#2083 GLA
Guided Learning Activity
This packet contains background
information for GLA 2083a, 2083b, etc. It
is intended for student and tutor use as
needed.
Adding Mixed Numerals
Author: Dennis Morrow
∑ SIGMA-MAC
College of the Canyons Mathematics Supplement
Addition with Mixed Numerals
Addition:
Adding mixed numerals is a matter of organizing them so that their fractional parts are
together and their whole number parts are together.
1
1
1
4
3
4
3 +4 = 3+
+ 4+
1
3
= 3+4 +
=7+
7
12
=7
7
1
4
+
1
3
=7+
3
12
+
4
12
12
The most convenient method of organizing the mixed numerals for addition is to align
them vertically, writing the fractions adjusted to their common denominator to the right.
3
+4
7
1
3
4 12
1 4
3 12
7
12
This is simple enough, but all answers must be in simple form. Simple form means the
fraction in the mixed numeral must be proper and reduced.
3
+4
7
The fraction
17
12
3
9
4 12
2 8
3 12
17
12
=7+1
5
12
=8
5
12
was not proper, so it was converted to a simple mixed numeral, and
5
then its whole number part was combined with the other whole number. 8 12 is a
17
simplified version of 7 12 , and it is the final answer.
Examples of Addition:
3
2
4
5
13 + 4
13
+4
17
5 20
23
20
3
3
5
31
+15
= 17 + 1
5 15
19
15
6 24
41
24
1
9
18
+85
= 31 + 1
4
3
6
3
8 24
5 20
1
24
5
44
39
20
3 15
3 9
2
+6
20
= 18
3
2 10
3
25
3
7 21
24 + 85
13 + 25 + 6
13
6
24
4 20
2 8
2
+6
5
8
3 15
25 + 6
25
7
24 + 15
4
15
= 32
4
15
18
1
18 18
3
18
7
13
8
9
18
24
3 12
5 10
+85
= 44 + 2
= 109
7
24
4 12
2 8
12
2
9
1
24 + 24 + 85
9
6 12
27
109
1
= 39 + 1
3
12
= 46
1
4
133
17
24
= 40
17
24
1
6
7 63
8 72
7 56
9 72
13 52
18 72
171
72
= 133 + 2
27
72
= 135
3
8
#2083a GLA
Student:____________________________
Guided Learning Activity
Course Instructor:___________________
Adding Mixed Numerals, Exercise
Date Completed:___________________
Set #1
Approved:_________________________
Author: Dennis Morrow
∑ SIGMA-MAC
Addition with Mixed Numerals, Exercise Set #1
Addition:
Adding mixed numerals is a matter of organizing them so that their fractional parts are
together and their whole number parts are together.
1
1
1
4
3
4
3 +4 = 3+
+ 4+
1
3
= 3+4 +
=7+
7
12
=7
7
1
4
+
1
3
=7+
3
12
+
4
12
12
The most convenient method of organizing the mixed numerals for addition is to align
them vertically, writing the fractions adjusted to their common denominator to the right.
3
+4
7
1
3
4 12
1 4
3 12
7
12
This is simple enough, but all answers must be in simple form. Simple form means the
fraction in the mixed numeral must be proper and reduced.
3
+4
7
The fraction
17
12
3
9
4 12
2 8
3 12
17
12
=7+1
5
12
=8
5
12
was not proper, so it was converted to a simple mixed numeral, and
5
then its whole number part was combined with the other whole number. 8 12 is a
17
simplified version of 7 12 , and it is the final answer.
Exercises:
1.
8
7
9
8
36 + 25
The LCD = 72. 72/9=8, 72/8=9. Fill in the blanks.
36
+25
8
9 72
7
8 72
____
2.
25
19
24
62
72
+8
15
16
= ____ + ____
+ 11
72
= ____
72
55
72
Ans: ___________
25
48
The LCD = 48. 48/24=2, 48/16=3, and 48/48=1. Fill in the blanks.
25
8
+ 11
19
24 48
15
16 48
25
46
48 48
____
48
= ____ + ____
48
= 46
12
48
1
4
Ans: ___________
Simplify the following completely. Execute the problems using mixed numerals,
and write the answers as mixed numerals.
3.
48
31
48
+ 31
7
16
LCD=________
Ans:_______
4.
2
5
3
6
42 + 21
LCD=________
Ans:_______
80
1
12
, 64
1
2
5.
7
11
9
36
53 + 23
LCD=________
Ans:_______
6.
73
11
24
+ 25
11
12
LCD=________
Ans:_______
7.
5
8
6
27
65 + 17
LCD=________
Ans:_______
8.
35
20
21
+ 21
5
7
LCD=________
Ans:_______
77
1
12
3
7
8
54
, 99 , 83
, 57
2
3
9.
7
7
9
45
21 + 31
+ 48
7
LCD=________
25
Ans:_______
7
7
9
16
10. 24 + 31
+ 43
7
LCD=________
48
Ans:_______
3
3
22
4
5
25
11. 1 + 2 + 1
+3
1
50
LCD=________
Ans:_______
12. 1
5
12
1
7
5
15
+1 +1
+1
5
48
LCD=________
Ans:_______
101
16
75
, 99
13
36
1
3
4
16
,9 ,5
#2083b GLA
Student:____________________________
Guided Learning Activity
Course Instructor:___________________
Adding Mixed Numerals, Exercise
Date Completed:___________________
Set #2
Approved:_________________________
Author: Dennis Morrow
∑ SIGMA-MAC
Addition with Mixed Numerals, Exercise Set #2
Addition:
Adding mixed numerals is a matter of organizing them so that their fractional parts are
together and their whole number parts are together.
