Fraction Multiplication

Addition is easy to explain. 3 + 5 = 8. You can see addition with a picture:

Capture1

However, I have been thinking about how to explain multiplication. For example, I know that 4 x 5 = 20. But how can I show that? One method is to think about repeated addition. 4 x 5 means that we take the number 4 and add it up 5 times.

4 + 4 + 4 + 4 + 4 = 20

Capture2

Now this extends very nicely when thinking about fractions. What is \frac{2}{3} \times 5 ?

We can use the method of repeated addition:

\frac{2}{3} + \frac{2}{3} + \frac{2}{3} + \frac{2}{3} + \frac{2}{3}

If you recall, when the bottom of the fraction (denominator) is the same, we can just add up all the tops (numerators).

\frac{2}{3} + \frac{2}{3} + \frac{2}{3} + \frac{2}{3} + \frac{2}{3} = \frac{10}{3}

Many of you could simply calculate:

\frac{2}{3} \times 5 = \frac{10}{3}

because you know that you can multiply the 2 and the 5. The above method shows why this trick is valid. See if you can figure out \frac{8}{3} \times 7 =

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