Please enable JavaScript.

Coggle requires JavaScript to display documents.

Maths (Number (Numbers (Prime numbers (Prime Factor Decomposition (An…

- - - - Example If want to find 10% of something, 'of' just means 'times'. So 10% of 150 = 10/100 × 150 = 15.
      - Example So if we say 50%, we mean 50/100 = 1/2 (after cancelling). So 50% means ½
    - - Example: The price of some apples is increased from 48p to 67p. By how much percent has the price increased by?
        % change = 67 - 48 × 100= 39.58%
      - new value - original value × 100/ original value
    - - percentage error = error × 100/real value.
      - Example: Nicola measures the length of her textbook as 20cm. If the length is actually 17.6cm, what is the percentage error in Nicola's calculation?
        
        % error = 20 - 17.6 × 100 / 17.6 = 13.64%
    - - Original value = New value × 100/ 100 + %change
      - Example: Amish buys a stamp collection and makes a 35% profit by selling it for £2700. Find the cost of the collection. It is the original value we wish to find, so the above formula is used.
        
        2700 × 100 / 100 + 35
        
        = £2000
    - - New value = 100 + percentage increase × original value / 100
      - Example:
        
        £500 is put in a bank where there is 6% per annum interest. Work out the amount in the bank after 1 year.
        
        In other words, the old value is £500 and it has been increased by 6%.
        
        Therefore, new value = 106/100 × 500 = £530 .
  - - - Integers are whole numbers (both positive and negative, including zero).
    - - is a number which can be written as a fraction where numerator and denominator are integers (where the top and bottom of the fraction are whole numbers)
    - - Are numbers which cannot be written as fractions, such as pi and √2. In decimal form these numbers go on forever and the same pattern of digits are not repeated.
    - - Numbers that are multiplied by themselves.
    - - Numbers left written as √n, where n is positive but not a square number.
    - - are numbers above 1 which cannot be divided by anything (other than 1 and itself) to give an integer
      - Prime Factor Decomposition
        
        An important fact is that any number can be written as the product (multiplication) of prime numbers in one way
        
        For example, 20 = 5 x 2 x 2 .
        
        For example 36 = 9 × 2 × 2 = 3 × 3 × 2 × 2.
    - - All real numbers can be written in decimal form (such as 3.165).
    - - The least (or lowest) common multiple (LCM) of two or more numbers is the smallest number into which they evenly divide.
        
        For example the LCM of 2, 3, 4, 6 and 9 is 36.
      - The highest common factor (HCF) of two or more numbers is the highest number which will divide into them both.
        
        For example the HCF of 6 and 9 is 3.