math unit6 indices and factors
TRANSCRIPT
Unit 6Indices and FactorsPresentation 1 Square and Square RootsPresentation 2 Cube and Cube RootsPresentation 3 Index NotationPresentation 4 Rules of IndicesPresentation 5 FactorsPresentation 6 Prime FactorsPresentation 7 HCF and LCMPresentation 8 Negative Indices
Unit 6 Indices and Factors
Square and Square Roots
What is
We say that 4 is the square root of 16
So is also a square root of 16
We write
What is
What is the square root of 25?
as
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Square and Square Roots
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Return to StartPresentation 2 Cube and Cube RootsPresentation 3 Index NotationPresentation 4 Rules of IndicesPresentation 5 FactorsPresentation 6 Prime FactorsPresentation 7 HCF and LCMPresentation 8 Negative Indices
Unit 6Indices and Factors
Cube and Cube Roots
What is
We say that the cube root of 125 is 5 and that
or
What is
Also
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Cube and Cube Roots
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Return to StartPresentation 1 Square and Square RootsPresentation 3 Index NotationPresentation 4 Rules of IndicesPresentation 5 FactorsPresentation 6 Prime FactorsPresentation 7 HCF and LCMPresentation 8 Negative Indices
Unit 6Indices and Factors
Index Notation
What is
What is
Find n if
So
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Index Notation
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Return to StartPresentation 1 Square and Square RootsPresentation 2 Cube and Cube RootsPresentation 4 Rules of IndicesPresentation 5 FactorsPresentation 6 Prime FactorsPresentation 7 HCF and LCMPresentation 8 Negative Indices
Unit 6Indices and Factors
Rules of Indices
Verify rule for(using rule)
But
(as before!)
m and n are integers
Verify rule for
But
(as before!)
Verify rule for
But
(as before!)
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Rules of Indices
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Return to StartPresentation 1 Square and Square RootsPresentation 2 Cube and Cube RootsPresentation 3 Index NotationPresentation 5 FactorsPresentation 6 Prime FactorsPresentation 7 HCF and LCMPresentation 8 Negative Indices
Unit 6Indices and Factors
Factors
A factor of a positive whole number is any positive whole number that will divide exactly into it.
Example: Find all the factors of 20
You can write 20 as:
So factors of 20 in increasing order are:
1 2 4 5 10 20
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Factors
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Return to StartPresentation 1 Square and Square RootsPresentation 2 Cube and Cube RootsPresentation 3 Index NotationPresentation 4 Rules of IndicesPresentation 6 Prime FactorsPresentation 7 HCF and LCMPresentation 8 Negative Indices
Unit 6Indices and Factors
Prime Factors
Any positive whole number can be written uniquely as the product of its prime factors.
Example: Write the number 276 as a product of its prime factor
This is unique
?
?
?
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Prime Factors
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Return to StartPresentation 1 Square and Square RootsPresentation 2 Cube and Cube RootsPresentation 3 Index NotationPresentation 4 Rules of IndicesPresentation 5 FactorsPresentation 7 HCF and LCMPresentation 8 Negative Indices
Unit 6Indices and Factors
HCF and LCM
The HCF (Highest Common Factor) of two (or more) positive integers is the largest number which is a factor of both (or all) the numbers.
Example: Find the HCF of 120 and 105
So, HCF = 3 x 5 = 15
Check: ,
The LCM (Lowest Common Multiple) of two (or more) positive integers in the lowest number into which both (or all) of the numbers can divide exactly.
Example: Find the LCM of 24 and 60
Multiples of 24 are:Multiples of 60 are:
So LCM = 120Check ,
24, 48,72, 96,120, 144, . . .60, 120, 180, 240, 300, . . .
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HCF and LCM
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Return to the StartPresentation 1 Square and Square RootsPresentation 2 Cube and Cube RootsPresentation 3 Index NotationPresentation 5 Negative IndicesPresentation 6 Standard FormPresentation 7 Calculations and Standard Form
Unit 6Indices and Factors
Negative Indices
We define
Evaluate
Evaluate
Evaluate
Evaluate
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Negative Indices
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Return to StartPresentation 1 Square and Square RootsPresentation 2 Cube and Cube RootsPresentation 3 Index NotationPresentation 4 Rules of IndicesPresentation 5 FactorsPresentation 6 Prime FactorsPresentation 7 HCF and LCM