Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.4 Adding and Subtracting...
17
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.4 Adding and Subtracting Mixed Numbers
-
Upload
derick-johnathan-riley -
Category
Documents
-
view
214 -
download
0
Transcript of Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 3.4 Adding and Subtracting...
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
3.4
Adding and Subtracting Mixed Numbers
Martin-Gay, Basic Mathematics, 4e 22
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Adding Mixed Numbers
Recall that a mixed number has a whole number part and a fraction part.
Adding or Subtracting Mixed NumbersTo add or subtract mixed numbers, add or subtract the fraction parts and then add or subtract the whole number parts.
1 13 3
4 4
P 204
Martin-Gay, Basic Mathematics, 4ed 33
Adding Mixed Numbers
EXAMPLE
SOLUTION
Add:
6
14
12
512
The LCD of 6 and 12 is 12.
6
14
12
512
2
21
1
12
24
12
512
Add the fractions.
Then add the whole numbers.12
716
P 204
Martin-Gay, Basic Mathematics, 4e 44
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example 1
Add:
mixed fractions improper rather than mixed
1 32 5
3 8
1 8 2 2
3 243 9
5
8
8
543 2
3
8
177
24
24
56
8
8
3
7
3
7
3
12
24
129
3
3
8
43
8
43
8
35
24
185
24
129
24
56
177
24
P 204
LCM = 24 for both
Martin-Gay, Basic Mathematics, 4e 55
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example 2
Add: 4 4
3 15 15
4 12 3 3
5 154 4
1 115 15
164
15
16 11
15 15
16 1 14 4 1 5
15 15 15
P 205
LCM = 15
Martin-Gay, Basic Mathematics, 4ed 66
Adding Mixed Numbers
Practice Problem 1
SOLUTION
Add:
6
15
5
24
The LCD of 6 and 5 is 30.
6
15
5
24
5
56
6
30
55
30
124
Add the fractions.
Then add the whole numbers.30
179
P 204
Martin-Gay, Basic Mathematics, 4e 77
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Step Example
Step 1: Write the prime factorization of each number.
Step 2:
Step 3:
Prime factorization for 5: 5Prime factorization for 6: 2, 3
325 LCM 30
P 205
Practice Problem 1
5 2, 3
6
15
5
24 Add
5
5
6
31
6
6
5
22
30
155
30
132
30
155132
30
179or
30
287
Adding Mixed Numbers – using improper fraction
6
31
5
22 Add
Martin-Gay, Basic Mathematics, 4ed 88
Adding Mixed Numbers
Practice Problem 2
SOLUTION
Add:
7
65
14
52
The LCD of 7 and 14 is 14.
7
65
14
52
2
21
1
14
125
14
52
Add the fractions.
Then add the whole numbers.14
177
14
38 isAnswer
P 205
Martin-Gay, Basic Mathematics, 4e 99
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example 4
Subtract: 3 2
9 57 21
3 9 9 9
7 212 2
5 521 21
7 14 4
21 3
P 206
Martin-Gay, Basic Mathematics, 4ed 1010
Subtracting Mixed Numbers
Practice Problem 4
SOLUTION
Subtract:
18
513
9
729
The LCD of 9 and 18 is 18.
1
12
2
18
513
18
1429
Subtract the fractions.
Then subtract the whole numbers.18
918
513
9
729
16
P 2062
116 isAnswer
Martin-Gay, Basic Mathematics, 4e 1111
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example 5
Subtract: 3 6
7 314 7
3 3 7 7
14 146 12
3 37 14
3 3 177 6 1 6
14 14 14
Need to borrow since you cannot subtract 3 – 12.
3 17 7 6
14 146 12
3 37 14
53
14
Martin-Gay, Basic Mathematics, 4ed 1212
Subtracting Mixed Numbers
Practice Problem 5
SOLUTION
Subtract:
5
35
15
79
The LCD of 5 and 15 is 15.
3
31
1
15
95
15
79
Subtract the fractions.
Then subtract the whole numbers.15
135
35
15
79
Because 7 is less than 9, we need to borrow 1 from 9.
3
P 20615
133 isAnswer
228
Martin-Gay, Basic Mathematics, 4e 1313
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Two packages of ground round are purchased. One package weight 2 3/8 pounds and the other 1 4/5 pounds. What is the combined weight of the ground round?
3 4Total Weight = 2 1
8 5
3 15 2 2
8 404 32
1 15 40
47 3
40
74
40
Martin-Gay, Basic Mathematics, 4e 1414
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
DONE
Martin-Gay, Basic Mathematics, 4e 1515
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Step Example
Step 1: Write the prime factorization of each number.
Step 2:
Step 3:
Prime factorization for 7: 7Prime factorization for 14: 2, 7
72 LCM 14
P 205
Practice Problem 27
65
14
52 Add
2
2
7
41
14
33
14
82
14
33
14
8233
14
38or
14
115
Adding Mixed Numbers
7
41
14
33 Add
Martin-Gay, Basic Mathematics, 4e 1616
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Step Example
Step 1: Write the prime factorization of each number.
Step 2:
Step 3:
Prime factorization for 9: 3, 3Prime factorization for 18: 2, 3, 3
332 LCM 18
P 206
Practice Problem 4
3, 3 2
18
513
9
729Subtract
18
239
2
2
9
268
18
239
18
536
18
239536
2
116
18
916or
18
297
Subtracting Mixed Numbers
18
234
9
268
Martin-Gay, Basic Mathematics, 4e 1717
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Step Example
Step 1: Write the prime factorization of each number.
Step 2:
Step 3:
Prime factorization for 5: 5Prime factorization for 15: 3, 5
53 LCM 15
P 206
Practice Problem 5
5 3
5
35
15
79Subtract
3
3
5
28
15
142
15
84
15
142
15
84142
15
133or
15
58
Subtracting Mixed Numbers
5
28
15
142
