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.

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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 This puts me at 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:

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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
Press the ‘=’ button, and you should get ‘ |
First we need to enter in ‘–5’. First you need to
type in ‘5’. Then we need to tell the calculator that it is Now we need to multiply by 3 – do this by pressing the button followed by the button. Now we need to Next, we need to tell the calculator that the
number to subtract is ‘-5’. Do this by pressing the button 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:

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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.