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Prealgebra

Alan S. Tussy, R. David Gustafson, Diane R. Koenig

Chapter 4

Fractions and Mixed Numbers - all with Video Answers

Educators


Section 1

An Introduction to Fractions

00:11

Problem 1

Fill in the blanks.
A __ describes the number of equal parts of a whole.

Amy Jiang
Amy Jiang
Numerade Educator
00:20

Problem 2

Fill in the blanks.
For the fraction $\frac{7}{8},$ the___ is 7 and the is 8.

Amy Jiang
Amy Jiang
Numerade Educator
00:39

Problem 3

Fill in the blanks.
If the numerator of a fraction is less than its denominator, the fraction is called a ___. If the numerator of a fraction is greater than or equal to its denominator it is called an ____.

Amy Jiang
Amy Jiang
Numerade Educator
00:15

Problem 4

Fill in the blanks.
Each of the following fractions is a form of ___. $\frac{1}{1}=\frac{2}{2}=\frac{3}{3}=\frac{4}{4}=\frac{5}{5}=\frac{6}{6}=\frac{7}{7}=\frac{8}{8}=\frac{9}{9}=\dots$

Amy Jiang
Amy Jiang
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00:13

Problem 5

Fill in the blanks.
Two fractions are ____if they represent the same number.

Amy Jiang
Amy Jiang
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00:12

Problem 6

Fill in the blanks.
Writing a fraction as an equivalent fraction with a larger denominator is called ___the fraction.

Amy Jiang
Amy Jiang
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00:16

Problem 7

Fill in the blanks.
A fraction is in ___ form, or lowest terms, when the numerator and denominator have no common factors other than 1.

Amy Jiang
Amy Jiang
Numerade Educator
00:27

Problem 8

Fill in the blanks.
Algebraic fractions, such as $\frac{1}{2}$ and $\frac{4 a^{2} b}{6 a b},$ are fractions that contain ____$\quad$ in the numerator, the denominator, or both.

Amy Jiang
Amy Jiang
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00:40

Problem 9

What concept studied in this section is shown on the right?
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:21

Problem 10

What concept studied in this section does the following statement illustrate?
$$\frac{1}{2}-\frac{2}{4}=\frac{3}{6}=\frac{4}{8}=\frac{5}{10}=\dots$$

Amy Jiang
Amy Jiang
Numerade Educator
00:45

Problem 11

Classify each fraction as a proper fraction or an improper fraction.
a. $\frac{37}{24}$
b. $\frac{1}{3}$
c. $\frac{71}{100}$
d. $\frac{9}{9}$

Amy Jiang
Amy Jiang
Numerade Educator
00:16

Problem 12

Remove the common factors of the numerator and denominator to simplify the fraction:
$$\frac{2 \cdot 3 \cdot 3 \cdot 5}{2 \cdot 3 \cdot 5 \cdot 7}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:28

Problem 13

What common factor (other than 1 ) do the numerator and the denominator of the fraction $\frac{10}{15}$ have?

Amy Jiang
Amy Jiang
Numerade Educator
00:12

Problem 14

Fill in the blank.
Multiplication property of 1: The product of any fraction and 1 is that ___.

Amy Jiang
Amy Jiang
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00:23

Problem 15

Fill in the blank.
Multiplying fractions: To multiply two fractions, multiply the ___ and multiply the denominators.

Amy Jiang
Amy Jiang
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00:26

Problem 16

a. Consider the following solution: $\frac{2}{3}=\frac{2}{3} \cdot \frac{4}{4}$
$$=\frac{8}{12}$$
To build an equivalent fraction for $\frac{2}{5}$ with a denominator of $12, \quad$ it by a factor equal to 1 in the form of ___.
b. Consider the following solution: $\frac{15}{27}=\frac{\sum_{i=5}^{1}}{z_{i} \cdot 9}$ $=\frac{5}{9}$
To simplify the fraction $\frac{15}{27}$ . a factor cqual
to 1 of the form ___.

