Checking answers

Mathematics

I do not know who to attribute all the various methods of doing mathematics which I am going to write on from today.  One of the earliest books to be written about these methods was written by Jakow Trachtenberg. He was a Russian who was born in 1888 and died in 1953.Subsequently many others have changed a little here and there and called it their own. All I can say is that I learnt all these as I was growing up and none of it is my own and now I share them with you.

Checking answers

If you have time left over after your mathematics test you should check to see if you have the right answers. The only way most of us know how to check answers is to do the problem again. But what if you got a different answer from the first time? Did you get it right the first time or the second time? As such, the only way is to do it again for the third time and see which two answers are identical and then write that as the answer. Even then the answer could be wrong if you had made the same mistake twice.

What if we can solve the problem in two different ways? If you learn what I am going to teach you and apply it you will not make as many mistakes in your mathematics as in the past.

Substitute numbers

When we check a calculation we can use substitute numbers instead of the real numbers we were working on.

Let us try one example today.

Let us say we have just done 12X13 = 156. We can check the answer in the following way:

The first number is 12. We add its digit together to get a substitute number. That is 1+2 =3      So 3 is our substitute number for 12.

The next number is 13. We add its digits to get a substitute number.

That is 1+3=4   So 4 is the substitute number for 13.

We now do the calculation using substitute numbers.

3X4 = 12

Twelve is a 2 digit number. We therefore add its digit together to get our check answer. 1+2 =3. Our check number is 3.

If our original answer to 12X13 gives the same check number as the check number above: 3 then our answer is correct.

Our original answer to 12X13 is 156.

Adding 1+5+6 = 12

Remember we have to reduce the number to a single digit …so 1+2 =3

Our check number is the same as this number. Therefore our answer to

12X13 of 156 is correct.

I am going to leave it here and hope you will take a few examples of your own and work it out by yourself to familiarize yourself with this method of checking.

Ask your mum or dad to help you if you find it difficult to follow.

Do comment in the comment section so that I know you understand and I can proceed further.

I hope there will be more of your friends invited to my site  nicer to share this site with a bigger group.

Luqman Michel

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7/27/12