Transcript Review of Numbers

Review of Numbers
Greatest Common Divisor
Exponents
Sections 1.2 & 1.3
Previous Information
Types of numbers
 Natural
Whole



Integers
Rational
Irrational
Purpose


In later mathematics, you will want
to work with numbers in simplest
form.
It is easier to work with small
numbers rather than large
numbers.
Prime Factorization


Breaking a number down into it’s
combination of prime factors
To start prime factorization, ask
yourself…
“Will 2 divide this number…,
Will 3 divide this number…,
Will 5 divide this number…”
Factors of 15


3
5
Factor Tree
15
3
3
Alternate
Method
3 15
5
5
1
5
1
3
1
5
1
Factors of 45


Alternate
Method
Factor Tree
3
5
45
3
15
3
3
3
3 45
3 15
5
2
5
5
1
3
2
5
1
Greatest Common Divisor
 Largest
factor of 2 or more
numbers
 When finding – use prime
factorization
Greatest Common Divisor of 15 & 45


3
5
45
15
Maximum number of
common factors in
each final row is one
three and one 5
Therefore, the GCD is
3*5 = 15
GCD is 15
3
3
3
15
5
1
5
1
3
3
3
2
5
5
1
Greatest Common Divisor of 8 & 27
Note:
there is
Therefore,
ThenoGCD =1
Common
Divisor,
What number
divides all
numbers evenly?
1
2
8
2
27
4
2
2
3
3
2
3
9
3
3
3
3
TEST YOURSELF
Find the GCD for the following pairs of numbers
1.
2.
3.
4.
5.
6.
12
12
18
32
12
18
&
&
&
&
&
&
18
24
32
64
54
54
6
12
2
32
6
18
18 & 64 2
8. 32 & 54 2
9. 24 & 64 8
10.54 & 72 18
11.14 & 15 1
7.
Exponents


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
Repeated Multiplication
be
 b = base
 e = exponent
So you would multiply b  e times
b*b*b*b*b*…*b {e times}
Examples
4
2
=2*2*2*2
=16
2
7
=7*7
=49
x3
=x*x*x
=
3
x
Rules of Exponents: MULTIPLICATION
Multiply
Add
am
an
am+n
32 * 34
2+4
3
like Bases
*
exponents
=
6
3
Rules of Exponents: Exponents
Exp
Multiply
(am
am*n
raised
to an Exp
)n
(32)4
exponents
2*4
3 =
8
3
Rules of Exponents: DIVISION
Divide
Subtract
am
n
a
am-n
34
2
3
4-2
3
like Bases
exponents
=
2
3
Quantity to an
Rules of Exponents: Exponent
Qty
Distribute
(ab)m
ambm
(3x)4
4
4
3 x
raised
to an Exp
exponents
Rules of Exponents: Negative Exp
Number
=
the
reciprocal
-2
3
1
32
raised to a
neg Exp
1
-m
a
m
a
=
1
9
TEST YOURSELF: Rules of Exponents
 23
* 24
 54/53
 (2/5)2
 -32
 (-3)2
 (6x)3
 6x3
 7(-2)
 23+4
= 27 = 128
 54-3 = 51 = 5
 22/52 = 4/25
 -32 = -9
 (-1)2 * 32
 63x3 = 216x3
 6x3
 1/72 = 1/49
Terminology






Factor
Prime number
Composite number
Prime Factorization
Exponential Form
Greatest Common
Divisor






Expanded Form
Sum
Difference
Product
Quantity
Reciprocal
Conclusion



Any two are more numbers have a
Greatest Common Divisor
(either 1 or some other Factor)
To find the GCD use Prime
Factorization
(match factors using the smallest
exponential value)
Rules of Exponents
Assignment
On-line
 12 GCD & Exponents