Amy Jiang
Amy Jiang
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00:21

Problem 17

Write the fraction $\frac{7}{-8}$ in two other ways.

Amy Jiang
Amy Jiang
Numerade Educator
00:15

Problem 18

Write each integer as a fraction.
a. 8
b. $-25$

Amy Jiang
Amy Jiang
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00:32

Problem 19

Complete each solution.
Build an equivalent fraction for $\frac{1}{6}$ with a denominator of $18 .$
$$
\begin{aligned}
\frac{1}{6} &=\frac{1}{6} \cdot \frac{3}{\square} \\
&={\square}/\frac{\cdot 3}{\square} \\
&=3/{\square}
\end{aligned}
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:45

Problem 20

Complete each solution.
Simplify:
$$
\begin{aligned}
\frac{18}{24} &=\frac{2 \cdot \cdot 3}{2 \cdot 2 \cdot 2 \cdot} \\
&=\frac{1 \cdot 3 \cdot 1}{2 \cdot 2 \cdot 2 \cdot 1} \\
&=3
\end{aligned}
$$

Amy Jiang
Amy Jiang
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00:17

Problem 21

Identify the numerator and denominator of each fraction.
$$\frac{4}{5}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:09

Problem 22

Identify the numerator and denominator of each fraction.
$$\frac{7}{8}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:15

Problem 23

Identify the numerator and denominator of each fraction.
$$\frac{17}{10}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:16

Problem 24

Identify the numerator and denominator of each fraction.
$$\frac{29}{21}$$

Amy Jiang
Amy Jiang
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00:21

Problem 25

Write a fraction to describe what part of the figure is shaded. Write a fraction to describe what part of the figure is not shaded.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:21

Problem 26

Write a fraction to describe what part of the figure is shaded. Write a fraction to describe what part of the figure is not shaded.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:22

Problem 27

Write a fraction to describe what part of the figure is shaded. Write a fraction to describe what part of the figure is not shaded.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:30

Problem 28

Write a fraction to describe what part of the figure is shaded. Write a fraction to describe what part of the figure is not shaded.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:17

Problem 29

Write a fraction to describe what part of the figure is shaded. Write a fraction to describe what part of the figure is not shaded.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:18

Problem 30

Write a fraction to describe what part of the figure is shaded. Write a fraction to describe what part of the figure is not shaded.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:20

Problem 31

Write a fraction to describe what part of the figure is shaded. Write a fraction to describe what part of the figure is not shaded.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:27

Problem 32

Write a fraction to describe what part of the figure is shaded. Write a fraction to describe what part of the figure is not shaded.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:24

Problem 33

Simplify, if possible.
a. $\frac{4}{1}$
b. $\frac{8}{8}$
c. $\frac{0}{12}$
d. $\frac{1}{0}$

Amy Jiang
Amy Jiang
Numerade Educator
00:24

Problem 34

Simplify, if possible.
a. $\frac{25}{1}$
b. $\frac{14}{14}$
c. $\frac{0}{1}$
d. $\frac{83}{0}$

Amy Jiang
Amy Jiang
Numerade Educator
00:23

Problem 35

Simplify, if possible.
a. $\frac{5}{0}$
b. $\frac{0}{50}$
c. $\frac{33}{33}$
d. $\frac{75}{1}$

Amy Jiang
Amy Jiang
Numerade Educator
00:23

Problem 36

Simplify, if possible.
a. $\frac{0}{64}$
b. $\frac{27}{0}$
c. $\frac{125}{125}$
d. $\frac{98}{1}$

Amy Jiang
Amy Jiang
Numerade Educator
00:21

Problem 37

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{7}{8},$ denominator 40

Amy Jiang
Amy Jiang
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00:23

Problem 38

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{3}{4},$ denominator 24

Amy Jiang
Amy Jiang
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00:33

Problem 39

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{4}{9},$ denominator 27

Amy Jiang
Amy Jiang
Numerade Educator
00:22

Problem 40

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{5}{7},$ cleilomilinal $(0,4)$

