## The Number Line

The number line is a diagram you can draw to help you understand and also perform calculations with positive and negative numbers.  It’s a horizontal line, with marks along it that represent numbers.

You can do addition and subtraction calculations using the number-line as well.  Say I have to find the answer to the following question:

 Calculate 3 – 8 – (–4) Solution Since this question only has additions and subtractions in it, I can work through it from left to right.  So first, I have a 3, which I can find on the number line: Now I have to take away 8.  When you take away or subtract using the number line, you move to the left.  So to take away 8, I need to move 8 steps towards the left: This puts me at negative five.  The next thing I need to do is subtract negative four.  We have to be a little bit careful here – we are subtracting a number (–4) that is already negative.  When you have: Something – a negative number It is the same as: Something + the positive of that number In our case, when we subtract ‘–4’ this is the same as adding ‘+4’.  When we do addition on the number line, we move to the right.  So, we need to move four places to the right: Now that we’ve carried out all the operations in the question, our current position on the number line is the answer: ‘–1’.

### Negative numbers on the calculator

Your calculator is a great way of checking whether what you’ve done with your positive and negative numbers is correct.  Say we had to find an answer to the following question:

Notice the little negative sign up high in front of the second ‘5’.  This is how people sometimes indicate a number is positive or negative, by putting the sign up high in front of the number.

There are two operations in this question, a ‘×’ and a ‘–’.  Multiplication is performed before subtraction, so it is done first. Here’s an explanation of how to solve this problem using two common types of calculators.

 First we need to enter in ‘–5’.  To indicate that the number is negative, we first need to press the  button.  Then we press the ‘5’ button. Next, we need to type in the multiply symbol , followed by the number we’re multiplying by: . The next operation is subtraction – so we press the  button. We are subtracting a negative number, so we need to tell the calculator that it is a negative number – we do this by pressing the  button again, before we type in the number: ‘5’.   Press the ‘=’ button, and you should get ‘’ as your answer. First we need to enter in ‘–5’.  First you need to type in ‘5’.  Then we need to tell the calculator that it is negative 5 – to do this press the  button.  You should see a negative sign appear in front of the ‘5’.  You can press the  button as many times as you want – the number on the screen will switch between being positive and negative.  For this question, we want negative 5 – so press it until ‘–5’ shows up on the screen. Now we need to multiply by 3 – do this by pressing the  button followed by the  button. Now we need to subtract negative five.  This can be done by first pressing the  button – this tells the calculator that we want to perform a subtraction. Next, we need to tell the calculator that the number to subtract is ‘-5’.  Do this by pressing the  button and then pressing the  button to tell the calculator it’s negative five. Finally, to get the answer, press the ‘=’ button.

### Composite numbers

Composite numbers are numbers that you can get by multiplying together two or more natural numbers which are not 1.  The two or more numbers that you multiply can be the same or different.  For instance, 8 is a composite number because you can get it by multiplying 4 by 2, or even by multiplying 2 by 2 by 2.  15 is a composite number because you can get it by multiplying 5 by 3.  7 is not a composite number because the only way you can get 7 is by multiplying 1 and 7.  Remember, to be a composite number, none of the numbers you multiply together to get it can be 1.

### Factors and products

Since we’re talking about numbers that multiply to give other numbers, we should learn what factors and products are.  The factors of a number are the natural numbers that multiply together to make that number.  Take for instance the number 15.  We can get 15 in two different ways:

Products are the numbers that you get by multiplying other numbers together.  So in the maths above, the number 15 is what we’re getting as a result of doing multiplication – 15 is the product.  The numbers on the right of the equals sign are the ones we are multiplying together to give 15, so they are the factors.  So the factors of 15 are 15, 1, 5, and 3 (yes, 15 is a factor).

### Prime numbers

Prime numbers are natural numbers which you can only get by multiplying 1 and themselves.  For instance, 5 is a prime number because you can only get 5 by multiplying 1 and 5 together.  4 is not a prime number because you can get 4 by multiplying 2 and 2 together.  Prime numbers have exactly two unique factors – themselves and 1.  For instance, take the prime number 7. The only factors (numbers that multiply together to give it) are 1 and 7.  Composite numbers on the other hand, have more than two factors.

Is 1 a prime number?

1 is a special type of number, and is not considered a prime number.  This sort of makes sense.  What natural numbers can you multiply together to get 1?  Well, we know that 1 by 1 gives you 1.  So the only factor of 1 is 1.  Since 1 has only one factor, it isn’t a prime number – prime numbers have exactly two unique factors.

### Square numbers

Square numbers are numbers that you can get by multiplying a natural number by itself.  For instance, if I start with the natural number 3, and multiply it by itself:

I get 9, which is a square number.  People sometimes call square numbers perfect squares.  Here’s a list of the first few square numbers:

 Number Square Number Square 1 1 11 121 2 4 12 144 3 9 13 169 4 16 14 196 5 25 15 225 6 36 16 256 7 49 17 289 8 64 18 324 9 81 19 361 10 100 20 400

### Integers

An integer is another type of number.  Integers are similar to natural, counting and whole numbers except for one thing.  –3 is an integer.  So is –10.  So is –55.  0 is also an integer.  So integers are like natural numbers but they can be negative as well.