Doubling & Halving Doubling & Halving with Multiplicationwith Multiplication

Doubling and halving works because of Doubling and halving works because of the relationship between the relationship between

multiplication and division. multiplication and division.

Since multiplication and division are Since multiplication and division are opposites, we can multiply one factor opposites, we can multiply one factor by 2 and divide the other factor by 2 by 2 and divide the other factor by 2

and the product does not change.and the product does not change.

This method of multiplication works well This method of multiplication works well with with somesome numbers. Numbers that numbers. Numbers that

are multiples of 5 and 10 work well. are multiples of 5 and 10 work well. Since it is more difficult to compute with Since it is more difficult to compute with

fractions and decimals, it works best fractions and decimals, it works best to take half of an even number. With to take half of an even number. With some experience, students soon find some experience, students soon find which numbers work nicely with this which numbers work nicely with this

method.method.

64 x 25 = ?64 x 25 = ?64 x 25 64 x 25 I can easily take half of 64 and double 25.I can easily take half of 64 and double 25.

32 x 50 32 x 50 I can easily take half of 32 and double 50.I can easily take half of 32 and double 50.

16 x 100 16 x 100 I can easily find this product!I can easily find this product!

16 x 100 = 160016 x 100 = 1600

“COOL”

Try one on your Try one on your own…own…

Choose a problem from these:Choose a problem from these:

33 x 5533 x 55

45 x 3645 x 36

5 x 1485 x 148

Did you choose this?Did you choose this? 5 x 148 5 x 148

5 x 1485 x 148 I can easily double 5.

I can take half of 148.

1100

74

x

10 x 74 = 740

Now it’s easy with 10.

How did you do?

This method of multiplying supports This method of multiplying supports mental math. This method also mental math. This method also supports the properties of supports the properties of multiplication and division. Students multiplication and division. Students feel SO powerful when they can use feel SO powerful when they can use this! this!