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Mr F’s Maths Notes
Number
1. Types of Number
1. Types of Number
1. Integers
“Integer” is just a fancy word for whole number.
The thing to remember is that integers can be positive or negative
So: 1, 7, 298, -3, 0 and -49 are all integers, but 2.5 is not!
2. Rational Numbers
Rational Numbers are numbers which can be written as fractions.
Don’t Forget: the top and bottom of the fraction (numerator and denominator)
must be whole numbers (integers).
So: 4 is a rational number as it can be written as: 4 1
or 8 2
0.6 is a rational number as it can be written as:
6
10
or
3
5
even 4.285714285714… is a rational number as it can be written as:
3. Irrational Numbers
30
7
Irrational Numbers are just the opposite of Rational Numbers
They cannot be written as a fraction.
In fact, when these numbers are written in decimal form, the numbers go on
forever and ever and the pattern of digits is not repeated.
e.g. The most famous Irrational Number is pi (π), which is 3.1415927…, but √2 and
√7 are irrational too
4. Square Numbers
You can get a Square Number by multiplying any whole number (integer) by itself
So: The first square number is 1, because 1 x 1 = 1.
The second square number is 4, because 2 x 2 = 4, and so on…
The first ten square numbers are: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Look:
You can also get all the square numbers
by counting the dots in square patters:
5. Triangle Numbers
You can get all the Triangle Numbers by starting with 1, and then adding 2, then
adding 3, then adding 4, and so on…
So: The first triangle number is 1
The second triangle number is 3 (1 + 2)
The third triangle numbers is 6 (1 + 2 + 3)
The first ten triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55
Look:
You can also get all the triangle numbers
by counting the dots in triangle patters:
Challenge:
By looking at the dot patterns, can you see why every time you add together two
consecutive triangle numbers, you get a square number?
e.g. 15 + 21 = 36, which is a square number, and 36 + 45 = 81, which is also a
square number!
6. Cube Numbers
You can get a Cube Number by multiplying any whole number (integer) by itself
and then by itself again.
So: The first cube number is 1, because 1 x 1 x 1 = 1.
The second cube number is 8, because 2 x 2 x 2 = 8, and so on…
The first ten square numbers are: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
Look:
If Mr Barton was in any way artistic, he would show you
that you can get all the cube numbers by counting dots
in cubes. Don’t take my word for it, try it yourself!
7. Factors
The Factors of a number are all the whole numbers (integers) that divide into
your number exactly (there must not be a remainder!)
Don’t forget: 1 is a factor of all numbers, and so is the number itself!
e.g. The factors of 12 are: 1, 2, 3, 4, 6 and 12
The factors of 55 are: 1, 5, 11, and 55
Challenge:
Have you any idea why all square numbers seem to have an odd number of factors?
8. Multiples
The Multiples of a number are all the numbers in your number’s times table
Don’t forget: you must count the number itself!
e.g. Some multiples of 7 are: 7, 14, 21, 28… but there are loads more, like 700 and 4445
Some multiples of 21 are: 21, 42, 63… but there are loads more, like 231 and 1050
9. Prime Numbers
For some reason, people always get confused with prime numbers, so try to remember this
definition and you won’t go wrong:
A prime number is a number that has exactly 2 factors, no more, no less
So: 1 is NOT a prime number, as it only has one factor (1)
2 is a prime number as it has two factors (1 and 2)
Don’t Forget: 2 is the only EVEN prime number!
7 is a prime number as it has two factors (1 and 7)
21 is NOT a prime number as it has four factors (1, 3, 7 and 21)
1061 is a prime number as it has just two factors (1 and 1061)
Look:
Unfortunately, there does not seem to be any patterns
to help us find all the prime numbers, but it’s not all bad news.
I think the prize for finding the largest prime number is about
$1million, and its even more if you find the pattern!
If you have a spare 5 minutes, why not give it a go.
Anyway, until then, here are all the prime numbers between 1 and 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89 and 97.
Good luck with
your revision!