How to Cross Multiply Proportions

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Cross multiplying proportions is a straightforward process that is the same as cross multiplying fractions. Cross multiply by multiplying a numerator by the other side's denominator with help from a math teacher in this free video on proportions in math.

Part of the Video Series: Fractions & Proportions
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Video Transcript

So how does one cross multiply proportions? Hi, I'm Jimmy, I've been teaching college math for nine years and once you see the process of cross multiplication and proportions you will actually find that it is a very straightforward exercise and one that can be picked up very quickly so here is an example as to where cross multiplication becomes very important. Now suppose you have a fraction let's just say 3/4 = and suppose you have another proportion but this time you don't know what one of the sides is. Let's just say you have x/9. Now you can cross multiple any time you have one fraction making up the left side = to another fraction making up the right side. Now to cross multiply you literally cross over, you take the denominator of one side and you multiply with the numerator on the other side so in this case you have 4 times x which is 4x and then you repeat on the other side, you take the 9 which is the denominator and you cross multiply with a numerator on the other side. So you have 9 x 3 and we are just going to give you 27 and then you have a little equation, no more fractions to work with and here you have to divide both sides by 4 so you get x = 27/4. Now what if x is on the denominator. Same exact strategy. Suppose you have 1/2 = 3/x. Same exact approach, take the denominator, multiply by the numerator on the other side, 2 x 3 is 6 and then take this denominator and multiply it by the numerator on the other side x times 1 = x and therefore you have x = 6 which means you don't have to do anything more but cross multiplication just involves multiplying the denominators on one side with the numerators on the other side and that's about as good as it gets so I am Jimmy and that is how you cross multiply proportions.

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