Chapter 1, An Introduction to Algebra Video Solutions, Elementary and Intermediate Algebra 5th

Section 2

Fractions

00:32

Problem 1

Fill in the blanks.
A factor is a number being ___.

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00:29

Problem 2

Fill in the blanks.
Numbers that have only 1 and themselves as factors, such as
$23,37,$ and $41,$ are called __numbers.

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00:37

Problem 3

Fill in the blanks.
When we write 60 as $2 \cdot 2 \cdot 3 \cdot 5,$ we say that we have written 60 in ___ form.

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00:42

Problem 4

Fill in the blanks.
The ___ of the fraction $\frac{3}{4}$ is $3,$ and the is 4

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00:38

Problem 5

Fill in the blanks.
Two fractions that represent the same number, such as $\frac{1}{2}$ and $\frac{2}{4}$, are called ___fractions.

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00:37

Problem 6

Fill in the blanks.
$\frac{2}{3}$ is the ___of $\frac{3}{2},$ because their product is 1

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00:43

Problem 7

Fill in the blanks.
The ___ common denominator for a set of fractions is the smallest number each denominator will divide exactly.

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00:45

Problem 8

Fill in the blanks.
The __ number $7 \frac{1}{3}$ represents the sum of a whole number and a fraction: $7+\frac{1}{3}$

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02:29

Complete each fact about fractions. Assume there are no divisions by $0 .$
a. $\frac{a}{a}=$
b. $\frac{a}{1}=$
c. $\frac{a}{b} \cdot \frac{c}{d}=$
d. $\frac{a}{b} \div \frac{c}{d}=$
e. $\frac{a}{d}+\frac{b}{d}=$
f. $\frac{a}{d}-\frac{b}{d}=$

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01:42

Problem 10

What two equivalent fractions are shown?
(FIGURE CANNOT COPY)

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01:53

Problem 11

Complete each statement.
a. To simplify a fraction, we remove factors equal to in the form of $\frac{2}{2}, \frac{3}{3},$ or $\frac{4}{4},$ and so on.
b. To build a fraction, we multiply it by $\quad$ in the form of $\frac{2}{2}, \frac{3}{3}$
or $\frac{4}{4},$ and so on.

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01:43

Problem 12

What is the L.CD for fractions having denominators of:
a. 3 and $7 ?$
b. 4 and $6 ?$

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01:40

Problem 13

Fill in the blanks.
a. Multiply $\frac{5}{6}$ by a form of 1 to
b. Remove common build an equivalent fraction factors to simplify $\frac{12}{42}$ with denominator $30 .$
$\frac{5}{6} \cdot \frac{11}{1}=$
$\frac{n}{n}-\frac{2}{2}-\frac{2}{3}=$

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02:48

Problem 14

Fill in the blanks.
a. Write $2 \frac{15}{16}$ as an improper fraction.
b. Write $\frac{49}{12}$ as a mixed number.

