Number

Everything about number for year 9

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Common Multiples

Numbers can share multiples. For example 24 is a multiple of 3 and 4. These are called common multiples. LCM (lowest common multiple) is the first number that is in both lists of multiples.
Eg. the LCM of 2 and 5 is 10

2, 4, 6, 8, 10, 12, 14, 16
5, 10, 15, 20, 25, 30, 35

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Factors

A number may be made by multiplying two or more other numbers together. The numbers that are multiplied together are called factors of the final number. All numbers have a factor of one since one multiplied by any number equals that number. All numbers can be divided by themselves to produce the number one. Therefore, we normally ignore one and the number itself as useful factors.

  • There are several clues to help determine factors.
  • Any even number has a factor of two
  • Any number ending in 5 has a factor of five
  • Any number above 0 that ends with 0 (such as 10, 30, 1200) has factors of two and five.
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Common Factors

When working out common factors of a number write out the multiples and then work out which ones are the same.

Eg. What are the common multiples of 18 and 24
18: 1, 2, 3, 6, 9, 18
24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors of 18 and 24 = 1, 2, 3, 6
In 18 and 24 the HCF (highest common factor) = 6

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Prime Numbers

Prime numbers are numbers that have exactly 2 factors.
First 10 prime numbers = 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.

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Composite Numbers

Composite numbers are numbers that have more than 2 factors
First 10 composite numbers = 4, 6, 8, 9, 10, 12, 14, 15, 16, 18.

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Prime Factors

Any composite number can be written by multiplying prime numbers only.
Eg. 4 x 7 = 24 is written as 2 x 2 x 7 = 24.

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Factor Tree

We keep dividing by prime numbers until we can't go any further
Eg.

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Square Roots, Cube Roots and Powers

The square root is the product of a number timesed by itself.
Eg. √9 = 3 because 3 x 3 = 9

The cube root is the product of a number timesed by itself 3 times
Eg. 273 = 3 because 3 x 3 x 3 = 27

25 = 2 x 2 x 2 x 2 x 2 = 32. 38 = 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 6561

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Adding Integers

Always start from where the first integer is then -
- Step RIGHT to add a positive
- Step left to add a negative

Eg. -2 + +3 =

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Subtracting Integers

- A positive and a negative make a negative (-n - +m = ?)
- A negative and a negative make a positive

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Multiplying and Dividing Integers

Rules

Multiplying Dividing
+ x + = + + ÷ + = +
+ x - = - + ÷ - = -
- x - = - - ÷ + = -
- x + = - - ÷ - = +

Thinking...
3 x 4 = 3 'lots' of +4
= +12
3 x -4 = 3 'lots' of -4
= -12

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BEDMAS

- Brackets
- Exponents
- Division
- Multiplication
- Addition
- Subtraction

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Rounding Decimals

Example
A 150cm plank of wood is divided equally into seven pieces.
How long is each piece?
= 150 ÷ 7
= 21.428571cm
This would be difficuilt in context so we round the number
To 1dp = 21.4 (1dp)
2dp = 21.43 (2dp)

NB: Dp means decimal point

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Rounding Rules

1. Decide which place you will round to. This will be the last didgit on your answer. It will either be rounded up or left unchanged.
2. Look to the didgit just right of the place.
3. If the didgit in 'step 2' is 5, 6, 7, 8 or 9 we round up
4. If the didgit in 'step 2' is 1, 2, 3, or 4 we leave the last didgit unchanged

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