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the sum or difference after computing the LCD.
PRACTICE
Find the sum or difference after computing the LCD.
SOLUTION✔

Chapter 1 FraCtions 19
DeMYstiFieD / algebra DeMYstiFieD / Gibilisco / 000-0 / Chapter 1
SOLUTIONS
1. 11
12 5
18 11
12 3
3 5
18 2
2 33
36 10
36 2
−= ⋅


 


−⋅ 

 


=−
=33
36
2. 7
15 9
20 7
15 4
4 9
20 3
3 28
60 27
60 55
6
+=
⋅


 


+⋅ 

 


=+
=
0011
12
=
3. 23
24 7
16 23
24 2
2 7
16 3
3 46
4821
48 6
+= ⋅


 


+⋅ 

 


=+
=77
48
4. 3
8 7
20 3
8 5
5 7
20 2
2 15
40 14
40 29
40
+=
⋅


 


+⋅ 

 


=+
=
5. 1
6 4
15 1
6 5
5 4
15 2
2 5
30 8
30 13
30
+=
⋅


 


+⋅ 

 


=+
=
6. 8
75 3
10 8
75 2
2 3
10 15
15 16
150 45
150
+=
⋅


 


+⋅ 

 


=+== 61
150
7. 35
54 7
48 35
54 8
8 7
48 9
9 280
432 63
43
−=
⋅


 


−⋅ 

 


=−
22 217
432
=
8. 15
88 3
28 15
88 7
7 3
28 22
22 105
616 66
+= ⋅


 


+⋅ 

 


=+
6
616 171
616
=
9. 119
180 17
210 119
1807
7 17
210 6
6 833
+= ⋅


 


+⋅ 

 


=
1
1260 102
1260 935
1260 187
252
+=
=
Adding More than Two Fractions
Finding the LCD for three or more fractions is pretty much the same as finding
the LCD for two fractions. One way to approach the problem is to work with
two fractions at a time. For instance, in the sum
5
6 3
4 1
10
++
, we can begin with
5
6 and 3
4. The LCD for these fractions is 12.
5
6 5
6 2
2 10
12
=⋅
= and 3
4 3
4 3
3 9
12
=⋅
=
The sum 5
6 3
4 1
10
++ can be condensed to the sum of two fractions.
5
6 3
4 1
10 5
6 3
4 1
10 10
12 9
12 1
10 19
++ =+

 


+=
+


 


+=
1
12 1
10
+
SOLUTIONS✔

20 alGebra D e myst i fieD DeMYstiFieD / algebra DeMYstiFieD / Gibilisco / 000-0 / Chapter 1
We can now work with 19
12 1
10
+. The LCD for these fractions is 60.
19
12 1
10 19
12 5
5 1
10 6
695
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
60288
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
⋅


 


+⋅ 

 


+⋅ 

 


=
1
180 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.

Chapter 1 FraCtions 21
DeMYstiFieD / algebra DeMYstiFieD / Gibilisco / 000-0 / Chapter 1
PRACTICE
Find the sum.
1.
5
36 4
97
12
++
=
2. 11
24 3
10 1
8
++
=
3. 1
4 5
6 9
20
++
=
4. 3
35 9
14 7
10
++
=
5. 5
48 3
16 1
6 7
9
++
+=
SOLUTIONS
1. 5
36 4
97
12 5
36 4
94
4 7
12 3
3 5
36 16
3
++
=+ ⋅


 


+⋅ 

 


=+
66 21
36 42
36 7
6
+=
=
2. 11
24 3
10 1
8 11
24 5
5 3
10 12
12 1
8 15
1
++
=⋅

 


+⋅ 

 


+⋅
55 55
120 36
120 15
120 106
120 53
60






=+
+==
3. 1
4 5
6 9
20 1
4 15
15 5
610
10 9
20 3
3
++
=⋅

 


+⋅ 

 


+⋅ 




=+
+= =
15
60 50
60 27
60 92
60 23
15
4. 3
35 9
14 7
10 3
35 2
2 9
14 5
5 7
10 7
7
++
=⋅

 


+⋅ 

 


+⋅ 




=+
+= =
6
70 45
70 49
70 100
70 10
7
5. 5
48 3
16 1
6 7
9 5
48 3
3 3
16 9
9 1
6 24
24
++
+= ⋅


 


+⋅ 
