- Chapter 1
- What multiplication is
- So, what did you come up with? Here’s the answer:
- Multiplication is just…..repeated addition.
- That’s it.
- (Is that what you came up with? If not, don’t worry.)
- Let’s look at this. Multiplication of two numbers tends to be thought of as
- ‘timesing two numbers together’. The word ‘times’ here, which has morphed
- into a verb over the years, actually refers to the number of times we add. This is
- very important. It is how many times we add.
- For example,
- 3 x 5 = 15
- Because we add 5… 3 times.
- So above, you probably read that as 3 times 5. Now read it as
- 3 times (we add) 5.
- 3 x 5 = 3 times (we add) 5 = 5 + 5 + 5 = 15.
- Another example
- 4 x 6 = 4 times (we add) 6 = 6 + 6 + 6 + 6 = 24
- And so on!
- 5 x 7 = 5 times (we add) 7 = 7 + 7 + 7 + 7 + 7 = 35
- How exciting. This is how easy it is.
Multiplication is just addition! So the ‘times’ is not another word for multiply, it
is actually the number of times we add. You can probably see that this is
Victorian sort of language, which has got dropped over the years. It sounds like
some kind of proverb – 5 times we add 7. Obviously the ‘we add’ part has
eroded away and now everyone thinks times = multiply, but it doesn’t.
Again, the ‘times’ is not another word for multiply, it is actually the number of
times we add.
So what?
Now we know that we can never get a multiplication wrong. If you can add, you
can multiply. You don’t actually need to memorise times tables anymore. You
could work each one out every time if you wanted! The memorisation of times
tables is okay when you understand why 5 x 7 = 35, but it’s basically useless if
you don’t.
Now you do.
Now you can do any multiplication.
Any.
Because you know that you could just add over and over.
I thought you said this was going to be optimised?
It is! But we need to understand what we’re doing first.
Let’s look at some more examples.
7 x 9 = 7 times (we add) 9 = 9 + 9 + 9 + 9 + 9 + 9 + 9 = 63
8 x 12 = 8 times (we add) 12 = 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 96
14 x 7 = 14 times (we add) 7
But wait. Here’s another concept. It doesn’t matter which order we do it in.