Addition is easy to explain. 3 + 5 = 8. You can see addition with a picture:
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
Now this extends very nicely when thinking about fractions. What is ?
We can use the method of repeated addition:
If you recall, when the bottom of the fraction (denominator) is the same, we can just add up all the tops (numerators).
Many of you could simply calculate:
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