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00:56

Problem 15

Find the prime factorization of each number.
$$
75
$$

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00:47

Problem 16

Find the prime factorization of each number.
$$
20
$$

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00:45

Problem 17

Find the prime factorization of each number.
$$
28
$$

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00:54

Problem 18

Find the prime factorization of each number.
$$
54
$$

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00:36

Problem 19

Find the prime factorization of each number.
$$
81
$$

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00:48

Problem 20

Find the prime factorization of each number.
$$
125
$$

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01:06

Problem 21

Find the prime factorization of each number.
$$
117
$$

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01:09

Problem 22

Find the prime factorization of each number.
$$
147
$$

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00:51

Problem 23

Find the prime factorization of each number.
$$
220
$$

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01:08

Problem 24

Find the prime factorization of each number.
$$
270
$$

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02:26

Problem 25

Find the prime factorization of each number.
$$
1,254
$$

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01:37

Problem 26

Find the prime factorization of each number.
$$
1,144
$$

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00:28

Problem 27

Multiply.
$$
\frac{5}{6} \cdot \frac{1}{8}
$$

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00:34

Problem 28

Multiply.
$$
\frac{2}{3} \cdot \frac{1}{5}
$$

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00:34

Problem 29

Multiply.
$$
\frac{7}{11} \cdot \frac{3}{5}
$$

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00:29

Problem 30

Multiply.
$$
\frac{13}{9} \cdot \frac{2}{3}
$$

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01:00

Problem 31

Divide.
$$
\frac{3}{4} \div \frac{2}{5}
$$

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01:11

Problem 32

Divide.
$$
\frac{7}{8} \div \frac{6}{13}
$$

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01:07

Problem 33

Divide.
$$
\frac{6}{5} \div \frac{5}{7}
$$

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01:00

Problem 34

Divide.
$$
\frac{4}{3} \div \frac{3}{2}
$$

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01:10

Problem 35

Build each fraction or whole number to an equivalent fraction with the indicated denominator.
$\frac{1}{3},$ denominator

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01:11

Problem 36

Build each fraction or whole number to an equivalent fraction with the indicated denominator.
$\frac{3}{8},$ denominator 24

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00:52

Problem 37

Build each fraction or whole number to an equivalent fraction with the indicated denominator.
$\frac{4}{9},$ denominator 54

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01:14

Problem 38

Build each fraction or whole number to an equivalent fraction with the indicated denominator.
$\frac{9}{16},$ denominator 64

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01:11

Problem 39

Build each fraction or whole number to an equivalent fraction with the indicated denominator.
$7,$ denominator 5

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00:49

Problem 40

Build each fraction or whole number to an equivalent fraction with the indicated denominator.
$12,$ denominator 3

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00:52

Problem 41

Build each fraction or whole number to an equivalent fraction with the indicated denominator.
$5,$ denominator 7

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00:46

Problem 42

Build each fraction or whole number to an equivalent fraction with the indicated denominator.
$6,$ denominator 8

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01:01

Problem 43

Simplify each fraction, if possible.
$$
\frac{6}{18}
$$

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00:43

Problem 44

Simplify each fraction, if possible.
$$
\frac{6}{9}
$$

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01:02

Problem 45

Simplify each fraction, if possible.
$$
\frac{24}{28}
$$

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00:59

Problem 46

Simplify each fraction, if possible.
$$
\frac{35}{14}
$$

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01:01

Problem 47

Simplify each fraction, if possible.
$$
\frac{15}{40}
$$

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00:44

Problem 48

Simplify each fraction, if possible.
$$
\frac{22}{77}
$$

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01:13

Problem 49

Simplify each fraction, if possible.
$$
\frac{33}{56}
$$

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01:01

Problem 50

Simplify each fraction, if possible.
$$
\frac{26}{21}
$$

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00:38

Problem 51

Simplify each fraction, if possible.
$$
\frac{26}{39}
$$

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01:17

Problem 52

Simplify each fraction, if possible.
$$
\frac{72}{64}
$$

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01:37

Problem 53

Simplify each fraction, if possible.
$$
\frac{36}{225}
$$

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01:37

Problem 54

Simplify each fraction, if possible.
$$
\frac{175}{490}
$$

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00:47

Problem 55

Perform the operations and, if possible, simplify.
$$
\frac{3}{5}+\frac{3}{5}
$$

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01:06

Problem 56

Perform the operations and, if possible, simplify.
$$
\frac{4}{9}-\frac{1}{9}
$$

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00:39

Problem 57

Perform the operations and, if possible, simplify.
$$
\frac{6}{7}-\frac{2}{7}
$$

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00:48

Problem 58

Perform the operations and, if possible, simplify.
$$
\frac{5}{13}+\frac{6}{13}
$$

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01:15

Problem 59

Perform the operations and, if possible, simplify.
$$
\frac{1}{6}+\frac{1}{24}
$$

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01:17

Problem 60

Perform the operations and, if possible, simplify.
$$
\frac{17}{25}-\frac{2}{5}
$$

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03:50

Problem 61

Perform the operations and, if possible, simplify.
$$
\frac{7}{10}-\frac{1}{14}
$$

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02:11

Problem 62

Perform the operations and, if possible, simplify.
$$
\frac{9}{8}-\frac{5}{6}
$$

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02:57

Problem 63

Perform the operations and, if possible, simplify.
$$
\frac{2}{15}+\frac{7}{9}
$$

