This visual method of multiplying fractions

was something that was shown to me last week

by the girls I tutor. Like most people I learned

to multiply fractions by multiplying numerator

by numerator, and denominator by denominator.

That's pretty much the gold standard of fraction

multiplication.

This method gives a visual sense of what it means

to multiply fractions. For our example we'll use:

2/5 x 1/3=

Draw a square. Divide in into three vertical portions

and color in one of the thirds. This represents 1/3.

For a real world styled word problem, think of this as

a brownie pan with only one third of the brownies

left in it.

Next, we represent the 2/5. Divide the square

horizontally into five portions. Using a different color,

fill in two of the fifths. The two colors will overlap,

this is a good thing.

For the word problem, think some comes and eats

2/5ths of the remaining brownies. How much of

the pan of brownies did they eat?

For our answer, count the total number of rectangles.

This number is our denominator. So for our problem,

this number is 15. The numerator is the number

of rectangles where our colors overlap. Here that

would be 2. So our answer is 2/15, or 2/15 of the

entire pan of brownies.

So, 2/5 x 1/3 = 2/15