Unit 6 Indices and Factors

Transcription

Unit 6 Indices and Factors
Unit 6
Indices and Factors
Presentation 1
Square and Square Roots
Presentation 2
Cube and Cube Roots
Presentation 3
Index Notation
Presentation 4
Rules of Indices
Presentation 5
Factors
Presentation 6
Prime Factors
Presentation 7
HCF and LCM
Presentation 8
Negative Indices
Unit 6
Indices and Factors
Square and Square Roots
What is
We say that 4 is the square root of 16
What
is
So
We write
is also a square root of 16
What is the square root of 25?
as
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Square and Square Roots
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Presentation 2
Cube and Cube Roots
Presentation 3
Index Notation
Presentation 4
Rules of Indices
Presentation 5
Factors
Presentation 6
Prime Factors
Presentation 7
HCF and LCM
Presentation 8
Negative Indices
Unit 6
Indices 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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Presentation 1
Square and Square Roots
Presentation 3
Index Notation
Presentation 4
Rules of Indices
Presentation 5
Factors
Presentation 6
Prime Factors
Presentation 7
HCF and LCM
Presentation 8
Negative Indices
Unit 6
Indices and Factors
Index Notation
What is
What is
Find n if
So
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Index Notation
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Presentation 1
Square and Square Roots
Presentation 2
Cube and Cube Roots
Presentation 4
Rules of Indices
Presentation 5
Factors
Presentation 6
Prime Factors
Presentation 7
HCF and LCM
Presentation 8
Negative Indices
Unit 6
Indices and Factors
Rules of Indices
m and n are integers
Verify rule for
(using rule)
But
(as before!)
Verify rule for
But
(as before!)
Verify rule for
But
(as before!)
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Rules of Indices
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Presentation 1
Square and Square Roots
Presentation 2
Cube and Cube Roots
Presentation 3
Index Notation
Presentation 5
Factors
Presentation 6
Prime Factors
Presentation 7
HCF and LCM
Presentation 8
Negative Indices
Unit 6
Indices 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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Presentation 1
Square and Square Roots
Presentation 2
Cube and Cube Roots
Presentation 3
Index Notation
Presentation 4
Rules of Indices
Presentation 6
Prime Factors
Presentation 7
HCF and LCM
Presentation 8
Negative Indices
Unit 6
Indices 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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Presentation 1
Square and Square Roots
Presentation 2
Cube and Cube Roots
Presentation 3
Index Notation
Presentation 4
Rules of Indices
Presentation 5
Factors
Presentation 7
HCF and LCM
Presentation 8
Negative Indices
Unit 6
Indices 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: 24, 48, 72, 96,120, 144, . . .
Multiples of 60 are: 60, 120, 180, 240, 300, . . .
So LCM = 120
Check
,
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HCF and LCM
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Presentation 1
Square and Square Roots
Presentation 2
Cube and Cube Roots
Presentation 3
Index Notation
Presentation 5
Negative Indices
Presentation 6
Standard Form
Presentation 7
Calculations and Standard Form
Unit 6
Indices and Factors
Negative Indices
We define
Evaluate
Evaluate
Evaluate
Evaluate
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Negative Indices
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Presentation 1
Square and Square Roots
Presentation 2
Cube and Cube Roots
Presentation 3
Index Notation
Presentation 4
Rules of Indices
Presentation 5
Factors
Presentation 6
Prime Factors
Presentation 7
HCF and LCM