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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
2.4
Multiplying Fractions and Mixed Numbers
Martin-Gay, Basic Mathematics, 4e 22
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Multiplying Fractions
Multiplying FractionsTo multiply two fractions, multiply the numerators and multiply the denominators.If a, b, c, and d represent positive whole numbers we have
a c a c
b d b d
P 141-142
Martin-Gay, Basic Mathematics, 4e 33
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Examples
Multiply.
a.
b.
c.
1 1
11 3
1 1
11 3
2 3
7 5
2 3
7 5
6
35
2 4
3 7
1
33
8
21
P 141-142
Martin-Gay, Basic Mathematics, 4e 44
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Examples
Multiply and simplify.
a.
b. 2 3 14
7 8 15
2 3 2 7
7 2 2 2 3 5
3 2 2 2
2 2 11
3 8
4 11
6
11
1
10
P 141-142
Martin-Gay, Basic Mathematics, 4e 55
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Practice Problems
Multiply and simplify.
1.
2.
3.
4.
P 141-142
78
53
56
15
7
5
8
3
6
1
3
1
63
11
18
1
8
5
55
6
855
56
440
30
8
3
15
4
120
12
1012
112
10
1
No common factors
No common Factors
Multiplying Fractions
4410
310
44
3
Martin-Gay, Basic Mathematics, 4e 66
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Practice Problems
Multiply and simplify.
5.
6.
7.
P 142
75
202
75
452
7
20
5
2
16
33
11
4
42211
31122
4
3
16
25
10
3
6
1
165232
5531
1622
5
Multiplying Fractions
64
5
7
42
7
8
Martin-Gay, Basic Mathematics, 4e 77
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Multiplying Fractions and Mixed Numbers or Whole Numbers
Multiplying Fractions and Mixed Numbers of Whole NumbersTo multiply with mixed numbers or whole numbers, first write any mixed or whole numbers as fractions and then multiply as usual.
P 143
Martin-Gay, Basic Mathematics, 4e 88
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Examples
Multiply.
a.
b. 2 3
59 8
2 43
9 8
8 7
3 8
2 72
3 8
7
3
2 2 2 7
3 2 2 2
1
or 23
2 43
3 3 2 2 2
43 7
136 36
P 143
Martin-Gay, Basic Mathematics, 4e 99
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Multiply.
7
108
5 2 7
1 2 2 2
35
4
3or 8
4
P 143
Martin-Gay, Basic Mathematics, 4e 1010
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Practice Problems
Multiply and simplify.
8.
9.
10.
11.
P 143-144
152
85
3
11or
3
4
15
8
2
12
183
2
13
182
1262
4
32
5
13
45
1116
45
1144
15
1135
15
56
1
5
351
565
3
218or
3
56
5
48or
5
44
Multiplying Fractions and Mixed Numbers or Whole Numbers
532
425
13
632
Martin-Gay, Basic Mathematics, 4e 1111
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
Multiply. Check by estimating.
2 12 1
9 4
20 5
9 4 25 7
or 29 9
5 2 2 5
3 3 2 2
Let’s check by estimating.
22
9rounds to 2, rounds to 1, and 2 · 1 = 2.
The estimate is close to the exact value, so our answer is reasonable.
11
4
P 144
Martin-Gay, Basic Mathematics, 4e 1212
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Example
An estimate for the measure of an adult’s wrist is of the waist size. If Jorge has a 34-inch waist, estimate the size of his wrist.
1
4
17 2 1
1 2 2
17
2
1or 8
234 1
1 4
Jorge’s wrist is about inches.1
82
P 145
Martin-Gay, Basic Mathematics, 4e 1313
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Practice Problem 14 similar
SOLUTION
About 1/3 of all plant and animal species in the United States are at risk of becoming extinct. There are 20,439 known species of plants and animals in the United States. How many species are at risk of extinction?
204393
1
13
204391
13
681331
6813
P 145
Solving Problems by Multiplying Fractions
Martin-Gay, Basic Mathematics, 4e 1414
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
DONE