Not knowing the multiplication table can waste a lot of time. If you have to look for a calculator to do simple arithmetic of if you have to think about 7 x 9 instead of instantly knowing it is 63, you waste a lot of time over the years. The only solution is to just learn the multiplication table--once and for always. Fortunately, there are some tricks that will help.
The easy numbers to learn on the multiplication table are the 1's, the 2's, the 5's and the 10's because they make an easy pattern that anyone can see. Some of the other numbers make patterns as well--the patterns are just not so obvious. Once you see the patterns, these rows and columns of the multiplication table become easy. For example, the 9's have a pattern. Look at 9 x 7 = 63; 6 is one less than 7 and 6 + 3 = 9. Look at 9 x 3 = 27; 2 is one less than 3 and 2 + 7 = 9. This is true for 9 x anything. Try it.
There is also a pattern when 6 is multiplied by an even number. Look at 6 x 2 = 12. The answer ends in 2 and the first digit of the answer is half of 2. Look at 6 x 8 = 48. The answer ends in 8 and the first digit of the answer is half of 8. This will be true for 6 x any even number. Try it.
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There are some specific patterns that work for only one multiplication, but they are still useful. For example, 3 x 7 = 21 and 2 + 1 = 3. Another of these is 6 x 9 = 54 and 5 + 4 = 9. One very unique multiplication is 56 = 7 x 8. Notice that all four digits (5, 6, 7 and 8) are in order. Finding patterns like this make everything easier.
When you start a new row (like the 7's), first learn the sequence of just the answers (7, 14, 21, 28, 35, and so on). Knowing the answers before hand makes learning the individual multiplications easier. It is also a nice change of pace to cut across the multiplication table in unusual ways, such as learning just the squares: 1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16, and so on.
Everybody learns in different ways. Some people who have difficulty remembering patterns of numbers are great at remembering songs, poems or dance steps. These people often have more success and more fun learning the multiplication table if they translate it into a realm that is more familiar. Exactly how to do this depends on the person, but an example is making up short raps about particularly difficult multiplication facts like " 7 is cool, 7 is fine, 7 times 7 is 49."