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1: 2: 3: 4: 5: 600 1280 68 578 168 216 72 120 768 288
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CHAPTER 1 Fractions
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1: 2: 3: 4: 5: 600 10 60 60 4 15 15 1280 10 128 128 4 32 32 68 2 34 34 17 2 2 578 2 289 289 17 17 17 168 6 28 28 4 7 7 216 6 36 36 4 9 9 72 12 6 6 2 3 3 120 12 10 10 2 5 5
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768 4 192 192 2 96 96 4 24 24 3 8 8 288 4 72 72 2 36 36 4 9 9 3 3 3 For the rest of the book, reduce fractions to their lowest terms
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Adding and Subtracting Fractions
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When adding (or subtracting) fractions with the same denominators, add (or subtract) their numerators
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CHAPTER 1 Fractions
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7 2 7 2 5 9 9 9 9 8 2 8 2 10 5 2 2 15 15 15 15 5 3 3
Practice
1: 2: 3: 4: 5: 4 1 7 7 1 3 5 5 1 1 6 6 5 1 12 12 2 9 11 11
Solutions
1: 2: 3: 4: 5: 4 1 4 1 3 7 7 7 7 1 3 1 3 4 5 5 5 5 1 1 1 1 2 1 6 6 6 6 3 5 1 5 1 4 1 12 12 12 12 3 2 9 2 9 11 1 11 11 11 11
CHAPTER 1 Fractions
When the denominators are not the same, you have to rewrite the fractions so that they do have the same denominator There are two common methods of doing this The rst is the easiest The second takes more e ort but can result in smaller quantities and less reducing (When the denominators have no common divisors, these two methods are the same) The easiest way to get a common denominator is to multiply the rst fraction by the second denominator over itself and the second fraction by the rst denominator over itself
Examples
In 1 3 the rst denominator is 2 and the second denominator is 7 2 7 Multiply 1 by 7 and multiply 3 by 2 : 2 7 7 2     1 3 1 7 3 2 7 6 13 2 7 2 7 7 2 14 14 14     8 1 8 2 1 15 16 15 1 15 2 15 2 2 15 30 30 30
Practice
1: 2: 3: 4: 5: 5 1 6 5 1 7 3 8 5 1 7 9 3 1 14 2 3 11 4 18
Solutions
1:     5 1 5 5 1 6 25 6 19 6 5 6 5 5 6 30 30 30
CHAPTER 1 Fractions
    1 7 1 8 7 3 8 21 29 3 8 3 8 8 3 24 24 24     5 1 5 9 1 7 45 7 38 3: 7 9 7 9 9 7 63 63 63     3 1 3 2 1 14 6 14 20 5 4: 14 2 14 2 2 14 28 28 28 7     3 11 3 18 11 4 54 44 98 49 5: 4 18 4 18 18 4 72 72 72 36 2: Our goal is to add/subtract two fractions with the same denominator In the previous examples and practice problems, we found a common denominator Now we will nd the least common denominator (LCD) For example in 1 1 3 6, we could compute     1 1 1 6 1 3 6 3 9 1 : 3 6 3 6 6 3 18 18 18 2 But we really only need to rewrite 1: 3   1 1 1 2 1 2 1 3 1 : 3 6 3 2 6 6 6 6 2 While 18 is a common denominator in the above example, 6 is the smallest common denominator When denominators get more complicated, either by being large or having variables in them, you will nd it easier to use the LCD to add or subtract fractions The solution might require less reducing, too In the following practice problems one of the denominators will be the LCD; you only need to rewrite the other
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