Success Tip In Example 6, did you notice that the denominator 5 is a factor of
the denominator 15, and that the LCD is 15. In general, when adding (or
subtracting) two fractions with different denominators,if the smaller denominator
is a factor of the larger denominator, the larger denominator is the LCD.Caution! You might not have to build each fraction when adding or
subtracting fractions with different denominators. For instance, the step in blue
shown below is unnecessary when solving Example 6.
2
511
15
2
5
3
3
11
15
1
1
246 Chapter 3 Fractions and Mixed Numbers
WHY To add (or subtract) fractions, the fractions must have likedenominators.
Solution
Since the smallest number the denominators 2 and 3 divide exactly is 6, the LCD is 6.1 1
To build and so that their denominators are 6,
multiply each by a form of 1. This fraction is in simplest form.1
6
Subtract the numerators and write the difference(^) over the common denominator 6.
15 14
6
Multiply the numerators. Multiply the denominators.(^) The denominators are now the same.
15
6
14
6
7
35
^72
32
2
5
2
7
3
5
2
3
3
Self Check 6Subtract:Now TryProblem 412
3
13
6
EXAMPLE 6
Subtract:
Strategy Since the smallest number the denominators 5 and 15 divide exactly is
15, the LCD is 15. We will only need to build an equivalent fraction for
WHY We do not have to build the fraction because it already has a denominator
of 15.
SolutionTo build so that its denominator is 15, multiply it by a form of 1.Multiply the remaining factors in the(^) denominator: 3 1 3.
1
3
To simplify, factor 15 as 35. Then remove the common(^) factor of 5 from the numerator and denominator.
5
13 5
1If it is helpful, use the subtraction rule and add the
opposite in the numerator: 6 (11) 5.
Write the sign in front of the fraction.5
15
Subtract the numerators and write the difference
over the common denominator 15.6 11
15
Multiply the numerators. Multiply the denominators.
The denominators are now the same.6
15
11
15
2
52
5
11
15
2
5
3
3
11
15
11
152
5.