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 Algebra: Proportions Solvers Lessons Answers archive Quiz In Depth

A proportion is an equation such as:

x:3 :: 4:6

Solving proportions is very easy. There is actualy a number of ways to do it, all of which yield same results, of course. We'll give you the easiest and most foolproof way to do it.

### Cross-multiply

You should multiply the opposing corners of your proportion, like this:

That is, you multiply both sides of the equation by 10 and 12. The multipliers will go to the sides of the equation that are opposite to where they were as denominators:

5*10 = x*12

Note that depending on where the x was, it may end up on the left as well as on the right side of the equation. That's ok, since as you know you can switch the sides of the equation: if Bob = Jim, then Jim = Bob.

If you got here, you have done most of what you need to solve the problem: what you have now is basically a trivial linear equation. What you need to do now is to divide both sides by the multiplier near x so that x is left totally alone. In our example, this would mean dividing both sides by 12. You would get:

To get the value of x, you need to evaluate the part of the equation that does not contain x.