20 alGebra De mystif ieD

We can now work with^1912 + 101. The LCD for these fractions is 60.

19

12

1

10

19

12

5

5

1

10

6

6

95

60

6

60

101

60

+=⋅+ ⋅= +=

To work with all three fractions at the same time, factor each denominator into

its prime factors and list the primes that appear in each. As before, the LCD

includes any prime number that appears in a denominator. If a prime number

appears in more than one denominator, the highest power is a factor in the LCD.

EXAMPLE

Find the sum.

4

5

7

15

9

20

++

SOLUTION

Prime factorization of the denominators:

5 = 5

15 = 3 ⋅ 5

20 = 2 ⋅ 2 ⋅ 5

The LCD = 2 ⋅ 2 ⋅ 3 ⋅ 5 = 60

4

5

7

15

9

20

++ =⋅









+⋅







+⋅







(^4) =+
5
12
12
7
15
4
4
9
20
3
3
48
60
288
60
27
60
103
60
+=
EXAMPLE
Find the sum.
3
10
5
12
1
18
++
SOLUTION
Prime factorization of the denominators:
10 = 2 ⋅ 5
12 = 2 ⋅ 2 ⋅ 3
18 = 2 ⋅ 3 ⋅ 3
LCD = 2⋅ 2 ⋅ 3 ⋅ 3 ⋅5 = 180
3
10
5
12
1
18
++=^3
10
18
18
5
12
15
15
1
18
10
10
 ⋅ 54



+⋅



+⋅




1180
75
180
10
180
139
180
++=
SOLUTION
Prime factorization of the denominators:
✔
SOLUTION
Prime factorization of the denominators:
✔
EXAMPLE
Find the sum.
EXAMPLE
Find the sum.