1
1
1
4
3
4
3 +4 = 3+
+ 4+
1
3
= 3+4 +
=7+
7
12
=7
7
1
4
+
1
3
=7+
3
12
+
4
12
12
The most convenient method of organizing the mixed numerals for addition is to align
them vertically, writing the fractions adjusted to their common denominator to the right.
3
+4
7
1
3
4 12
1 4
3 12
7
12
This is simple enough, but all answers must be in simple form. Simple form means the
fraction in the mixed numeral must be proper and reduced.
3
+4
7
The fraction
17
12
3
9
4 12
2 8
3 12
17
12
=7+1
5
12
=8
5
12
was not proper, so it was converted to a simple mixed numeral, and
5
then its whole number part was combined with the other whole number. 8 12 is a
17
simplified version of 7 12 , and it is the final answer.
Exercises:
1.
7
5
9
8
37 + 28
The LCD = 72. 72/9=8, 72/8=9. Fill in the blanks.
37
+28
7
9 72
5
8 72
____
2.
35
22
25
66
72
+ 18
11
15
= ____ + ____
+ 11
72
= ____
72
29
72
Ans: ___________
11
75
The LCD = 75. 75/25=3, 75/15=5, and 75/75=1. Fill in the blanks.
35
18
+ 11
22
25 75
11
15 75
11
65
75 75
____
75
= ____ + ____
75
= 65
57
75
19
25
Ans: ___________
Simplify the following completely. Execute the problems using mixed numerals,
and write the answers as mixed numerals.
3.
5
7
6
24
84 + 31
LCD=________
Ans:_______
4.
2
8
3
15
41 + 26
LCD=________
Ans:_______
1
1
8
5
116 , 68
5.
73
25
27
+ 23
11
LCD=________
18
Ans:_______
6.
4
6
32
5
7
35
73 + 25 + 15
LCD=________
Ans:_______
7.
3
1
7
4
6
12
75 + 21 + 15
LCD=________
Ans:_______
8.
35
20
21
5
29
7
42
+ 21 + 12
LCD=________
Ans:_______
97
29
54
4
1
5
7
2
14
, 115 , 112 , 70
9.
8
2
25
9
3
36
22 + 41 + 57
LCD=________
Ans:_______
2
2
3
15
10. 34 + 21
+ 23
3
LCD=________
4
Ans:_______
1
2
1
2
5
10
11. 1 + 2 + 1
+2
6
7
LCD=________
Ans:_______
1
5
8
3
6
15
12. 1 + + 3
+1
2
7
LCD=________
Ans:_______
1
11
4
20
122 , 79
6
69
7
70
,7 ,6
#2083c GLA
Student:____________________________
Guided Learning Activity
Course Instructor:___________________
Adding Mixed Numerals, Exercise
Date Completed:___________________
Set #3
Approved:_________________________
Author: Dennis Morrow
∑ SIGMA-MAC
Addition with Mixed Numerals, Exercise Set #3
Addition:
Adding mixed numerals is a matter of organizing them so that their fractional parts are
together and their whole number parts are together.
1
1
1
4
3
4
3 +4 = 3+
+ 4+
1
3
= 3+4 +
=7+
7
12
=7
7
1
4
+
1
3
=7+
3
12
+
4
12
12
The most convenient method of organizing the mixed numerals for addition is to align
them vertically, writing the fractions adjusted to their common denominator to the right.
3
+4
7
1
3
4 12
1 4
3 12
7
12
This is simple enough, but all answers must be in simple form. Simple form means the
fraction in the mixed numeral must be proper and reduced.
3
+4
7
The fraction
17
12
3
9
4 12
2 8
3 12
17
12
=7+1
5
12
=8
5
12
was not proper, so it was converted to a simple mixed numeral, and
5
then its whole number part was combined with the other whole number. 8 12 is a
17
simplified version of 7 12 , and it is the final answer.
Exercises:
1.
4
7
9
8
25 + 17
The LCD = 72. 72/9=8, 72/8=9. Fill in the blanks.
25
+17
4
9 72
7
8 72
____
2.
43
72
5
15
6
16
37 + 18
= ____ + ____
+ 12
72
= ____
72
23
72
Ans: ___________
2
3
The LCD = 48. 48/6=8, 48/16=3, and 48/3=16. Fill in the blanks.
35
18
+ 11
22
25 48
11
15 48
11
69
75 48
____
48
= ____ + ____
48
= 69
48
7
16
Ans: ___________
Simplify the following completely. Execute the problems using mixed numerals,
and write the answers as mixed numerals.
3.
2
17
3
24
84 + 34
LCD=________
Ans:_______
4.
2
10
3
21
45 + 36
LCD=________
Ans:_______
3
1
8
7
119 , 82
5.
93
23
24
+ 23
13
LCD=________
15
Ans:_______
6.
3
7
11
4
8
12
72 + 27 + 18
LCD=________
Ans:_______
7.
58
13
15
3
17
5
25
+ 23 + 15
LCD=________
Ans:_______
8.
47
19
36
+ 35
1
18
+ 21
13
LCD=________
24
Ans:_______
117
33
40
, 119
13
24
, 98
11
75
, 104
1
8
9.
3
22
4
25
47 + 78
+ 64
9
20
LCD=________
Ans:_______
6
1
5
7
4
12
10. 36 + 67 + 45
LCD=________
Ans:_______
11. 1
5
14
1
5
40
2
7
49
+1 +2 +1
LCD=________
Ans:_______
8
4
13
9
5
15
12. 2 + 1 +
+2
2
3
LCD=________
Ans:_______
191
2
25
, 149
11
21
,7
19
49
,8
2
9