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02:18

Problem 64

Perform the operations and, if possible, simplify.
$$
\frac{7}{25}+\frac{3}{10}
$$

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03:42

Problem 65

Perform the operations and, if possible, simplify.
$$\frac{13}{28}-\frac{1}{21}$$

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04:19

Problem 66

Perform the operations and, if possible, simplify.
$$
\frac{13}{24}-\frac{3}{40}
$$

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01:13

Problem 67

Perform the operations and, if possible, simplify.
$$
16\left(\frac{3}{2}\right)
$$

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01:01

Problem 68

Perform the operations and, if possible, simplify.
$$
30\left(\frac{5}{6}\right)
$$

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01:09

Problem 69

Perform the operations and, if possible, simplify.
$$
18 \cdot \frac{2}{9}
$$

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00:55

Problem 70

Perform the operations and, if possible, simplify.
$$
14 \cdot \frac{3}{7}
$$

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03:12

Problem 71

Perform the operations and, if possible, simplify.
$$
\frac{2}{3}+\frac{5}{18}-\frac{1}{6}
$$

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02:50

Problem 72

Perform the operations and, if possible, simplify.
$$
\frac{3}{5}+\frac{7}{20}-\frac{7}{10}
$$

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04:40

Problem 73

Perform the operations and, if possible, simplify.
$$
\frac{5}{12}+\frac{1}{3}-\frac{2}{5}
$$

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03:28

Problem 74

Perform the operations and, if possible, simplify.
$$
\frac{7}{15}+\frac{1}{5}-\frac{4}{9}
$$

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01:42

Problem 75

Perform the operations and, if possible, simplify.
$$
4 \frac{2}{3} \cdot 7
$$

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02:16

Problem 76

Perform the operations and, if possible, simplify.
$$
7 \cdot 1 \frac{3}{28}
$$

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02:19

Problem 77

Perform the operations and, if possible, simplify.
$$
8 \div 3 \frac{1}{5}
$$

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02:58

Problem 78

Perform the operations and, if possible, simplify.
$$
15 \div 3 \frac{1}{3}
$$

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03:53

Problem 79

Perform the operations and, if possible, simplify. See Examples 9 and $10 .$
$8 \frac{2}{9}-7 \frac{2}{3}$

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01:38

Problem 80

Perform the operations and, if possible, simplify.
$$
3 \frac{4}{5}-3 \frac{1}{10}
$$

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04:02

Problem 81

Perform the operations and, if possible, simplify.
$$
3 \frac{3}{16}+2 \frac{5}{24}
$$

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04:00

Problem 82

Perform the operations and, if possible, simplify.
$$
15 \frac{5}{6}+11 \frac{5}{8}
$$

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02:11

Problem 83

Perform the operations and, if possible, simplify.
$$
\frac{3}{5}+\frac{2}{3}
$$

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01:55

Problem 84

Perform the operations and, if possible, simplify.
$$
\frac{4}{3}+\frac{7}{2}
$$

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01:36

Problem 85

Perform the operations and, if possible, simplify.
$$
21\left(\frac{10}{3}\right)
$$

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01:35

Problem 86

Perform the operations and, if possible, simplify.
$$
28\left(\frac{4}{7}\right)
$$

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02:10

Problem 87

Perform the operations and, if possible, simplify.
$$
6 \cdot 2 \frac{7}{24}
$$

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01:07

Problem 88

Perform the operations and, if possible, simplify.
$$
3 \frac{1}{2} \cdot \frac{1}{5}
$$

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03:28

Problem 89

Perform the operations and, if possible, simplify.
$$
\frac{2}{3}-\frac{1}{4}+\frac{1}{12}
$$

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02:45

Problem 90

Perform the operations and, if possible, simplify.
$$
\frac{3}{7}-\frac{2}{5}+\frac{2}{35}
$$

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01:31

Problem 91

Perform the operations and, if possible, simplify.
$$
\frac{21}{35} \div \frac{3}{14}
$$

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02:04

Problem 92

Perform the operations and, if possible, simplify.
$$
\frac{23}{25} \div \frac{46}{5}
$$

