What is cross-multiplying?

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Let's go back to fractions. We know that:

If we multiply both sides by 4 and divide both sides by 6, we get:

You will notice that all we did was switch the 4 and 6. The other thing we could have done is multiply both sides by 6 and 8 to get 3 x 8 = 4 x 6. That is the basic idea behind cross-multiplying.

Suppose you have this:

Because 4 = 4/1, all we have to do is cross-multiply the x and 4 to get:

Of course, the answer is 6.

Just one warning about cross-multiplying:

THE DENOMINATOR OF EITHER FRACTION CANNOT BE ZERO BEFORE OR AFTER CROSS-MULTIPLYING!!!!

That way, you can avoid garbage solutions like for this problem:

Cross-multiplying, we get:

Then subtracting x from both sides, we find that -1 = -2. If anyone ever proves that for real, maybe we should nominate them for the Nobel Prize for Mathematics.