#2084 GLA
Guided Learning Activity
This packet contains background
information for GLA 2084a, 2084b, etc. It
is intended for student and tutor use as
needed.
Subtracting Mixed Numerals
Author: Dennis Morrow
∑ SIGMA-MAC
College of the Canyons Mathematics Supplement
Subtraction with Mixed Numerals
Subtraction:
Subtraction is organized similarly to addition. The fractions are aligned, and the whole
numbers are aligned. However, both parts of the bottom number are subtracted from
the top number.
6
−4
2
1
4
3 12
1 3
4 12
1
12
=2
1
12
The tricky part of subtraction comes in the borrowing. If the bottom fraction is bigger
than the top fraction one unit must be borrowed from the top’s whole number, but that
one unit is not ten of the fraction’s pieces unless the fraction’s denominator is ten.
6
−4
This time we must subtract
4
12
from
12
3
12
1
3
4 12
1 4
3 12
. We cannot subtract 4 from 3, so we borrow a
3
3
unit from the 6. The 6 becomes 5 12 . Now the 6 12 , also known as 6 + 12 , becomes
12
3
15
5 12 + 12 or 5 12 , and the problem becomes:
5
−4
1
15
12
4
12
11
12
Done from the beginning without the explanations it would look like:
5
1
6
−4
15
3
4
1
12
4
3
12
11
1
12
Examples of Subtraction:
6
−4
1
3
4
2
12
8
3
12
5
6
−4
1
16
−9
3
15
4 20
4 16
5
20
15
16
−9
6
15
3
15
12
8
−5
12
7
2
6
5 15
2 10
3
15
14
15
−5
9
12
35
15
25
20
16
−15
20
19
10
20
4
12
5
2
15
2
15
15
10
15
21
6
15
10
15
11
15
= 10
2
3
For the purpose of instruction the first three of those examples were made to look
longer than necessary. This is how they would appear if they were done without the
need to be instructive:
5
1
6
−4
1
15
3
4
2
12
8
3
12
7
12
14
2
15
−5
9
21
6
5
2
15
10
3
15
11
15
15
3
16
−9
6
35
15
4
4
20
16
5
20
19
20
#2084a GLA
Student:____________________________
Guided Learning Activity
Course Instructor:___________________
Subtracting Mixed Numerals,
Exercise Set #1
Date Completed:___________________
Approved:_________________________
Author: Dennis Morrow
∑ SIGMA-MAC
Subtraction with Mixed Numerals, Exercise Set #1
Subtraction:
Subtraction is organized similarly to addition. The fractions are aligned, and the whole
numbers are aligned. However, both parts of the bottom number are subtracted from
the top number.
6
−4
2
1
4
3 12
1 3
4 12
1
12
=2
1
12
The tricky part of subtraction comes in the borrowing. If the bottom fraction is bigger
than the top fraction one unit must be borrowed from the top’s whole number, but that
one unit is not ten of the fraction’s pieces unless the fraction’s denominator is ten.
6
−4
This time we must subtract
4
12
from
12
3
12
1
3
4 12
1 4
3 12
. We cannot subtract 4 from 3, so we borrow a
3
3
unit from the 6. The 6 becomes 5 12 . Now the 6 12 , also known as 6 + 12 , becomes
12
3
15
5 12 + 12 or 5 12 , and the problem becomes:
5
15
−4
4
1
12
12
11
12
And without explanation it looks like:
5
1
6
−4
1
15
3
4
1
12
4
3
12
11
12
Exercises:
1.
5
7
9
8
36 − 25
The LCD = 72. 72/9=8, 72/8=9. Fill in the blanks.
________
36
−25
______
5
9 72
7
8 72
____
2.
25
13
24
10
−8
49
72
Ans: ___________
72
47
48
The LCD = 48. 48/24=2 and 48/48=1. Fill in the blanks.
________
25
−8
______
13
24 48
47
16
48 48
____
48
= __________
9
16
Ans: ___________
Simplify the following completely. Execute the problems using mixed numerals,
and write the answers as mixed numerals.
3.
48
31
48
− 31
13
16
LCD=________
Ans:_______
4.
1
2
6
3
42 − 21
LCD=________
Ans:_______
5
1
6
2
16 , 20
5.
2
11
9
36
53 − 23
LCD=________
Ans:_______
6.
73
1
24
− 25
11
12
LCD=________
Ans:_______
7.
1
13
6
18
65 − 17
LCD=________
Ans:_______
8.
35
1
21
− 21
5
7
LCD=________
Ans:_______
29
11
12
1
4
1
8
9
3
, 47 , 47 , 13
9.
1
4
6
15
51 − 31
LCD=________
Ans:_______
10. 81
7
16
− 43
25
48
LCD=________
Ans:_______
11. 18
1
108
− 12
5
54
LCD=________
Ans:_______
12. 102
1
48
− 81
2
15
LCD=________
Ans:_______
19
9
10
, 37
11
12
,5
11
12
, 20
71
80
#2084b GLA
Student:____________________________
Guided Learning Activity
Course Instructor:___________________
Subtracting Mixed Numerals,
Exercise Set #2
Date Completed:___________________
Approved:_________________________
Author: Dennis Morrow
∑ SIGMA-MAC
Subtraction with Mixed Numerals, Exercise Set #2
Subtraction:
Subtraction is organized similarly to addition. The fractions are aligned, and the whole
numbers are aligned. However, both parts of the bottom number are subtracted from
1
1
the top number. 6 3 − 4 4 is done as follows:
6
−4
2
1
4
3 12
1 3
4 12
1
12
=2
1
12
The tricky part of subtraction comes in the borrowing. If the bottom fraction is bigger
than the top fraction one unit must be borrowed from the top’s whole number, but that
one unit is not ten of the fraction’s pieces unless the fraction’s denominator is ten.
