Multiply Your Maths

Chinese Tangram Game

2011-06-04T13:02:00.000-07:00

As many people are aware, the Ancient Chinese made considerable advances in the field of mathematics. One of the primary aims of these early Chinese mathematicians was to devise methods for quick calculation for everyday use. In my next post I will look at a very unique and fast method of multiplication, which is still taught today in Chinese schools.

Below however is a Chinese Tangram Game, one of the oldest Chinese puzzles.

Tangram

Play free Games - a game from Puzzle | Logic Games

The Problem With Math - Symbols

2011-05-05T06:52:00.000-07:00

Why is math so confusing to the vast majority of people? What is it about this subject that makes it so intimidating? In my opinion at least, the biggest problem with mathematics is the use of symbols.

Now by 'problem', I mean that this is the element of mathematics that puts most people off at the outset. It is why many complicated math equations look much scarier than they actually are. Hopefully by the end of this post you will agree that while these symbols are actually necessary (and very useful), they're not really as complex as they seem!

Let's take a look at symbols and how we think about them.

A lot of people who do not study maths at college level will look at the expression above and think, 'Wow, what a complicated piece of maths!'

Now look at the picture above. Let's be honest. Those of us who do not read Arabic have practically no hope of understanding this text. However, we normally wouldn't say, 'Wow, what a complicated sentence!' Instead we accept that we do not understand this text simply because we do not know what the symbols represent and because we do not speak the language.

This is exactly the case with maths!

In mathematics symbols are used as a shorthand. All they are is a quick and very precise way of explaining what is happening in your calculation. Even the numbers we use in our day to day lives are symbols (in fact they are Arabic symbols), because writing a squiggly line '2', followed by an oval shape '0', is a lot easier than drawing twenty lines on a page. The difference with these numerical symbols is that they are familiar to us, because we use them every day.

To see how effective the use of symbols in math is, and why it is absolutely necessary, let's take a small segment of the expression pictured above.

Using mathematical symbols this expression takes up only about half a line. Now let's have a look at it in English.

'Minus three, multiplied by an unknown term labelled P subscript zero which is taken to the power of minus one, which is then multiplied by the rate of change of P subscript zero with respect to an unknown term labelled y, also multiplied by an unknown term known as b hat subscript minus one, minus three times P subscript zero to the power of minus one, times the rate of change of P subscript zero with respect to an unknown term labelled x, multiplied by an unknown term known as a hat subscript minus one.'

Firstly you're forgiven for not reading all of that. Now can you imagine trying to work with that chunk of text as part of a much bigger equation? Using symbols mathematicians can clearly see what is happening in a calculation, and they can quickly jot down intricate concepts without having to write a book the size of War and Peace.

Another important point to note here is that there is nothing in that expression that most adults cannot understand. The letters just stand for numbers that have not been decided yet, or that need to remain as general as possible. After that it's just multiplication, with a little bit of basic calculus.

Hopefully by now you can see what I'm getting at. Once you know what a symbol stands for, reading maths is just like reading any other language. If you approach maths with this in mind, you will accept that a lot of your study of mathematics involves just learning what the symbols stand for, and what they mean in plain English. Once you know what the sums are saying to you, then you stand a much better chance of solving them!

Only In Math...

2011-05-04T07:42:00.001-07:00

Multiplication Trick - 9 Times Tables

2011-05-03T19:02:00.000-07:00

Here is a little multiplication trick I learned from a teacher in primary school. It shows you how to remember the 9 times table all the way up to 9 x 10.

To use this simple multiplication trick, you just need to count on your fingers and the answer will be supplied to you!

Ok, so let's say I want to work out

2 x 9

Open your two hands and spread your fingers out, palms down.
Start counting from the pinky finger of your left hand. Count two fingers.
Bend the second finger down.
Look at your hands. You should have 1 finger upright, then a gap, followed by 8 upright fingers. So the answer to 2 x 9 is 1 and 8, or 18.

Let's try again. This time we'll look at

6 x 9

Again, the steps are:

Open your two hands and spread your fingers out, palms down.
Start counting from the pinky finger of your left hand. Count 6 fingers.
Bend the sixth finger down. This should be the thumb of your right hand.
Look at your hands. You should have 5 fingers upright, then a gap, followed by 4 upright fingers. So the answer to 6 x 9 is 5 and 4, or 54.

There you go, it's as simple as that!

Another handy tip to check that you have the right answer:

IF YOU ADD THE TWO DIGITS IN YOUR RESULT, THEY SHOULD EQUAL 9!

Let's check:

2 x 9 = 18

1 + 8 = 9

6 x 9 = 54

5 + 4 = 9

These multiplication tricks are very handy when working on the 9 times tables, but remember that they only work up to 9 x 10.

