Learn Tables only till 5x5. Rest can be derived from that...

Lets get back to our school days of 1st standard where we were forced to learn tables upto some where around 15... And now a days even worse, children learn tables upto some 23... My question is "Is it all really required??". No, not really.., you need to know tables only till 5x5, the rest can be derived very easily and with out even piece of paper and pencil. You can recite tables at the same speed as you recite it after memorizing. And for sure no body is going to know how you are reciting it... Here ill explain a very simple technique to derive  the multiples of larger numbers ranging from 6.., teach this method to children and make them practice it for a few days and you can see them directly reciting tables of 43 without even learning the tables of 6... With this you can reduce their burden and yeah even yours to a very large extent ;-)

So here we go assuming you know the tables upto 5x5. Now assuming this suppose we wanna find the value of 8x7..., how do we do that...?? Write down a small chart as show below..,

Here we have two numbers 8 and 7 whose product is to be found.

• Initially write down those numbers one below the other as shown in the first column of the chart.
• Now consider the first number 8. It is 2 less than the base 10 i.e 10-2=8. So writ down -2 on its left.
• Next consider number 7 which is less than 10 by 3. So write down -3 next to 7.
• Now multiply the numbers 2x3=6 and write it down below as shown in the second column of chart which form one part of answer. 
• Now do cross subtraction of either 8-3=5 or 7-2=5. So the number 5 form the other part of the result. 
• Combine both to get the final result 56.

Frankly speaking you need to practice with the chart only initially for two or three days. Again it deppends on you. If you are good enough no need to practice at all. You can do all the work mentally and the result is there within no time... 

Now consider another example of 13*6. The chart is again shown below...,

•  Write down 13 and 6 one below other as in first column of chart.
• 13 is 3 more than 10. so write +3 next to 13
• 6 is 4 less than 10. so write -4 next to 6.
• multiply (+3)x(-4) = -12 and write down as shown in the chart. Here -1 is a carry and -2 is written down below.
• now since negative value cannot be there in result, we borrow 10 from left and write the result 10-2=8. which forms one part of answer.
• Since we borrowed 10 from left we now have on the left -1-1=-2.
• Now cross add 6+3 or 13-4 to get 9. and writ down as below.
• Now we have 9-2=7. which forms other part of answer. 
• So final result is 78....,

This example says what to be done for the numbers above the base and also what to do if there is a carry. The carry must be added to the left or effectively speaking here we have borrowed one because of the negative sign. If it was a positive sign we just simply need to add it to the left part of the answer. Hope this method will help those who find difficulty dealing with the tables... :-) Thank you...,