Doubling: Number composed entirely of Small digits

Doubling or adding a number to itself is among the first exercises in advanced addition done by young learners. We can often hear them recite, “One plus one equals two. Two plus two equals four. Four plus four equals eight. Eight plus eight equals sixteen…”

Mastering doubling in this manner leads to another skill: adding consecutive numbers. 6 + 7 for example can be evaluated as 6 + (6 + 1) or (6 + 6) + 1 = 12 + 1 = 13.

Then in multiplication, next to multiplying by 0 and 1, the 2 times table is the easiest to memorize.

If we arrange our numbers from 0 to 9 into two columns, the “small digits” 0, 1, 2, 3 and 4 on the left and the “large digits” 5, 6, 7, 8 and 9 on the right, we can observe some interesting things:

1. In one line, the digit on the right is 5 more than the the digit on the left: 5 = 0 + 5, 6 = 1 + 5; 7 = 2 + 5; 8 = 3 + 5 and 9 = 4 + 5.
2. When the digits were multiplied by two, the resulting products in one line end in the same digit but differs exactly by 10: 0 and 10, 2 and 12, 4 and 14, 6 and 16 and 8 and 18  

0 x 2 = 0                              5 x 2 = 10

1 x 2 = 2                              6 x 2 = 12

2 x 2 = 4                              7 x 2 = 14

3 x 2 = 6                              8 x 2 = 16

4 x 2 = 8                              9 x 2 = 18

Knowing this table by heart will enable a learner to double even longer numbers mentally from left to right using this simple procedure:

1. Read the number to be doubled to see the face value and the place value of each digit (234, 314): two hundred thirty-four thousand three hundred fourteen.
2. Since all the digits are small, the answer can be announced immediately, easily:
3. 2 x 2 = four hundred
4. 3 x 2 = sixty
5. 4 x 2 = eight thousand
6. 3 x 2 = six hundred
7. 1 x 2 = twenty
8. 4 x 2 = eight

We will consider examples with small and large digits next week.

Practice by multiplying the following numbers by two:

1. 123
2. 402
3. 4, 123
4. 4, 432
5. 33, 243
6. 21, 342
7. 421, 231
8. 342, 221
9. 232,323
10. 333,444

Here are the answers to last week’s practice exercises:

1. 457 – 359 = 98
2. 784 – 589 = 195
3. 872 – 584 = 288
4. 657 – 478 = 179
5. 2, 345 = 1, 354 = 991
6. 5, 734 – 4, 845 = 889
7. 8, 547 – 5, 668 = 2, 879
8. 12, 345 – 11, 477 = 868
9. 45, 784 – 34, 885 = 10, 899
10. 364, 257 – 176,378 = 187, 879