# Number

Revision notes on numbers

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### Page 1

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…

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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…

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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.

Example: `Find the LCM of…

### Page 5

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…

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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

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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%…

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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
e.g. 8
= 8
2 = 4 = 2
b 2

3) a + b - NOTHING DOING

4) (a + b) 2 = (a +…