Step by Step Multiplication Quiz

2011-05-03T17:09:00.000-07:00

Please read the 'Step by Step Multiplication' post before trying this quiz. If you can, do these sums in your head, otherwise use a pen and paper.

Quizzes by Quibblo.com

Step by Step Multiplication

2011-05-03T08:42:00.000-07:00

For an overview on multiplication please read the 'Multiplication - The Faster Way to Add' post on this site.

Let's get going straight away with some Multiplication. When you're done, why not try out the Multiply Your Maths Step-by-Step Multiplication quiz?

First off, you're going to have to know your multiplication tables. There are a number of methods out there to help people learn these off by heart, so it's simply a matter of finding what works best for you.

Once you know your 'times tables', simple multiplication is just a matter of remembering the correct answer for each problem. E.g.:

2 x 3 = 6

4 x 7 = 28

and so on.

Long multiplication might seem more tricky but it actually isn't. All it involves is repeated steps of simple multiplication. Let's try a quick problem to see how this works.

23 x 2 = ?

To solve this, we just multiply each digit by 2. So we have 2 x 3, which is equal to 6, and 2 x 2, which is 4. Looking at the sum written out below, we write:

So,

x 2

That's really all there is to multiplication. Next time we will look at multiplying two 2-digit numbers together. For now, why not try out the Multiply Your Maths Step-by-Step Multiplication Quiz?

Multiplication - The Faster Way To Add

2011-05-03T07:50:00.000-07:00

Sadly, like most elements of the math education system multiplication is taught in a way that is largely divorced from reality. It is something to be studied and slaved over when in school, and then abandoned immediately straight after the final maths exam.

Let's try take multiplication back to basics, and look at it not just as a method but as a useful tool. When most people hear the word 'multiplication', they probably think of multiplication tables and hours of learning by rote. While multiplication tables are very useful, they tend to distract people from the essential aim of multiplication. At heart, multiplication is simply a faster way to add.

Take a look at the picture below.

If you are presented with 4 boxes, each holding 10 pencils, how do you know how many pencils you have?

You have two options:

The Slow Way: You can add 10 + 10 + 10 + 10.
The Fast Way: Multiply 10 x 4.

Multiplication is just a quicker way to add up 'blocks' of numbers.

I find the boxes images helps a lot with this visualisation. The expression:

7 x 6

is just a shorthand way of saying 'I have 7 boxes of 6 items'. When you read the mathematical symbols above aloud or in your head, it is a good idea to say 'seven sixes'. Read the Building Blocks post titled Step by Step Multiplication to get a better look at the methods used to work out multiplication problems.

Look For The 10's Quiz

2011-04-29T17:33:00.000-07:00

Please read through the Look for the 10's - Addition Made Easy post before trying this quiz. Try to do the addition in your head, without using a calculator or a pen and paper. There is no time limit, so feel free to spend as much time as you need on each question.

Quizzes by Quibblo.com

Look For The 10's - Addition Made Easy

2011-04-29T17:12:00.000-07:00

Here we will look at a more user friendly approach to addition. When you are finished reading, why not try out the Look for the 10's quiz?

Our number system is based on 10's. This is especially true with addition. Don't believe me? Ask yourself this:

Which is easier to add?

57 + 26

40 + 20

Adding numbers that have zeros as their last digits is much easier than adding numbers with many different digits. This is because the zeros can essentially be ignored when you're doing the sum.

Another issue that affects a lot of people is the manner in which they were taught to add. Normally children are shown to add by summing the units, and then carrying any tens to the left. While this obviously works, it has some serious drawbacks. Firstly it confuses many people, who end up following a method rather than engaging with the problem. Secondly it does not work very well as a method of mental arithmetic.

Like most people I learned to do addition in the manner mentioned above. However over time I realised that there is a faster and easier way to do problems like this, which can be 'summed up' (excuse the pun) as Look for the 10's.

Put simply, you find groups of tens, and add them. That's essentially it. This approach works best when you are adding numbers and you need to 'carry' digits, but it can be used for any sum.

Let's start with the sum mentioned above. To make this explanation simpler, let's pretend we're adding apples. That just makes things a little bit easier to visualize. So we have two piles of apples. One pile has 57 apples in it, the other has 26. So we have to calculate

57 + 26

Try looking at the biggest number.

If we could turn that into a number that ended in zero, it would be easier to do the addition. How about trying to make it into 60?

Well if we want to turn 57 into 60, we will need to add 3 to it. So instead of taking the whole pile of 26 apples, we can just take three of them. We put them with the 57 apples to get 60. Now we have a pile of 60 apples, and another pile of 23 apples.

60 + 23

Let's ignore the 3 for a moment and just Look for the 10's.

60 + 20

That's fairly simple to add, as 60 + 20 = 80. Now just put the 3 we ignored back in there to get 83. Now we know

57 + 26 = 83

So we have our answer.

