How numbers work

CHAPTER 1

This is how numbers work.

They do work, they always work, they never fail to work.

Numbers are reliable, always there for you when you need them and they always, always, do the same thing.

No matter how many times you do the same sum, no matter where you do it or what you do it for the answer will always be the same. It can never be anything else but the right answer to that sum.

The change from a Twenty Pound Note for a £17.25 amount owed is £2.75. It always will be. It never changes. That is the correct change and anyone who tries to tell you otherwise is wrong and you need to ask yourself why they say it could be otherwise when this book says it as it is and this book is telling you it is always the same answer to the same sum.

Numbers are like that. They tell it like it is and never fail to do so.

 

Numbers start at the beginning and keep on going, forever they will keep on going until you want your numbers to stop. Numbers that do not belong to anyone just never stop. Honest!

Numbers have names so you know which is which, just like with brothers and sisters and things.

Because remembering too many names gets confusing it is customary to keep on using the same few over and again and just modify them to mean other ways of using them.

They start out with number one, just like counting your fingers.

Most people have ten fingers.

Count yours to check. One 1, two 2, three 3, four 4, five 5, six 6, seven 7, eight 8, nine 9, ten 10.

You knew that already, I could tell.

But that is most of what you need to know, one two three four five six seven eight nine ten.

1 2 3 4 5 6 7 8 9 10

Now look at the tape measure, and stick a wall chart on the wall with the number one at the bottom.

Low down near the floor because one is a very low number and ten is higher, it is always higher.

Numbers know their place.

You only have to respect that to be able to use them and own them. Numbers are a way of coping with the world around you. They are only a tool, they are not frightening at all – never believe anyone who says maths is difficult. Maths is actually easier than walking up and down stairs.

Each number is called a digit, just like each finger and thumb can be called a digit.

The first few numbers have one digit names, but then they double up. Like standing side by side in order, a queuing system for numbers as if waiting for service at the checkout. No queue jumping allowed, numbers know their place.

There is another number, a special secret number that means nothing.

0

It stands for nothing on its own. But it is not a nothing number when it gets together in its right place. That is the number zero. 0

When you have zero and nothing else you know you have nothing at all.

But when you have zero with a number standing in front of it you have shed-loads.

It can be ten, or 20 or with two zeros it is in the hundreds.

Chapter 2

ADDITION AND SUBTRACTION

HNW Chapter 3

You would think it is impossible to take away from a number an amount that is greater than that number and you are right. If you only have 3 pennies and the thing you want costs 4 pennies you cannot buy it - unless someone lends you the other penny right there and then. If they lend you their penny they do not have it to spend on something they want for themselves. They will have to forgo buying what they want so that you can buy what you want.

Would they do that for you, for nothing in return? If they do they are very good friends and you must make sure you pay them back as soon as you possibly can so as to be able to keep being able to have that friendship.

You cannot give away what you haven’t got. You cannot pay with money you haven’t got. You can only give something that exists, so if you want to give something you haven’t got you might try and borrow either the thing or the money to get the thing and pay back the debt, that is the amount owing, at the earliest convenient opportunity according to the terms on which that thing or that money was loaned.

Percentages.

“Per cent” means of a hundred, remember that in America there are one hundred Cents to the Dollar? It means hundredths. So 10% might look frightful but is simply ten parts of a hundred, ten of a hundred. It shows you a proportion so that you can equate one amount with another more easily. Imagine someone wants streaks put in their hair so that the overall appearance changes the colour to being lighter. If you put in blonde streaks that make up a small percentage of the total amount of hair the overall look would not be of a blonde headed person but of a dark haired person with blonde highlights. If you want to put in a great many streaks so that the overall look is of a blonde haired person you would figure out how much to do in proportion to the whole – and that is what percentages are for. To equate numbers with actual facts.

To figure out, or calculate, ten per cent of a hundred, is dead easy and anyone who tells you otherwise is a rat. 

Ten percent of a hundred is ten. 10% of a 100 is 10. Notice anything funky about the way it is written in numbers and maths jargon? It uses the same numbers with the end one missing. You just chop off the end, or move the decimal point. If you want 10% of £200.00 again you just move the dot and get £20.00. 10% of 300 beans is 30 in the same way.

Ten per cent of eight hundred and thirty is eighty three. 10% of 830 is 83.

Ten per cent of two hundred and sixty eight is twenty six point eight. 10% of 268 is 26.8.

Ten per cent of three hundred and forty five is thirty four point five. 10% of 345 is 34.5.

You just move the decimal point.

“Decimal” is a word that comes from the Latin, like Cent did, and means to do with the number hundred. Latin was the language of the Roman Empire. Romans were not much good at maths because they hadn’t figured out how to write them down and play with them as we have. With no marks to use as numbers they used letters, teaching their children which letter meant how much. C was the way they said 100. D was 500 and L was 50. M stands for a thousand (1000). It makes little sense and is so hard to use that these days the whole system is only used by the BBC and quiz question creators. But the principle of basing things around an easy number of 10 (ten),100 (hundred), 1000 (thousand), 10,000 (ten thousand), 100,000 (hundred thousand), 1,000,000 (million) sticks with us because it is useful. And easy to understand because we normally have ten fingers to count on. Any ten fingers tend to be valued differently in real life. The forefinger that you use most. The big middle finger that isn’t even in the middle. Horses use their own equivalent of that big middle finger to run on, their hoof is the equivalent of a finger nail on a long middle finger and a long middle toe. You have the ring finger and the little finger and a thumb. But when thinking of them as numbers it helps to think of them as all the same and of equal value. No special talents in numbers, like beans, all the same. If you start counting at the little finger the number four comes up as your favourite finger, but if you start at the thumb the number four is the ring finger – very different fingers but the value and position makes no difference if they are being used only for pretending to be numbers. 

One way to make sense of percentages in your mind, and probably the reason why we tend to use them, is that you can see your own ten fingers and relate to that number. Imagine ten pairs of hands, that is 100. To imagine what 10% means think of it as one finger out of the ten you have. And notice the others. 90% is what the others amount to. Almost all but not quite. 50% is one whole hand but not the other, it is two equal shares and is the same as saying half. If value added tax on goods and services is 17.5% you can see how much of your hand that is really – almost two whole fingers! 

The Romans used the number 100 to run things on, sending out soldiers in batches of 100. If they got cross with a group of soldiers they could decimate them – this meant killing 10 per cent of them, one in ten taken out to leave the other 90 feeling inclined to behave themselves better (or run away).

Taking 10% from a batch of any number is pretty easy. Ten per cent of 2500 is 250, and taken away (or killed) leaves 2250 still standing. 

Patterns in numbers. Pretty.

So here is the practice part. Say you want to find out what 4 out of 12 is as a percentage you do, 4 x 100 and divide that by 12.