Amy Jiang
Amy Jiang
Numerade Educator
00:29

Problem 41

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{5}{6},$ denominator 54

Amy Jiang
Amy Jiang
Numerade Educator
00:21

Problem 42

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{2}{3},$ denominator 27

Amy Jiang
Amy Jiang
Numerade Educator
00:25

Problem 43

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{2}{7},$ denominator 14

Amy Jiang
Amy Jiang
Numerade Educator
00:19

Problem 44

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{3}{10},$ denominator 50

Amy Jiang
Amy Jiang
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00:20

Problem 45

Write each whole number as an equivalent fraction with the indicated denominator.
$4,$ denominator 9

Amy Jiang
Amy Jiang
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00:15

Problem 46

Write each whole number as an equivalent fraction with the indicated denominator.
$4,$ denominator 3

Amy Jiang
Amy Jiang
Numerade Educator
00:19

Problem 47

Write each whole number as an equivalent fraction with the indicated denominator.
$6,$ denominator 8

Amy Jiang
Amy Jiang
Numerade Educator
00:14

Problem 48

Write each whole number as an equivalent fraction with the indicated denominator.
$3,$ denominator 6

Amy Jiang
Amy Jiang
Numerade Educator
00:16

Problem 49

Write each whole number as an equivalent fraction with the indicated denominator.
$3,$ denominator 5

Amy Jiang
Amy Jiang
Numerade Educator
00:17

Problem 50

Write each whole number as an equivalent fraction with the indicated denominator.
$7,$ denominator 4

Amy Jiang
Amy Jiang
Numerade Educator
00:14

Problem 51

Write each whole number as an equivalent fraction with the indicated denominator.
$14,$ denominator 2

Amy Jiang
Amy Jiang
Numerade Educator
00:15

Problem 52

Write each whole number as an equivalent fraction with the indicated denominator.
$10,$ denominator 9

Amy Jiang
Amy Jiang
Numerade Educator
00:32

Problem 53

Are the following fractions in simplest form?
a. $\frac{12}{16}$
b. $\frac{3}{25}$

Amy Jiang
Amy Jiang
Numerade Educator
00:34

Problem 54

Are the following fractions in simplest form?
a. $\frac{9}{24}$
b. $\frac{7}{36}$

Amy Jiang
Amy Jiang
Numerade Educator
00:30

Problem 55

Are the following fractions in simplest form?
a. $\frac{35}{36}$
b. $\frac{18}{21}$

Amy Jiang
Amy Jiang
Numerade Educator
00:41

Problem 56

Are the following fractions in simplest form?
a. $\frac{22}{45}$
b. $\frac{21}{56}$

Amy Jiang
Amy Jiang
Numerade Educator
00:43

Problem 57

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

Meredith Moody
Meredith Moody
Numerade Educator
00:19

Problem 58

Simplify each fraction, if possible.
$$\frac{15}{20}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:18

Problem 59

Simplify each fraction, if possible.
$$\frac{16}{20}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:18

Problem 60

Simplify each fraction, if possible.
$$\frac{25}{35}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:18

Problem 61

Simplify each fraction, if possible.
$$\frac{5}{15}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:15

Problem 62

Simplify each fraction, if possible.
$$\frac{6}{30}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:14

Problem 63

Simplify each fraction, if possible.
$$\frac{2}{48}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:14

Problem 64

Simplify each fraction, if possible.
$$\frac{2}{42}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:12

Problem 65

Simplify each fraction, if possible.
$$\frac{16}{17}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:18

Problem 66

Simplify each fraction, if possible.
$$\frac{14}{25}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:36

Problem 67

Simplify each fraction, if possible.
$$\frac{36}{96}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:22

Problem 68

Simplify each fraction, if possible.
$$\frac{48}{120}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:20

