What is the doubling and halving strategy?

The doubling and halving strategy is a mathematical technique used for simplifying multiplication problems. The idea is to make one of the numbers in a multiplication problem easier to work with, by doubling one number and halving the other. This works because when you double one number and halve the other, the overall product remains the same.

Let's look at an example with the multiplication problem 6 x 16.

Step 1: Choose one number to double and the other to halve. It's usually best to halve an even number because you'll end up with a whole number. So in this case, we will halve 16 (to get 8) and double 6 (to get 12).

Step 2: Multiply the new pair of numbers. So then you would calculate 12 x 8.

Step 3: Realize that these two problems, 6 x 16 and 12 x 8, are equivalent. They both have the same product, which is 96.

So, using the doubling and halving strategy you've transformed a possibly harder multiplication problem into an easier one, without changing the final product.