# Multiplying by 4 and 8.

Young children who have not yet mastered the “times tables” of bigger numbers may find knowledge of doubling very useful.

For example, the techniques in doubling may be applied directly to multiplying by 4 and 8. (Please see pp. 17-18 of 25 Math Short Cuts by Virgilio Y. Prudente).

Since 4 = 2 x 2, multiplying a number by 4 is just doubling it twice.

212 x 4 = 212 x (2 x 2) = (212 x 2) x 2 = 424 x 2 = 848

432 x 4 = 432 x (2 x 2) = (432 x 2) x 2 = 864 x 2 = 1728

648 x 4 = 648 x (2 x 2) = (648 x 2) x 2 = 1296 x 2 = 2592

To multiply by 8, perform the doubling operation thrice.

314 x 8 = 314 x (2 x 2 x 2) = (314 x 2) x (2 x 2) = (628 x 2) x 2 = 1256 x 2 = 2512

562 x 8 = 562 x (2 x 2 x 2) = (562 x 2) x (2 x 2) = (1124 x 2) x 2 = 2248 x 2 = 4496

783 x 8 = 783 x (2 x 2 x 2) = (783 x 2) x (2 x 2) = (1566 x 2) x 2 = 3132 x 2 = 6264

Try multiplying the following numbers by 4 and by 8 by doubling twice or thrice:

1. 23
2. 36
3. 47
4. 64
5. 237
6. 348
7. 639
8. 488
9. 4387
10. 8756