Problem 69

Simplify each fraction, if possible.
$$\frac{55}{62}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:14

Problem 70

Simplify each fraction, if possible.
$$\frac{41}{51}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:18

Problem 71

Simplify each fraction, if possible.
$$\frac{50}{55}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:23

Problem 72

Simplify each fraction, if possible.
$$\frac{22}{88}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:25

Problem 73

Simplify each fraction, if possible.
$$\frac{60}{108}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:25

Problem 74

Simplify each fraction, if possible.
$$\frac{75}{275}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:25

Problem 75

Simplify each fraction, if possible.
$$\frac{180}{210}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:22

Problem 76

Simplify each fraction, if possible.
$$\frac{90}{120}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:24

Problem 77

Simplify each fraction, if possible.
$$\frac{306}{234}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:32

Problem 78

Simplify each fraction, if possible.
$$\frac{208}{117}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:21

Problem 79

Simplify each fraction, if possible.
$$\frac{105}{42}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:22

Problem 80

Simplify each fraction, if possible.
$$\frac{120}{80}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:38

Problem 81

Simplify each fraction, if possible.
$$\frac{420}{144}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:36

Problem 82

Simplify each fraction, if possible.
$$\frac{216}{189}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:13

Problem 83

Simplify each fraction, if possible.
$$-\frac{4}{68}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:12

Problem 84

Simplify each fraction, if possible.
$$-\frac{3}{42}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:27

Problem 85

Simplify each fraction, if possible.
$$-\frac{90}{105}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:27

Problem 86

Simplify each fraction, if possible.
$$-\frac{98}{126}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:17

Problem 87

Simplify each fraction, if possible.
$$-\frac{16}{26}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:37

Problem 88

Simplify each fraction, if possible.
$$-\frac{81}{132}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:18

Problem 89

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{1}{2},$ denominator $6 a$

Amy Jiang
Amy Jiang
Numerade Educator
00:20

Problem 90

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{1}{3},$ denominator $12 b$

Amy Jiang
Amy Jiang
Numerade Educator
00:22

Problem 91

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{9}{10},$ denominator $50 c$

Amy Jiang
Amy Jiang
Numerade Educator
00:25

Problem 92

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{11}{16},$ denominator $32 n$

Amy Jiang
Amy Jiang
Numerade Educator
00:20

Problem 93

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{5}{4 n},$ denominator $44 n$

Amy Jiang
Amy Jiang
Numerade Educator
00:24

Problem 94

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{9}{7 n},$ denominator $63 n$

Amy Jiang
Amy Jiang
Numerade Educator
00:26

Problem 95

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{14}{15 x},$ denominator $45 x$

Amy Jiang
Amy Jiang
Numerade Educator
00:23

Problem 96

Write each fraction as an equivalent fraction with the indicated denominator.
$\frac{12}{13 r},$ denominator $39 r$

Amy Jiang
Amy Jiang
Numerade Educator
00:14

Problem 97

Simplify each fraction, if possible.
$$\frac{7}{14 a}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:11

Problem 98

Simplify each fraction, if possible.
$$\frac{5}{25 y}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:12

Problem 99

Simplify each fraction, if possible.
$$\frac{3 x}{12}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:13

Problem 100

Simplify each fraction, if possible.
$$\frac{7 x}{35}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:21

Problem 101

Simplify each fraction, if possible.
$$\frac{4 m^{5}}{25 m^{4}}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:13

Problem 102

Simplify each fraction, if possible.
$$\frac{2 n^{4}}{13 n^{2}}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:21

Problem 103

Simplify each fraction, if possible.
$$\frac{6 b^{4}}{9 b}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:19

Problem 104

Simplify each fraction, if possible.
$$\frac{4 c^{4}}{10 c^{3}}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:27

Problem 105

Simplify each fraction, if possible.
$$\frac{35 a^{3} b^{2}}{25 a^{2} b^{3}}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:39