6
−4
This time we must subtract
4
12
from
unit from the 6. The 6 becomes 5
12
3
15
12
12
3
12
1
3
4 12
1 4
3 12
. We cannot subtract 4 from 3, so we borrow a
. Now the 6
3
12
, also known as 6 +
3
12
, becomes
5 12 + 12 or 5 12 , and the problem becomes:
5
15
−4
4
1
12
12
11
12
And without explanation it looks like:
5
1
6
−4
1
15
3
4
1
12
4
3
12
11
12
Exercises:
1.
4
5
9
8
47 − 35
The LCD = 72. 72/9=8, 72/8=9. Fill in the blanks.
________
47
−35
______
4
9 72
5
8 72
____
2.
29
19
24
11
−8
59
72
Ans: ___________
72
47
48
The LCD = 48. 48/24=2 and 48/48=1. Fill in the blanks.
________
29
−8
______
19
24 48
47
____
20
48 48
48
= __________
13
16
Ans: ___________
Simplify the following completely. Execute the problems using mixed numerals,
and write the answers as mixed numerals.
3.
118
4
15
− 65
2
3
LCD=________
Ans:_______
4.
102
11
48
− 53
9
16
LCD=________
Ans:_______
3
2
5
3
52 , 48
5.
4
19
9
36
78 − 47
LCD=________
Ans:_______
6.
87
5
24
− 39
7
12
LCD=________
Ans:_______
7.
1
7
6
18
95 − 47
LCD=________
Ans:_______
8.
87
4
21
− 52
6
7
LCD=________
Ans:_______
30
11
12
5
7
1
8
9
3
, 47 , 47 , 34
9.
5
14
6
15
91 − 49
LCD=________
Ans:_______
10. 72
3
16
− 45
25
48
LCD=________
Ans:_______
11. 38
11
120
− 23
13
60
LCD=________
Ans:_______
12. 93
7
48
− 71
19
30
LCD=________
Ans:_______
41
9
10
2
7
41
3
8
80
, 26 , 14 , 21
#2084c GLA
Student:____________________________
Guided Learning Activity
Course Instructor:___________________
Subtracting Mixed Numerals,
Exercise Set #3
Date Completed:___________________
Approved:_________________________
Author: Dennis Morrow
∑ SIGMA-MAC
Subtraction with Mixed Numerals, Exercise Set #3
Subtraction:
Subtraction is organized similarly to addition. The fractions are aligned, and the whole
numbers are aligned. However, both parts of the bottom number are subtracted from
the top number.
6
−4
2
1
4
3 12
1 3
4 12
1
12
=2
1
12
The tricky part of subtraction comes in the borrowing. If the bottom fraction is bigger
than the top fraction one unit must be borrowed from the top’s whole number, but that
one unit is not ten of the fraction’s pieces unless the fraction’s denominator is ten.
6
−4
This time we must subtract
4
12
from
12
3
12
1
3
4 12
1 4
3 12
. We cannot subtract 4 from 3, so we borrow a
3
3
unit from the 6. The 6 becomes 5 12 . Now the 6 12 , also known as 6 + 12 , becomes
12
3
15
5 12 + 12 or 5 12 , and the problem becomes:
5
15
−4
4
1
12
12
11
12
And without explanation it looks like:
5
1
6
−4
1
15
3
4
1
12
4
3
12
11
12
Exercises:
1.
2
3
9
8
39 − 24
The LCD = 72. 72/9=8, 72/8=9. Fill in the blanks.
________
39
−24
______
2
9 72
3
8 72
____
2.
23
17
24
14
−8
61
72
Ans: ___________
72
43
48
The LCD = 48. 48/24=2 and 48/48=1. Fill in the blanks.
________
23
−8
______
17
24 48
43
14
48 48
____
48
= __________
13
16
Ans: ___________
Simplify the following completely. Execute the problems using mixed numerals,
and write the answers as mixed numerals.
3.
1
2
6
3
68 − 59
LCD=________
Ans:_______
4.
102
5
48
− 51
7
16
LCD=________
Ans:_______
1
2
2
3
8 , 50
5.
4
25
9
36
103 − 23
LCD=________
Ans:_______
6.
93
7
24
− 28
11
12
LCD=________
Ans:_______
7.
5
17
6
18
74 − 37
LCD=________
Ans:_______
8.
65
8
21
− 41
5
7
LCD=________
Ans:_______
3
3
8
2
4
8
9
3
79 , 64 , 36 , 23
9.
1
7
6
15
78 − 51
LCD=________
Ans:_______
10. 69
5
16
− 47
23
48
LCD=________
Ans:_______
11. 41
7
150
− 22
13
60
LCD=________
Ans:_______
12. 98
7
48
− 76
7
30
LCD=________
Ans:_______
26
7
10
5
83
6
100
, 21 , 18
, 21
73
80