Transcript GOOD MORNING

GOOD MORNING
Shania QQ:1246640685
MSN: [email protected]
www.themegallery.com
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Contents
Math words quiz
Factors-prime factors
Multiples-LCM
Patterns and sequences
SETS!!!
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Math words quiz
10 minutes!!!
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Factors
Factors of a number
are the whole numbers
that multiply together
to give the original
number

E.g. The factors of 12 are?

12 is the the original number

So which numbers can multiply
together to give 12?

1×12, 2×6, 3×4

That is, 1,2,3,4,6,12 are factors of
12.

We use F(12) as a short way of
writing factors of 12.

F(12)={1,2,3,4,6,12}

Factor pairs of 12 are (1,12), (2,6),
(3,4)

Among these 6 factors 2 and 3 are
prime factors.
[Prime factors of a number are
factors of the number that are also
prime number.]
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Writing numbers as the product of prime factors
Prime factors
2,3,5,7,11,13…
12=4×3,but 4 is not prime number,
we break 4 down further
12=2×2×3 that we have written 12
as the product of prime factors
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Steps
•Step 1
Try to divide the given number by the first prime number -- 2
• Step 2
Continue until 2 will no longer divide into it
•Step 3
Try the next prime number, 3, then 5, 7 and so on,
until final answer is 1
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Examples
Write 60 as a product of prime
factors.
Write 3465 as a product of prime
factors.
So 3465=3×3×5×7×11
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Several rules
The number is ended by 0,2,4,6,8 can be divided
by 2.
The sum of all digits of the number can be divided
by 3, that is, the number can be divided by 3.
3465 3+4+6+5=18 18/3=6
so 3465 can be divided by 3
So does 5, 7, 11 and 13
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Multiples
Definition: the multiples of number
are the products of that numbers
and 1,2,3,4,5…(Natural number)
 E.g. The multiples of 3 are???
 3, 6, 9, 12, 15…
 The first five multiples of 3:
M(3)={3,6,9,12,15}
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LCM-Lowest common multiple
最小公倍数
The smallest number that is a
multiple of two or more numbers
12, 24, 36 are multiples of 3 and 4.
BUT, 12 is the smallest one, that is,
12 is the LCM of 3 and 4.
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Two ways to find LCM
ONE: ①List the multiples of each
numbers of each numbers ②and then
pick out the lowest number that
appears in every one of the lists.
(applicable for small numbers)
ANOTHER: Expressing each number as
a product of prime factors
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Sets
Any collection of objects – have sth
in common, some connection with
each other.
{ } braces
, comma
The object in a set we called
element of the set ∈
5 ways to express sets
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5 ways
1. Listed set {1,2,3,4.5}
2. Described set {first five natural
numbers}
3. Set builder notation to describe
sets mathematically {x:x≦10 and x
is an even number}
4. Represented by a name or a letter
{red, blue, yellow} {Thomas, Joise}
5. Venn diagram
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Special sets
Finite sets and infinite sets
Universal set
rectangular Venn diagram
It can change from problem to problem
{ }
empty set
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Relationships between sets
Equal sets: same cardinality and
same elements “=“
Equivalent sets: same number of
elements
Subsets: A is the subset of set B if
all of the elements of A are
elements of B
A⊂ B（子集） B⊃ A (superset扩散集）
In our book，
different from Chinese book
How many subsets? Include {} and equal set
Use permutation and combination to prove.
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Continue
Complement set A’ contains all of
the elements of the universal set
not in A. set A and its complement
A’ are disjoint- A∩A’=empty set
Power set: All subsets of a given
set A
If a set has n elements it will have
2^n subsets
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Intersection and union of sets
A∪B : the union of sets A and B.
A∩B : the intersection of sets A and
B. The elements common to set A
and B.
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Laws
1. A ∩ A = A
2. A ∩ B = B ∩ A (commutative law)
3. A ∩ B ∩ C = A ∩ (B ∩ C) (associative
law)
4. A ∩ φ = φ ∩ A = φ
5. A ∪ (A ∩ B) = A
6. A ∩ (A ∪ B) = A
7. A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)
(distributive law)
8. A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)
(distributive law)
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Homework
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