Types of Numbers

Odd and Even

An odd number is something that cannot divide by 2 to give a whole number.
For example: $4 \div 2 = 2$ would be an even number whilst $5 \div 2 = 2.5$ so it must be an odd number.

Is 0 an odd number or an even number?

• 0 is actually a even number because $0 \div 2 = 0$

Integers and Fractions

An integer is a whole number. Such as: $-1 , 0 , 4$

A fraction is a number divided by another number. Or it represents a portion of another number. A better explanation can be found here.

Rational and Irrational

Rational numbers are numbers that can be written as a fraction.For example:
$2 \div 5 = \frac{2}{5}$
$\approx$ means approximately equal to

All integers are rational numbers as well because:
$\frac{5}{1} = 5$

• However $5 \div 0$ cannot work because 0 can go into 5 infinitely many times because 0 is nothing.
• There are also some numbers which go on forever without repeating, these can't be written as a fraction. For example $\pi \approx 3.14, \sqrt{2} \approx 1.4$ These can't be written as fractions because nothing will be able to exactly equal them (although you can make some pretty good estimates). For example $\frac{22}{7} \approx 3.1428$ but it doesn't equal pi.

Irrational numbers are never-ending, non-repeating decimals. These are where numbers such as $\pi$ fall into. Some roots of positive integers: $\sqrt{2}$ are also irrational.

Prime Numbers

A prime number is something that 2 other numbers cannot multiply up to make. The only way to make a prime number is $1 * \text{itself}$. For example: 2, 3, 5 and 7 do not appear on the other times tables so are prime numbers.

How to work out if a number is prime

1. All prime numbers (after 2) are ODD numbers.
2. All prime numbers end in 1,3,7 or 9.
3. Divide the number by 3 and 7. If it doesn't divide exactly it is prime.

For example, to work out if 89 is a prime number.

1. 89 is odd
2. 89 ends in 9.
3. $\begin{aligned} 89 \div 3 = 29.6... \\ 89 \div 7 = 12.7... \end{aligned}$
   89 must be a prime number.