By Michael Hartley
Elsewhere on this site, I gave some general times tables tips. This page zooms in on the eight times table. I'll try to help you help your kids spot the patterns in the eight times table, and make it easier for them to learn. Keep in mind that if you can get your kids to see the pattern themselves, it will be much more meaningful than you just telling them about it. You could try asking some directed questions.
Anyway, let's have a look at the eight times table. Printable versions of this and other multiplication times tables are available elsewhere on this site.
| 8 | x | 1 | = | 8 |
| 8 | x | 2 | = | 16 |
| 8 | x | 3 | = | 24 |
| 8 | x | 4 | = | 32 |
| 8 | x | 5 | = | 40 |
| 8 | x | 6 | = | 48 |
| 8 | x | 7 | = | 56 |
| 8 | x | 8 | = | 64 |
| 8 | x | 9 | = | 72 |
| 8 | x | 10 | = | 80 |
| 8 | x | 11 | = | 88 |
| 8 | x | 12 | = | 96 |
If you have a look at the tens digits here, you'll see a very interesting in the first five rows :
| 8 | x | 1 | = | 08 |
| 8 | x | 2 | = | 16 |
| 8 | x | 3 | = | 24 |
| 8 | x | 4 | = | 32 |
| 8 | x | 5 | = | 40 |
- Eight times 1 starts with 0,
- eight times 2 starts with 1,
- eight times 3 starts with 2,
- eight times 4 starts with 3, and
- eight times 5 starts with 4.
The next few rows have a similar pattern
| 8 | x | 6 | = | 48 |
| 8 | x | 7 | = | 56 |
| 8 | x | 8 | = | 64 |
| 8 | x | 9 | = | 72 |
| 8 | x | 10 | = | 80 |
- Eight times 6 starts with 4,
- eight times 7 starts with 5,
- eight times 8 starts with 6,
- eight times 9 starts with 7, and
- eight times 10 starts with 8.
The next block of 5 rows has, again, a similar pattern.
- Eight times 11 starts with 8,
- eight times 12 starts with 9,
- eight times 13 starts with 10,
- eight times 14 starts with 11, and
- eight times 15 starts with 12.
Well, that might help remember the tens digit, but what about the ones digit?
Note that within each block of five rows, the ones digit follows a very simple pattern
If your child has a good handle on the two and ten times tables, then it is not too hard perhaps to mentally multiply by eight. To multiply something by eight, remember that eight times a number is ten times the number minus two times the number. This is because 8 = 10 - 2. For example
- To work out 8 times 7 :
- 10 times 7 is 70
- 2 times 7 is 14
- 70 - 14 is 60 - 4, or 56.
Alternatively, if their four times table is strong, eight times a number is four times the number, added to four times the number. That is, eight times is twice four times. For example
- To find 8 times 7
- 4 times 7 is 28, and
- 28 + 28 is 56.
Another nice pattern appears in the digits used in certain rows of the table. Check out the following two sums.
8 x 6 = 4 8
Notice that you can get one from the other just by shifting all the digits sideways. Another pair of sums like this is
8 x 3 = 2 4
I used one of these pairs as the inspiration for one of the times table mazes on this site.
Before I close, let me mention this... Did you know that to test if a number is divisible by 8, you only need to look at the last 3 digits? Here's how the test works.
- Firstly, the last digit should be 8, 6, 4, 2 or 0.
- If the last digit is 0, 4 or 8 (a multiple of 4), the second last digit should be even.
- If the last digit is 2 or 6 (a multiple of 2, but not 4), the second last digit should be odd.
- If the last two digits make up a multiple of 8, then the third last digit must be even.
- If the last two digits don't make up a multiple of 8, then the third last digit must be odd.
It's worth giving a few examples of applying these rules...
- 314159 is not a multiple of 8. It fails the first test, so it's not even a multiple of 2. The last digit is 9, not 8,6,4,2 or 0.
- 314158 passes the first test. The last digit is 8. The next test requires that the second last digit be even, but it's not. So 314158 is not a multiple of 4, let alone 8.
- 314162 passes the first test also. The last digit is 2. If the last digit is 2 ot 6, the next test requires the second last digit to be odd. Again, the number fails to be a multiple of 4!
- 314156 passes the first and second tests! So it's a multiple of 4. The last two digits make up 56, which is a multiple of 8. The third and final test tells us that the third last digit should be even. But it's odd! So 314156 is a multiple of 4, but not of 8. (On the other hand, 314256 is a multiple of 8, by this very same test)
- 314152 passes the first and second tests also! So it's a multiple of 4. The last two digits make up 52, and since I know my 8 times table, I know that 52 is not eight times anything. The third and final test tells me that the third last digit should be odd - and it is! So 314152 is, indeed, a multiple of 8 - and so would be any number at all ending in 152.
Well, that's all for this page on the eight times table. I hope it proves helpful to the chilren in your care!