How to Solve Fractions & Proportions With Letters

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Solving fractions and proportions with letters is something that will require you to assign each letter a value. Solve fractions and proportions with letters with help from an experienced mathematics educator in this free video clip.

Part of the Video Series: Math Lessons & Tips
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Video Transcript

Hi, my name is Marija, and today I'm gonna tell you how to solve fractions and proportions with letters. So proportion is two fractions that are actually equal. So for example, if we had two over three equals x over 12, this is called a proportion because there's two fractions or ratios that are equal. And the way that you solve them is by cross multiplying. So I would take the three and multiply by the x to get 3x, and I would take the 12 and multiply by the two to get 24. So now what results once you cross multiply is just a one step equation. And now I just solve this one step equation by using inverse operations. So I'm trying to get x alone. So I divide by three on both sides, and when I do that, I get x equals eight. So that means that eight would be the value of x that would actually complete the proportion and make these two fractions equal. I'll do another example. Let's say we had x over four equals, let's say three over 10. Again we're gonna cross multiply, so we're gonna get x times 10 is 10x equals three times four is 12, and then we're gonna divide by 10 on both sides, and when we do that, this time we're gonna get a fraction as an answer, so we're gonna get one and two-tenths, or one and one-fifth. So to solve fractions and proportions that have letters or variables, you just cross multiply and solve the equation.


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