The current expectations are that children should know their times tables, including division as an inverse, by the end of year 4. However, very few will know these and most adults have to think about them! Here are a few tips.
The 4, 6 and 8 times tables can be worked out using double the 2, 3 and 4 times tables.
The 11 times table is just the number repeated (up to 99).
The 9 times table is easy and quick on your fingers for all calculations up to 10 x 9. If you can teach your children this one, they won't make an error again!
Lay your hands out in front of you, face up or face down. Assign the first finger on the left the number one, the next two and so on. If you are asked to multiply 9 x 6, simply fold down the sixth finger and read how many fingers there are standing up on each side of this finger. There should be five to the left, four to the right. The answer is 'five, four' or 54!
This also works in reverse, for division sums. If you're asked to work out 72 ÷ 9, simply hold your fingers as before and count out seven from the left (thus making the '7' of '72'). Then fold down the next finger - it will be finger number eight and that is your answer.
When you need to know whether a number is prime or whether a particular number can be divided into another, there are some tips which help.
If a number ends in 2, 4, 6, 8 or 0 then it is in the 2x table.
If a number can have its individual digits added together and divided by three, the number is in the 3x table. For example, 966 is in the 3x table as 9+6+6=21, which is in the 3x table.
If a number ends in two digits which themselves are in the 4x table, the whole number is in the 4x table. For example, 544 is in the 4x table as 44 is.
If a number ends in 5 or 0 it will be in the 5x table.
If a number is in the 6x table then it is also in the 3x table - therefore the individual digits will add up to something divisible by 3. However, remember that it is not possible to say that ALL numbers which have digits adding up to something divisible by 3 WILL be in the 6x table. For example, 63 (6+3=9) is divisible by 3 but not 6. You can only prove something is NOT in the 6x table because it doesn't have digits which add up to something divisible by 3, e.g. 202 is not as 2+0+2=4.
If a large number has the final three digits in the 8x table, the whole number is divisible by 8. For example, 55 408 is in the 8x table because the number made of the final three digits, 408, is divisible by 8.
If a number is divisible by 9 then you will be able to add together all of the digits and the answer will be divisible by 9. For example, 459 is divisible by 9 as 4+5+9=18, which is in the 9x table.