Transcript Section 1.2

1.2
1.
2.
3.
4.
Fractions
Write equivalent fractions.
Write equivalent fractions with the LCD.
Write the prime factorization of a number.
Simplify a fraction to lowest terms.
Copyright © 2011 Pearson Education, Inc.
Fractions
3
4
 Numerator
 Part
 Denominator
 Whole
Equivalent Fractions
∙2
2 4

3 6
∙2
∙3
2 6

3 9
∙3
3 ?
6


8 16 16
∙2
∙2
÷3
9
27 9
 
30 ? 10
÷3
Factors:
Expressions that are being multiplied.
Prime number:
A natural number that has only 1 and
the number itself as factors.
2, 3, 5, 7, 11, 13, 17, 19, 23,…
Prime factorization: A factorization that contains only
prime factors.
1, 2, 3, 4, 6 and 12 are factors of 12.
Prime factorization of 12 is 2 ∙ 2 ∙ 3.
Find the prime factorization of 20.
Factor Tree
20
45
225
Factor Tower
5
2 10
10
2 2 20
20
Divide by prime numbers!
2, 3, 5, 7, 11, …
0, 2, 4, 6, 8
259:
372:
23 + 57 + 92 = 16
12
5, 10, 15, 20, …
10, 20, 30, 40, …
Find the prime factorization of 60.
Factor Tree
Factor Tower
60
6  10
2325
2235
5
3 15
15
22 30
30
22 2 60
Find the prime factorization of 48.
Factor Tree
48
68
2324
23222
22223
Factor Tower
3
26
6
22 12
12
222 24
24
2222 48
Find the LCD.
Using Multiples
5
3
and
6
10
6:
6, 12, 18, 24, 30, 36, 42, 48, 54, 60
10:
10, 20, 30, 40, 50, 60
LCD = 30
Use when numbers are small.
Find the LCD.
Using Prime
Factorization
5
3
and
6
10
2∙3
LCD:
2∙3 ∙5
2∙5
= 30
Find the LCD.
Using Multiples
5
2
and
12
9
12: 12, 24, 36, 48, 60
9:
9, 18, 27, 36
LCD = 36
Find the LCD.
Using Prime
Factorization
5
2
and
12
9
3∙3
2∙2∙3
LCD: 2∙2∙3 ∙ 3 = 36
Write the fractions as equivalent fractions with the LCD.
5
7
and
8
12
LCD: 24
∙3
5 15

8 24
∙2
7 14

12 24
Write the fractions as equivalent fractions with the LCD.
Suggestion:
5
7

and 
16
36
2∙2∙2∙2
5
7
and
16
36
2∙2∙3∙3
LCD: 2∙2∙2∙2∙3∙3 = 144
5 ∙9
45


16
144
∙4
7
28


36
144
Reduce Fractions.
Using Prime
Factorization
9
33

12
223
Using Greatest
Common Factor
9
12
GCF: 3
3
4
3

4
3

4
Reduce Fractions.
Using Greatest
Common Factor
30
42
GCF: 6
5
7
5

7
Using Prime
Factorization
2 35
30
5


2 37
42
7
Reduce Fractions. GCF: ?
Using Greatest
Common Factor
Common Factor: 10
Common Factor: 2
220
22

2380
238
11
11

119
119
Using Prime
Factorization
2  2  5 11
220
11


2380 2  2  5  7 17
119
At a company, 225 of the 1050 employees have
optional eye insurance coverage as part of their
benefits package. What fraction of the employees have
optional eye insurance coverage?
÷5
225
1050
45

210
÷5
9

42
÷3
3

14
225
3355
3


1050 2  3  5  5  7 14
Answer 3 out of 14 employees have optional eye
insurance.