Multiplication - the Halving and Doubling Strategy
Learning math at elementary school age is a little bit like collecting tools for a tool kit.
Here's a useful tool that can come in handy to simplify some tricky looking multiplication.
Multiplying using the halving and doubling strategy
When you're faced with a multiplication like:
4 x 16 = ?
You have a number of methods to use:
Short multiplication - the written method we all learnt at school - here's a video to remind you
The grid method as discussed in this article
The distributive law - which sounds scary but basically means 'splitting' it into two easy multiplications - so 4 x 16 becomes (4 x 10) + (4 x 6)
Or sometimes, such as in this example, it's just perfect for the Half and Double Method
Using the halving and doubling method, we can halve one side of the multiplication as long as we double the other - and the answer remains the same.
4 x 16
8 x 8 = 64
Here is another example which looks a little tricky at first:
34 x 5 = ?
But after using the half and double method it becomes:
17 x 10 = 170
The method also works very well with some fractions like this:
3½ x 12 = ?
Doubling removes the fraction so it becomes:
3½ x 12 = 7 x 6 = 42
Likewise with decimals:
4.5 x 8 = 9 x 4 = 36
The key to using the halving and doubling strategy is choosing when it makes the problem easier. Here is a guide:
Is one of the sides 5? If so, doubling will give 10 which is easy.
Is the side I need to halve even?
Does one side include a half or 0.5? If so doubling will remove it.
And that's it. A handy little multiplication strategy to add to your 'math toolkit'.
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