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01:47

Problem 93

Perform the operations and, if possible, simplify.
$$
\frac{4}{3}\left(\frac{6}{5}\right)
$$

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01:52

Problem 94

Perform the operations and, if possible, simplify.
$$
\frac{21}{8}\left(\frac{2}{15}\right)
$$

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03:39

Problem 95

Perform the operations and, if possible, simplify.
$$
\frac{4}{63}+\frac{1}{45}
$$

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04:14

Problem 96

Perform the operations and, if possible, simplify.
$$\frac{5}{18}+\frac{1}{99}$$

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01:28

Problem 97

Perform the operations and, if possible, simplify.
$$
3-\frac{3}{4}
$$

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01:24

Problem 98

Perform the operations and, if possible, simplify.
$$
4-\frac{7}{3}
$$

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00:48

Problem 99

Perform the operations and, if possible, simplify.
$$
\frac{1}{5} \cdot \frac{3}{5}
$$

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00:46

Problem 100

Perform the operations and, if possible, simplify.
$$
\frac{3}{4} \cdot \frac{5}{7}
$$

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02:41

Problem 101

Perform the operations and, if possible, simplify.
$$
3 \frac{1}{3} \div 1 \frac{5}{6}
$$

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02:27

Problem 102

Perform the operations and, if possible, simplify.
$$
2 \frac{1}{2} \div 1 \frac{5}{8}
$$

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01:20

Problem 103

Perform the operations and, if possible, simplify.
$$
\frac{11}{21}-\frac{8}{21}
$$

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01:16

Problem 104

Perform the operations and, if possible, simplify.
$$
\frac{19}{35}-\frac{12}{35}
$$

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04:48

Problem 105

Perform the operations and, if possible, simplify.
$$
\frac{7}{30}+\frac{1}{50}-\frac{19}{75}
$$

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05:00

Problem 106

Perform the operations and, if possible, simplify.
$$
\frac{11}{12}-\frac{7}{15}-\frac{9}{20}
$$

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02:54

Problem 107

Perform the operations and, if possible, simplify.
$$
1 \frac{31}{32}+7 \frac{1}{9}
$$

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02:33

Problem 108

Perform the operations and, if possible, simplify.
$$
3 \frac{1}{16} \cdot 4 \frac{4}{7}
$$

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06:12

Problem 109

Perform the operations and, if possible, simplify.
a. $\frac{4}{9}+\frac{3}{7}$
b. $\frac{4}{9}-\frac{3}{7}$
c. $\frac{4}{9} \cdot \frac{3}{7}$
d. $\frac{4}{9} \div \frac{3}{7}$

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10:14

Problem 110

Perform the operations and, if possible, simplify.
a. $4 \frac{1}{8}+1 \frac{5}{6}$
b. $4 \frac{1}{8}-1 \frac{5}{6}$
c. $4 \frac{1}{8} \cdot 1 \frac{5}{6}$
d. $4 \frac{1}{8} \div 1 \frac{5}{6}$

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02:38

Problem 111

A ranger cut down a tree and measured the widths of the outer two growth rings.
a. What was the growth over this 2 -year period?
b. What is the difference in the widths of the rings?
(FIGURE CANNOT COPY)

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06:08

Problem 112

To secure the bracket to the stock, a bolt and a nut are used. How long should the threaded part of the bolt be?
(FIGURE CANNOT COPY)

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04:17

Problem 113

Each year, the Transportation Security Administration (TSA) screens more than 500 million pieces of luggage. On many flights, airlines do not accept luggage whose total dimension (length $+$ width $+\text { height })$ exceeds 62 inches. What is the total dimension figure for the suitcase shown below?
(FIGURE CANNOT COPY)

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02:21

Problem 114

How much butter is left in a $10 \frac{1}{2}$ -pound tub of butter if $4 \frac{3}{4}$ pounds are used to make a wedding cake?
(FIGURE CANNOT COPY)

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03:31

Problem 115

How many inches of molding are needed to make the square picture frame?
(FIGURE CANNOT COPY)

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05:31

Problem 116

The materials used to make a pillow are shown below. Examine the inventory list to decide how many pillows can be manufactured in one production run with the materials in stock.
(FIGURE CANNOT COPY)

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02:27