Doubling from left to right

Multiplying a number by two, also called “doubling” is a short cut for adding a number to itself. It is perhaps, the first lesson in multiplication mastered by children.

We all know that numbers are composed of a combination of ten digits, from 0 to 9. These digits can be classified into two:

“small” digits,  0, 1, 2, 3 and 4 which when when doubled, will result into single even digits, 0, 2, 4, 6 and 8 respectively.

“big” digits,  5, 6, 7, 8 and 9 which when multiplied by 2 will give two-digit products 10, 12, 14, 16 and 18 respectively.

A number composed entirely of small digits can be easily multiplied by two by doubling each digit starting from the left. This will enable us to give the answer orally.

For example,  twice 2,413 is “(2 x 2) four thousand, (2 x 4) eight hundred (1 x 2) twenty- (3 x 2) six.

We can also start from the left in doubling numbers with big digits.  Here, we anticipate regrouping or carrying. Before writing down or announcing the partial result, look at the next digit on the right. If it is “big” add 1 to the partial product. Then double the next digit but write or recite only the last digit since the leading 1 has already been added or carried in the previous step.

When doubling 3,748, for example,  we have “[(3 x 2) + 1] seven thousand, [(2 x 7) – 10] four hundred [(4 x 2) + 1] ninety [(8 x 2) – 10] six.

The preceding computation can be further simplified if we take into account that a “big” digit when deducted by 5 will give a corresponding “small” digit. This pair when doubled will have the same last digits.

5 – 5 = 0; 2 x 5 = 10 and 0 x 2 = 0

6 – 5 = 1; 2 x 6 = 12 and 1 x 2 = 2

7 – 5 = 2; 2 x 7 = 14 and 2 x 2 = 4

8 – 5 = 3; 2 x 8 = 16 and 2 x 3 = 6

9 – 5 = 4; 2 x 9 = 18 and 2 x 4 = 8

Using this in our example, 3,748 x 2, we get “[(3 x 2) + 1] seven thousand, [(7- 5) x 2] four hundred [(4 x 2) + 1] ninety [(8 -5 ) x 2] six.

Doubling is further explained in pages 15 to 18 of our book 25 Math Short Cuts, which is available at MATH-Inic Philippines (https://www.facebook.com/MATHInicPhils).

Try doubling these numbers mentally:

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