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
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