Fundamentals of Mathematics, 2008a

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CHAPTER 5. ADDITION AND SUBTRACTION OF FRACTIONS,
COMPARING FRACTIONS, AND COMPLEX FRACTIONS
12 ÷ 6 = 2
12 ÷ 4 = 3
1
6 + 3 4
= 1·2
12 + 3·3
12
2
=
12 + 9
12
Now the denominators are the same.
2+9
=
12
Add the numerators and place the sum over the common denominator.
11
=
12
Example 5.11
. The denominators are not the same. Find the LCD of 2 and 3.
1
2 + 2 3
LCD = 2 · 3 = 6
Write each of the original fractions as a new, equivalent fraction having the common denominator
6.
1
2 + 2 3 = 6 + 6
To nd a new numerator, we divide the original denominator into the LCD. Since the original
denominator is being multiplied by this quotient, we must multiply the original numerator by this
quotient.
6 ÷ 2 = 3 Multiply the numerator 1 by 3.
6 ÷ 2 = 3 Multiply the numerator 2 by 2.
1
2 + 2 3
= 1·3
6 + 2·3
6
3
=
6 + 4 6
3+4
=
6
= 7 6 or 1 1 6
Example 5.12
. The denominators are not the same. Find the LCD of 9 and 12.
5
9 − 5 12
9 = 3 · 3 = 3 2
12 = 2 · 6 = 2 · 2 · 3 = 2 2 · 3 } LCD = 22 · 3 2 = 4 · 9 = 36
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