# Number

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NUMBERS
Prime Numbers
Prime numbers don't divide by anything except 1 and themselves.
1 is not a prime number
The first four prime numbers are 2, 3, 5, and 7
ALL prime numbers end in 1, 3, 7 or 9
NOT ALL numbers ending in 1, 3, 7 or 9 are prime numbers.
Finding Prime Numbers
For a number to be prime:
E.g. "Decide whether or not 233 is a prime number."
1) Does it end in 1, 3, 7 or 9? Yes
2) Find its square root: 233 = 15.264
3) List all primes which are less than this square root: 2, 3, 5, 7, 11 and 13
4) Divide all of these primes into the number under test:
233/3 = 77.6667 233/7 = 33.2857 (obviously won't divide by 5 and 2)
233/11= 21.181818 233/13= 17.923077
5) Since none of these divide cleanly into 233 then it is a prime number.
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Multiples, Factors and Prime Factors
Multiples
The multiples of a number are simply its times table.
E.g. the multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, etc.
Factors
The factors of a number are all of the numbers that divide into it.
There is a method of finding them.…read more

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LCMs and HCFs
LCM ­ `Lowest Common Multiple'
Lowest Common Multiple ­ The SMALLEST number that will DIVIDE BY ALL the numbers
in question.
Method
1) List the multiples of all the numbers.
2) Find the smallest one that is in all of the lists.…read more

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Recurring Decimals Into Fractions
Example: `Convert 0.22... into a fraction'
Solution:
Consider X = 0.22...
Multiply the equation by 10 10x = 2.22...
Subtract the two equations 9x = 2
Divide through by 9 X = 2/9
X is now a fraction.
NB. Always check if the fractions will CANCEL DOWN.…read more

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Fractions
1) Multiplying
Multiply top and bottom separately:
3/5 X 4/7 = 3 x 4/ 5 x 7 = 12/35
2) Dividing
Turn the second fraction upside down and the multiply:
3/4 ÷ 1/3 = 3/4 x 3/1 = 3 x 3/4 x 1 = 9/4
Add or subtract TOP LINES ONLY but only if the bottom numbers are the same.…read more

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Percentages
There are three types of questions for percentages.
Type 1
`Find x% of y' ­ e.g. Find 15% of £46 0.15 x 46 = £6.90
Type 2
`Express x as a percentage of y'
E.g. Give 40p as a percentage of £3.34 (40 ÷ 334) x 100 = 12%
Type 3 (Be careful)
Identified by NOT giving the `ORIGINAL VALUE'
Example: `A house increases in value by 20% to £72000.
Find what it was worth before the rise.…read more

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Manipulating Surds
Rules
1) a x b = ab e.g. 2 x 3 = 2 x 3 = 6
2) a
= a
b