# Means & Extremes in Algebra

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Means and extremes in algebra refer to ratios and proportions, with the mean being the middle numbers and the extreme being the outside numbers of the equation. Find out how to determine the means and extremes of a fractional equation with information from a math teacher in this free video math lesson.

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## Video Transcript

Alright so what are some means and extremes in Algebra, what exactly is that? Hi I'm Jimmy Chang and I have been teaching college mathematics for nine years and we are here to discuss a definition of what means and extremes are and then give an example to see how those terms can be used and solved for. Now means and extremes are used often in ratios and proportions and so what I want you to look at first is this ratio A to B and then you notice a set of double colons here, C to D. Now part of where a mean gets its meaning from is middle that comes from the word that means middle. Now if you notice here B and C are the letters most in the middle so that is why B and C by definition they are called your means. A and D being on the outside they would be called your extremes. So D is considered an extreme here and A is considered an extreme here. Now to write this in fraction form A to B that means A is on top, B is at the bottom and C to D means C is on top and D is on the bottom. So if you are in fraction form the B and C are your means and your A's and D's are your extremes here. Now here is the case and point on how to solve one of these. Suppose you have 3/2 = 5/x. Now your means are the 2 and the 5 and your extremes are your 3 and your x but if you are o'kay with cross multiplication solving this becomes very straightforward and this is all you have to do. Just take the denominator and multiply by the numerator on the other side so X x 3 is going to be 3x and then take this denominator and multiply it by the other numerator so 2 x 5 is going to be 10. Solving for x, divide 3 on both sides and so x is = to 10/3 and that is how you solve it. So I'm Jimmy and you have just learned how means and extremes work in Algebra.

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