Saturday, 28 February 2009

Keep your maths neat

I will get slightly more complicated with this maths so try to stay with me. If you multiply a number by the same number e.g. the number two, you end up with four, or two squared. If you take the square route of four you end up with two. Now think of a chessboard. 8x8=64. You can see why it is called eight squared. The square root (or the number that you need to start with to make that number) of 64 is 8.

There may be a reason to simplify square roots. If you are asked to simplify the square root of 27 (√27) then it always pays to go back to basics and think about the maths that you know is correct. You know that 3x3 = 9 and you know that 3x9=27. So another way of writing √27 is √3x9. You know that the square root of 9 is 3. So √27 = 3√3

When you convert √27 to 3√3 you end up with a number that you can relate to. It may be that you are good enough to know about √27 but 3√3 is a logical simplification, and logical thinking is something we should be doing all the time. Think of simplifying as trying to make the maths look neater and more importantly more accessible. You have a better chance of having that rough idea of the number that you are talking about. Having a rough idea is so important in everyday life. How much wallpaper do you need for the living room? How much does it cost for a year at the local gym? Have a rough idea and you will roughly know whether you can afford it.

Logical thinking is a mathematical characteristic that can be applied to all walks of life.

That sums it up

Friday, 27 February 2009

Deal or no deal?

Have you seen the channel 4 programme 'deal or no deal'? I am amazed at the number of people who do not understand the odds. It should be so easy to analyse the probabilities but hardly anyone does it. In fact it makes a refreshing change when someone is able to come up with a sensible basis for making a decision. It is a game of chance but once the first box has been chosen then you can use mathematics to help your decisions.

The chances of actually getting on the programme are pretty slim, so for most of us the closest we get to gambling may be at the bookies or with the lottery. Now if you are a mathematician you will realise that gambling does not make sense, particularly the lottery. So never worry about your maths leading you astray in the world of gambling. In fact maths will keep you on the straight and narrow. You can still gamble as a mathematician, but you will not be thinking of winning, just about the thrill of possibly winning.

That sums it up

Thursday, 26 February 2009

Multiply by ten

If you start with the number one and multiply it by ten then you add a zero to make 10. Multiply by another ten and you add another zero to make 100. Take any number and multiply it by ten and you end up moving the decimal point one place to the right, so 15.67 becomes 156.7

Now divide by 10 and you move the decimal point to the left. This time 15.67 becomes 1.567. I hope that it is fairly easy to understand multiplication and division by ten, because some people get confused when they see a lot of numbers.

Take any number - it could be 48 374 589.245 and if you multiply it by ten it becomes 483 745 892.45 If it helps you then think of the numbers in threes - that is why we leave gaps or use commas. Multiply by 10x10 and the decimal point moves twice. Multiply by 10x10x10 and it moves three times.

That sums it up

Wednesday, 25 February 2009


Last time I mentioned that there are many things that I like about maths, and nobody can complain at your 1+1=2. If you had 1+2+3=6 there are different ways of getting the right answer and all can be good ways. You could add 1+2 first or you may go for the 2+3. It doesn't really matter in this case but with more complicated calculations there may be easier ways to get the right answer.

Have you watched Countdown and seen how the exact number can be achieved in a few ways. Very often the two contestants will say they have worked out the result in exactly the same way, but it doesn't have to be the case.

Take a simple example for multiplication. Take the numbers 2, 3, and 4. If you work out 2 x 3 you get 6. Then multiply it by 4 and you get 24. You can also multiply the 3 and the 4 to make 12, then multiply by the 2 and you end up with 24. It works with multiplication and with division. Take the same numbers but this time divide by 2. 3 x 4 divided by 2 is 6 and this is exactly the same as 3 divided by 2 (1.5) x 4=6, or even 3 x (4 divided by 2)2 =6.

Maths does get more complicated than this but it is really important to get the basics right so that you can understand the more difficult techniques.

That sums it up.

Tuesday, 24 February 2009

Understanding Concepts

I think maths is an easy subject. I heard someone on TV today who said they were very critical of themselves when they wrote something. There is nothing wrong with a bit of self-criticism but you can gain a lot of confidence if you are good at maths. It is the only school subject that I know of where pupils can consistently gain top marks. If you are writing something for an English class then there is always another word that may be more apt. The person who reads this blog may prefer the last sentence to read...there is always another word that may be better. However with maths nobody can say that your 1+1=2 is wrong or it could
be better.

There are many things that I like about maths, and one of them is that it is about understanding. If you know how to multiply then you can adapt it to the number of fish fingers needed for a meal, or it can be used for the number of litres of petrol that will fill the tank in the car. As soon as you understand the concept then it is there. You don't need to read a novel about multiplication. You don't need guidance notes. You don't need to interpret it, although there are usually a few ways to do things in maths. Understand the concept and the work is done.

That sums it up

Monday, 23 February 2009


Today we mostly use Arabic numerals, such as 1, 2 and 3, which we join together to make numbers like 123. The Romans had the start of a system where position was important, but with Arabic numbers every position is important. The individual numerals are called digits. This comes from the Latin digitus, meaning finger, and tells us how counting was done originally.

The decimal system is fairly easy. The units count single items. 1 = one, 2 = two and so on. But then in the next position everything is multiplied by ten. 10 = ten, 20 = twenty and so on. In the third position along from the right, we multiply by ten again, which means that this position is for hundreds (ten times ten equals a hundred). And the next position is for thousands, and then for tens of thousands, and so on. As big as you like!

The 0 (zero) is an important idea that we got from the Arabs, along with the whole Arabic numeral thing. Before it, we had no way to write zero. Zero wasn’t even thought of as a number. There’s no way to write zero in Roman numerals. That brings me back to Roman numerals, and the answer to yesterday’s question. MCMXCIX is 1999 in decimal. Did you get it?

That sums it up.

Sunday, 22 February 2009

Roman Numerals

The Romans had a way for joining symbols together to make big numbers which is still used today on some clock faces, and you’ll see it on some BBC programmes where they show the year it was made. In this system, every letter stands for a number. I = one,
V = five, X = ten, L = fifty C = a hundred, D = five hundred and
M = one thousand.

It may seem tricky at first, but all you have to learn is seven symbols and just one rule, and you can untangle even the most complicated year. The rule is: if a symbol for a small number is put before the symbol for a big number instead of after it, then you take the small number away from the big one.

I like to remember 400 because it is CD. You know I is one and V is five. You probably know X is 10. If you know what a millenium is you only have to learn that L is 50 and you know all the Roman numerals. MMIX is two M’s which are a thousand each, and a I (one) which we take away from the X (ten) because it comes before the X. That’s two thousands and nine = 2009. You may see MMIX on TV if it is this year’s programme.

Try one yourself: What is MCMXCIX? I'll let you know next time.

That sums it up.

Saturday, 21 February 2009

What is Maths?

What is maths? As a word it’s short for mathematics, of course, which comes from the Greek word mathema, meaning science or knowledge. That shows how much importance the Greeks gave to the subject. To them it wasn’t just an add-on, something which helped them to gain science or knowledge. It was science. It was the core of knowledge, because even in a world full of uncertainties there are mathematical truths of which we can be certain. One plus one equals two, you can be sure of that.

Maths began with measurement, and measurement probably began with counting. Ug the caveman founded maths when he came up with the concepts of 'one', 'two', and 'many'.

It is a little bit more complicated today as we have things like ‘three’ and ‘four’ to complicate the picture, and by joining symbols together we can even give a name to any number, no matter how big. Maths is simple, just learn one bit at a time.

That sums it up.