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Take 2/3 plus 1/6, for instance.

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In order to add the fractions, we need to make the denominators the same. [arrow points to denominators of fractions]

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We do this by multiplying the top and bottom of the fraction by the same number.

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In this case, we take two-halves times two-thirds to get four-sixths.

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Remember… two-halves, or 2 divided by 2, equals 1… [fraction of 2 over 2 equals 1]

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… so we're actually just multiplying by 1.

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Now the denominators are the same…

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… so we can add them. We get 4/6 plus 1/6 equals 5/6.

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It works for subtraction, too.

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Subtracting, we get 4/6 minus 1/6 equals 3/6… and of course we can reduce it to get ½.

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Sometimes both of the denominators need to be changed. [man looking worried at changing nappies]

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Like 1/8 plus 1/3. What's the common denominator there?

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You have to multiply them. 3 times 8 is 24.

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So we need to multiple 3 up here and get 3/24 and 1/3 you need to multiply by 8/8...

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and you get 8/24.

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That gives us 3/24 plus 8/24. Add the 3 and the 8, you get 11/24. Voila!

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It's annoying when someone is copying you all the time… [A couple arguing]

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… but hey, imitation is the sincerest form of flattery.

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