As a math tutor, you’re bound to teach this quick method for solving proportions.

When you encounter

what do you do? Well, the easiest approach is probably what many call “cross multiplying”. I learned it in grade 7.

Cross multiplying argues that when two fractions are equivalent, their diagonals multiply to the the same amount. For instance, consider

Notice that the diagonals both mutliply to 10:

We can use the handy principle that equal fractions have equal diagonals to solve virtually any rate or proportion question – including percents.
Consider, again, our first problem:

We now know that, since the left fraction equals the right fraction, the diagonals must multiply to be the same:

Next, we divide both sides by 12:

We arrive at

We’ll be looking at some applications of this very old – and extremely useful – method in future posts.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.