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: or 0.6 is a rational number as it can be written as: or even 4.285714285714… is a rational number as it can be written as: 3. Irrational Numbers 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!