copyright © 2011 pearson education, inc. fractions 1.2 1.write equivalent fractions. 2.write...
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Copyright © 2011 Pearson Education, Inc.
Fractions1.21.2
1. Write equivalent fractions.2. Write equivalent fractions with the LCD.3. Write the prime factorization of a number.4. Simplify a fraction to lowest terms.
Prime factorization:
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,…
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.
10202 20102202
Divide by prime numbers!
2, 3, 5, 7, 11, …
Find the prime factorization of 20.
20
54
522
Factor Tree Factor Tower
5102202
Find the prime factorization of 60.
60
106
5232
Factor Tree Factor Tower
5322
30602
15302602
5153302602 60
Find the prime factorization of 48.
48
86
4232
Factor Tree Factor Tower
32222
22232 24482
12242482
6122242482 48
362
122242482
Find the LCD.
103
and 65
6, 12, 18, 24, 30, 36, 42, 48, 54, 606:
10, 20, 30, 40, 50, 6010:
LCD = 30
Using Multiples
Use when numbers are small.
Write the fractions as equivalent fractions with the LCD.
127
85
and
LCD: 24
127
85
and
2485
24127 24
1585
2414
127
∙3∙2
Write the fractions as equivalent fractions with the LCD.
LCD: 2∙2∙2∙2∙3∙3
367
165 and
144165
144367 144
45165
14428
367
2∙2∙2∙2 2∙2∙3∙3
∙9 ∙4
= 144
367
165
and
Suggestion:
Reduce Fractions.Using Prime Factorization
129 33
32233
43
129
Using Greatest Common Factor GCF: 3
3
443
30
42
Reduce Fractions.
Using Prime Factorization
Using Greatest Common Factor
30
42
2 3 5
2 3 7
5
7
5
7
5
7
GCF: 6
220
2380
2 2 5 11
2 2 5 7 17
11
119
Reduce Fractions.
Using Prime Factorization
Using Greatest Common Factor
GCF: Common Factor: 10
11
119
2380220
23822
Common Factor: 2
11911
?
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?
Answer 3 out of 14 employees have optional eye insurance.
225
1050
÷ 5
21045
÷ 5
429
÷ 3
143
225
1050
3 3 5 5
2 3 5 5 7
3
14