Doubling by Number Splitting

Last week, when we started discussed doubling from left to right, we explained how to anticipate “carrying” when the next digit to the right is “big”. But this process might be hard to explain to younger kids. It might be easier if we will introduce the number-splitting technique to them first.

Numbers can be split into two or more addends. In doubling, we can start by splitting a big digit into 5 and a small digit: 6 is 5 + 1, 7 is 5 + 2, etc.

To double 6, we can double 5 and 1 separately the add the results: 2 x 6 = 2 (5 + 1) = 10 + 2 = 12

Similarly, we can double 9 as follows: 2 x 9 = 2 x (5 + 4) = 10 + 8 = 18.

We can see that our technique for doubling from left to right is just an application of number splitting.

Last week, we wrote “for example,  twice 2,413 is “(2 x 2) four thousand, (2 x 4) eight hundred (1 x 2) twenty- (3 x 2) six.” This is because 2,413 can be split into 2,000 + 400 + 10 +3.

Now a number like 47 can be split into 40 + 5 + 2 and when doubled will give 80 + 10 + 4 = 94.

Later after “mastering” that 2 x 5 = 10, then 45 can be easily double as 2 ( 40 + 5) as 80 + 10  or 90.

(2 x 47) then is easily 2 ( 45 + 2) = 90 + 4 = 94.

Longer numbers can be split into shorter parts composed of only one or two digits. A big digit can be paired with a preceding small digit.

Examples:

2 x 428 = 2 x (400 + 20 + 8) = 800 + 40 + 16 = 856

           Or 2 x  (400 + 25 + 3) = 800 + 50 + 6 = 856

2 x 3629 = 2 x (3500 + 100 + 25 + 4) =  7000 + 200 + 50 + 8 = 7258

        Or 2 x (3600 + 29) = 7200 + 58 = 7258.

or simply 2 x 36/29 = 72/58 = 7258

Try doubling last week’s figure by number splitting:

1. 432
2. 163
3. 2,043
4. 2,637
5. 12,403
6. 38,274
7. 402,314
8. 255,366
9. 3,424,202
10. 7,727,489