Maths Can Be Easy - A Nice Story

This is about something that happened about 30 years ago and I was reminded of it recently.

I know that many people have problems doing maths and sometimes it's an inability and other times it can be a matter of just thinking it's too hard. Quite often there are ways around it.

Amongst all the other things I used to do was giving private tuition to help people through exams. One day, in my hairdressing salon, one of my staff was chatting to her client and he mentioned that he was worried about his son's exam that was taking place the following day. It turned out that he had failed his maths O Level and was doing the retake the next day. His main problem was that he had trouble with multiplication and in those days you weren't allowed to use a calculator.

I said to the client that I had a spare half hour that evening during my staff training time and I would be happy to see him then. My comment to the father was that if he just seemed to have a mental block about multiplication but could do everything OK with a calculator I reckoned that I could easily solve the problem in that half hour - which turned out to be the case and he passed his exams.

A couple of weeks ago at a meeting a stranger came up to me and introduced himself. He said that he owned a thriving small scientific company and it was all because of me. I thought he was mad until he reminded me that he was that boy.

All I did was teach him a different way of multiplication which was longer but much easier for him. All it took was to be able to multiply and divide by two (so nothing fancy) and to be able to add up. It took him less than 15 minutes to get the idea.

I taught him a method known as Russian Multiplication (also known by many other names) which is a system that uneducated peasants have used for hundreds of years (it's sometimes called Peasant's Multiplication).

I'll give you two examples, with the first being quite simple and the second a bit more complex. Follow my instructions whilst looking at the figures I have put below and it will be a lot easier than it sounds.

Let's pick 17 x 13

You put the two numbers in columns alongside each other and start by dividing the first number by 2 and enter that number below the first one. If the answer contains a half you then just throw away the half and enter the result. Continue until you are left with the number 1.

Then go to the second column and multiply the number by two and enter its result below the original and alongside the number in the first column. Keep multiplying by two until there are numbers alongside all the numbers in the first column.

Then, looking at the first column cross through any even number and also cross through the number in the column alongside. Then simply add up the remaining numbers in the second column and you have your answer. (I've put a x alongside the row you would cross out as I don't know how to cross numbers through on the computer )

17 - 13
8 - 26 x
4 - 52 x
2 - 104 x
1 - 208

So, in this example you would just add up 13 + 208 = 221 which is the answer

A more complicated multiplication is 39 x 79 but getting the answer is just as simple.

39 - 79
19 - 158
9 - 316
4 - 632 x
2 - 1264 x
1 - 2528

So you add up 79 + 158 + 316 + 2528 = 3081 which is the answer.

There is a similar (but not quite so simple) method for division generally known as Egyptian Division - which I won't go into .

If anyone is interested in simpler ways to do basic maths then a good book is called Trachtenbergs Speed System Of Basic Mathematics (it does contain the methods above) which was devised by Jakow Trachetenberg. He worked out this system of doing maths in your head when he was in a concentration camp during WWII. He eventually escaped from the camp and in 1950 set up the Mathematics Institute in Zurich.

Sorry, being a nerd is natural for me

 

It's a good system for people that have problems with multiplication because they can use the same method for everything. Although the first example is an easy one a lot of them couldn't multiply 17 by 3 so they would have to use the 'Peasant' method.

Some of us are lucky that we have no problem with numbers. I used to have the opposite problem when doing maths exams. When I read the question I was able to write the answer down straight away and used to be told off as I didn't show my 'working'. I couldn't quite understand what they were getting at . The first time it happened my teacher said I had to show how I arrived at the answer and I said 'but the answer is obvious'.

Fortunately, the teacher understood my problem and gave me private tuition in how to work backwards from the answer so that I could show how I arrived at it (this is getting complicated so let's forget it :D). Suffice it to say I happen to be able to see patterns and connections with numbers and the answer just appears in my head.

My experience with problems made me want to help people and I get a lot out of it.