1.1 Number Systems & Operations
Integers: A number which is whole, meaning it has no value after its decimal. It can be positive, negative or zero
Rational Numbers: A number which can be expressed as a fraction of two integers.
For example: -3, 0, 7, 42, 1332492483, -1294982
Non-Integers: A number which has a value after its decimal point. It can also be positive, negative or zero
For example: -3.14, 0.0, 2.718, 0.3333, -0.0001, 2/3
Numbers can either be rational or irrationalRational Numbers: A number which can be expressed as a fraction of two integers.
For example: 1/2, -4, 0.75, 5.0, -2/3
Irrational Numbers: A number which cannot be expressed as a fraction of two integers. Their decimal representation is non-terminating and non-repeating.
For example: π (3.14159...), √2 (1.41421...), e (2.71828...)
🧮 Rational Number Checker
Brackets - Indices - Division - Multiplication - Additon - Subtraction
Remember this! You will have to use it in each and every maths expression you ever do! (Note: Indices means either when a number is to the power of something or square roots)
Remember this! You will have to use it in each and every maths expression you ever do! (Note: Indices means either when a number is to the power of something or square roots)
Example using all BIDMAS rules:
Calculate: (2 + 3)² ÷ 5 × 4 + 8 - 2
Step-by-step solution:
Brackets first: (2 + 3) = 5
Expression becomes: 5² ÷ 5 × 4 + 8 - 2
Indices next: 5² = 25
Expression becomes: 25 ÷ 5 × 4 + 8 - 2
Division: 25 ÷ 5 = 5
Expression becomes: 5 × 4 + 8 - 2
Multiplication: 5 × 4 = 20
Expression becomes: 20 + 8 - 2
Addition: 20 + 8 = 28
Expression becomes: 28 - 2
Subtraction: 28 - 2 = 26
Final Answer: 26
Calculate: (2 + 3)² ÷ 5 × 4 + 8 - 2
Step-by-step solution:
Brackets first: (2 + 3) = 5
Expression becomes: 5² ÷ 5 × 4 + 8 - 2
Indices next: 5² = 25
Expression becomes: 25 ÷ 5 × 4 + 8 - 2
Division: 25 ÷ 5 = 5
Expression becomes: 5 × 4 + 8 - 2
Multiplication: 5 × 4 = 20
Expression becomes: 20 + 8 - 2
Addition: 20 + 8 = 28
Expression becomes: 28 - 2
Subtraction: 28 - 2 = 26
Final Answer: 26
Multiples are a series of numbers which can be divided by a certain number. It is basically the times tables of a number.
Any number can be split up into a tree of its factors, up until they all become prime numbers. For example, take the number 60:
For example, the multiples of 3 are: 3, 6, 9, 12, 15, 18, 21 and so on into infinity.
Factors are numbers which can divide into another number exactly with no remainder.
For example, the factors of 12 are: 1, 2, 3, 4, 6 and 12. Or take 36, its factors are 1, 2, 3, 4, 6, 12, 18, 36
A prime number is a number which only has two factors, 1 and itself.
For example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 and so on into infinity.
Fun fact: There is a hunt for the largest prime number in the world, known as the Mersenne prime discovery. A mersenne prime is a prime number which is found by 2^p-1 where p also has to be a prime number, so it's basically finding a prime with primes.
The factor tree:Any number can be split up into a tree of its factors, up until they all become prime numbers. For example, take the number 60:
60 can be split into 6 and 10
6 can be split into 2 and 3 (both prime)
10 can be split into 2 and 5 (both prime)
So the prime factorisation of 60 is 2 × 2 × 3 × 5 or 2² × 3 × 5
The Lowest Common Multiple (LCM) is the smallest number which is a multiple of two or more numbers.6 can be split into 2 and 3 (both prime)
10 can be split into 2 and 5 (both prime)
So the prime factorisation of 60 is 2 × 2 × 3 × 5 or 2² × 3 × 5
For example, the LCM of 4 and 5 is 20, because 20 is the smallest number which both 4 and 5 can divide into exactly.
Highest Common Factor (HCF) is the largest number which can divide into two or more numbers exactly.
For example, the HCF of 12 and 15 is 3, because 3 is the largest number which can divide into both 12 and 15 exactly.