In step by step form the Look for the 10's approach to addition would be:

Change one number so that it ends in 0.
Add the tens.
Just put the units back on the end.

Let's try one more example. How about:

68 + 34

Look at the 68. How many apples do we need to take from the other pile to make 70? Only 2. So now our sum is:

70 + 32

Well you can see that

70 + 30 = 100

And then we put the 2 back in there to get 102. So:

68 + 34 = 102

I don't know about you, but for me this is a faster and easier way to do addition. Why not try it out with some of the questions in the Look for the 10's quiz? There's no time limit, so take your time and see how this approach works for you. You can also try out one of the math games at the bottom of the page. Thanks for reading and feel free to tell us what you think in the comments!

Math Quiz - Adding Coins at the Store

2011-04-28T15:39:00.000-07:00

Please read through the associated post "Adding Coins at the Store" before you take this quiz. Don't forget to mouse over the questions to get the full text!

Quizzes by Quibblo.com

Adding Coins at the Store

2011-04-28T09:05:00.000-07:00

Let's start off with a basic math problem involving addition with money. When you are finished why not test yourself for fun with this post's quick math quiz?

So you're standing in the queue for the checkout with a few things you've picked up for your lunch. The day's been going well so far and you're feeling pretty good, that is until you reach into your pocket for your wallet to find it's not there. You've left your wallet and all your money in the office.

Quickly you rummage through your pockets and feel a surge of relief when your fingers hit some cool metallic coins and soft dollar bills. You pull them out to find that you are holding 3 dollar bills, 3 2-cent coins, 2 half dollars (=50 cents), 1 quarter (= 25 cents), 1 dime (=10 cents) and 8 cents. From past experience you know that your lunch will cost you $4.50. The question is - do you have enough money?

The queue is moving quickly, and you have a lot of coins in your hand. It's about now that a lot of us get flustered and confused, especially if we're not too confident in our ability to add up quickly on the spot. But don't worry, this kind of situation is what Multiply Your Maths is all about. All you have to do is remember 2 SIMPLE RULES.

1 - Start Big

2 - Look for the 10's.

Start Big is a reminder to add the biggest units first. This gives you a simple plan that means you won't lose track of your coins.

You have:

- 3 Dollars

- 2 Fifty cents

- 25 cents

- 10 cents

- 3 two cents

- 8 one cent coins

First off you have 3 dollars.

What next? 2 fifty cents. Ok so we'll add those to get 1 dollar.

3 + 1 = 4

Now you have 4 dollars, and some change in your hand. It's looking like you will get to eat today!

Now move on to the next biggest - your quarter. You now have 4 dollars and 25 cents, which doesn't really take any addition.

Next up is the dime, which adds easily to give you $4.35.

$4.25 + 10 cents = $4.35

Now for the small change. This is when it's a good idea to apply Rule 2 - Look for the 10's. You have 8 one cent coins, so you have 8 cents. And you've got three 2 cent coins. Easiest way to make a 10? Put one of the two cent coins with your 8 cents.

8 + 2 = 10.

$4.35 + 10 cents = $4.45

Now you've got $4.45. Finally you have two 2 cent coins, or 4 cents. Add it on, and you have $4.49.

2 + 2 = 4

$4.45 + 5 cents = $4.49

....

$4.49! You're a cent short.

But wait! After you look through your pockets you find 5 cents. Add it on by remembering to Look for the 10's. You already have $4.49, so with another cent you can make an even $4.50. Use one cent from your 5 cents and put it with the 49 cents to make $4.50. Now you still have 4 cents left that you haven't used. Add that on and you will have $4.54. Success!

As you go through this post you may notice that all of the actual addition is just using small numbers. It's really that simple! Once you break up your sum following these two rules you will be able to add quickly and easily, always adding small figures. Why not try out some math in one of our free online math games, or by taking the quick math quiz attached to this post.

Hi there!

2011-04-27T16:06:00.001-07:00

Hello and welcome to Multiply Your Maths, a site that is dedicated to helping people of all ages improve the way they think about and use maths. If you want to learn math tips, get basic math help or try out some math quizzes and math games then this is the place for you. On this site you will find everyday examples of math problems involving multiplication, division etc., all explained in straightforward language.

Multiply Your Maths is divided into two main categories – Maths for Life and Building Blocks.
In Maths for Life you will find math problems that come up in daily life, for example when dealing with household budgets, savings and pension plans, bills, etc. Building Blocks gives simple step by step instructions that will help you get to grips with the basics of mathematics, in the quickest and most simple way possible.

After you have read through some of the material on Multiply Your Maths, you may wish to test yourself with a math worksheet or quiz. Or you may wish to take a break from multiplication and addition to have fun with one of our math games. Whatever you do on this site, you will find that your confidence in your own mathematical ability will grow and your knowledge and understanding of maths will multiply!