Transcript Ch. 1.1 power point

Chapter 1
Section 1
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
1.1
1
2
3
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Fractions
Learn the definition of factor.
Write fractions in lowest terms.
Multiply and divide fractions.
Add and subtract fractions.
Solve applied problems that involve
fractions.
Interpret data in a circle graph.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Definitions
Natural numbers: 1, 2, 3, 4,…,
Whole numbers: 0, 1, 2, 3, 4,…,
Numerator
2
15
1
Fractions: , ,
Fraction Bar
2 3 7
Denominator
Proper fraction: has a value of less then 1; the numerator
is smaller than or equal to the denominator.
Improper fraction: has a value of greater then 1; the
numerator is larger than the denominator.
Mixed number: is a combination of a whole number and a
fraction.
12
2
Ex. The improper fraction
can be written 2 , a mixed number.
5
5
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Objective 1
Learn the definition of factor.
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Learn the definition of factor.
In the statement 2 × 9 = 18, the numbers 2 and 9 are called
factors. Other factors of 18 include 1, 3, 6, and 18. The number
18 in this statement is called a product.
The number 18 is factored by writing it as a product of two or
more numbers.
Ex. 6 ·3, 18 × 1, (2)(9), or 2(3)(3)
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Learn the definition of factor. (cont’d)
A natural number greater than 1 is prime if its products
include only 1 and itself.
Ex. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,…
A natural number greater than 1 that is not prime is called a
composite number.
Ex. 4, 6, 8, 9, 10, 12,…
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EXAMPLE 1
Factoring Numbers
Write 90 as the product of prime factors.
Solution:
 2  45
 2  3 15
 2  3 3 5
Starting with the smallest prime factor is not necessary. No matter
which prime factor is started with the same prime factorization will
always be found.
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Objective 2
Write fractions in lowest terms.
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Writing fractions in lowest terms.
A fraction is in lowest terms, when the numerator and
denominator have no common factors other than 1.
Basic Principle of Fractions:
If the numerator and denominator are multiplied or
divided by the same nonzero number, the fraction remains
unchanged.
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Writing fractions in lowest terms. (cont’d)
Writing a Fraction in Lowest Terms:
Step 1: Write the numerator and the denominator as the
product of prime factors.
Step 2: Divide the numerator and denominator by the
greatest common factor, the product of all
factors common to both.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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EXAMPLE 2
Writing Fractions in Lowest
Terms
12
Write
in lowest terms.
20
Solution:
3
3 4
=
54
5
When writing fractions in lowest terms, be sure to
include the factor 1 in the numerator or an error may
result.
Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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Objective 3
Multiply and divide fractions.
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Multiply and divide fractions.
Multiplying Fractions:
a c
c
a c
a
If
and
are fractions, then ·
=
.
b d bd
d
b
That is, to multiply two fractions, multiply their numerators
and then multiply their denominators.
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Multiply and divide fractions. (cont’d)
Dividing Fractions:
c
a
ad
a
c
If
and
are fractions, then ÷ =
.
d
d
b
bc
b
That is, to divide two fractions, is to multiply its reciprocal;
the fraction flipped upside down.
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EXAMPLE 3
Multiplying Fractions
Find each product, and write it in lowest simple terms.
Solution:
7 12 7  3  2  2 2



9 14
33 2  7 3
5
1 3 10 7 2  5  7 35
or 5
3 1   

6
3 4
6
3 4 3 2  2
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EXAMPLE 4
Dividing Fractions
Find each quotient, and write it in lowest terms.
Solution:
9 3
335 3
1
95
or 1
 


10 5 10  3 2  5  3 2
2
3
1 11 10 11  3 33

2 3  

4 3 4 10 40
4
3
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Objective 4
Add and subtract fractions.
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Add and subtract fractions.
Adding Fractions:
a
c
ac
a
c
If
and are fractions, then b + b = b .
b
b
That is, to find the sum, the result of adding the numbers,
having the same denominator, add the numerators and keep the
same denominator.
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Add and subtract fractions. (cont’d)
If the fractions do not share a common denominator. The least
common denominator (LCD) must first be found as follows:
Step 1: Factor each denominator.
Step 2: Use every factor that appears in any factored form. If
a factor is repeated, use the largest number of repeats
in the LCD.
Step 3: Find the number that can be multiplied by the
denominator to get the LCD and multiply the numerator
and denominator by that number.
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Add and subtract fractions. (cont’d)
Subtracting Fractions:
a
c
a c ac
If
and
are fractions, then  
.
b
b
b b
b
That is, to find the difference, the result of subtracting the
numbers, between two fractions having the same denominator
subtract the numerators and keep the same denominator.
If fractions have different denominators, find the LCD using
the same method as with adding fractions.
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EXAMPLE 5
Adding Fractions with the
Same Denominator
1 5
Find the sum  , and write it in lowest terms.
9 9
Solution:
1 5
6 23 2
 

9
9 33 3
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EXAMPLE 6
Adding Fractions with Different
Denominators
Find each sum, and write it in lowest terms.
Solution:
55
7 3
2  2 21  4 25
7
2






90
30 45 30  3 45  2
90 2  3  3  5
5

18
5
1 29 7  2 29  14 43
1
or 7
4 2 



6
3
6
6 3 2
6
6
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EXAMPLE 7
Subtracting Fractions
Find each difference, and write it in lowest terms.
Solution:
3  2 1 5
65
3 1
1

 


10 4 10  2 4  5
20
20
7
3 1 27 3  4
27  12 15
or 1

3 1 


8 24
8
8 2
8
8
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Objective 5
Solve applied problems that
involve fractions.
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EXAMPLE 8
Adding Fractions to Solve an
Applied Problem
A gallon of paint covers 500 ft2. To paint his house,
2
Tran needs enough paint to cover 4200 ft . How many
gallons of paint should he buy?
Solution:
2
4200 gal
500
ft
1gal
2
2

4200 ft 
 4200 ft 
2
500
1gal
500 ft
42 100 gal 42
2

gal.  8

5
5 100
5
Tran needs to buy 9 gallons of paint.
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Objective 6
Interpret data in a circle graph.
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EXAMPLE 9
Using a Circle Graph to
Interpret Information
In November 2005, there were about 970 million
Internet users world wide.
Which region had the second-largest number of
Internet Users in November 2005?
Estimate the number of Internet users in Europe.
How many actual Internet users were there in
Europe?
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EXAMPLE 9
Solutions
Solution:
a)
Europe
b)
3
1000million   300million
10
c)
3
970million   291million
10
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