Problem 106

Simplify each fraction, if possible.
$$\frac{56 n^{2} p^{4}}{28 n p^{5}}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:38

Problem 107

Simplify each fraction, if possible.
$$-\frac{16 n^{5} p}{24 n p}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:41

Problem 108

Simplify each fraction, if possible.
$$-\frac{36 c d^{6}}{54 c d^{4}}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:25

Problem 109

Tell whether each pair of fractions are equivalent by simplifying each fraction.
$$\frac{2}{14} \text { and } \frac{6}{36}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:23

Problem 110

Tell whether each pair of fractions are equivalent by simplifying each fraction.
$$\frac{3}{12} \text { and } \frac{4}{24}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:34

Problem 111

Tell whether each pair of fractions are equivalent by simplifying each fraction.
$$\frac{22}{34} \text { and } \frac{33}{51}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:37

Problem 112

Tell whether each pair of fractions are equivalent by simplifying each fraction.
$$\frac{4}{30} \text { and } \frac{12}{90}$$

Amy Jiang
Amy Jiang
Numerade Educator
00:18

Problem 113

Refer to the dental chart.
a. How many teeth are shown on the chart?
b. What fraction of this set of
teeth have fillings?
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:33

Problem 114

For each clock, what fraction of the hour has passed? Write your answers in simplified form. (Hint: There are 60 minutes in an hour.)
(FIGURES CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:58

Problem 115

The illustration below shows a ruler.
a. How many spaces are there between the numbers 0 and $1 ?$
b. To what fraction is the arrow pointing? Write
your answer in simplified form.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:12

Problem 116

The illustration below shows a side view of a drop in the sidewalk near a sinkhole. Describe the movement of the sidewalk using a signed fraction.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:35

Problem 117

The graph shows the number of Democrat and Republican governors of the 50 states, as of February $1,2009$
a. How many Democrat governors are there? How many Republican governors are there?
b. What fraction of the governors are Democrats? Write your answer in simplified form.
c. What fraction of the governors are Republicans? Write your answer in simplified form.
(GRAPH CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
00:12

Problem 118

Write fractions to describe the amount of gas left in the tank and the amount of gas that has been used.
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
01:13

Problem 119

The model below shows a new condominium development. The condos that have been sold are shaded.
a. How many units are there in the development?
b. What fraction of the units in the development have been sold? What fraction have not been sold? Write your answers in simplified form.

(FIGURE CANNOT COPY)

Dushyant Barot
Dushyant Barot
Numerade Educator
14:57

Problem 120

The illustration shows a side view of the finger position needed to produce a length of string (from the bridge to the fingertip) that gives low $\mathrm{C}$ on
a violin. To play other notes, fractions of that length are used. Locate these finger positions on the illustration.
a. $\frac{1}{2}$ of the length gives middle $C$.
b. $\frac{3}{4}$ of the length gives $F$ above low $\mathrm{C}$
c. $\frac{2}{3}$ of the length gives G.
(FIGURE CANNOT COPY)

Mark Mathison
Mark Mathison
Numerade Educator
00:34

Problem 121

Explain the concept of equivalent fractions. Give an example.

Amy Jiang
Amy Jiang
Numerade Educator
00:30

Problem 122

What does it mean for a fraction to be in simplest form? Give an example.

Amy Jiang
Amy Jiang
Numerade Educator
00:21

Problem 123

Why can't we say that $\frac{2}{5}$ of the figure below is shaded?
(FIGURE CANNOT COPY)

Amy Jiang
Amy Jiang
Numerade Educator
01:10

Problem 124

Perhaps you have heard the following joke:
A pizza parlor waitress asks a customer if he wants the pizza cut into four pieces or six pieces or eight pieces. The customer then declares that he wants either four or six pieces of pizza "because I can't eat eight." Explain what is wrong with the customer's thinking.

Amy Jiang
Amy Jiang
Numerade Educator
00:24

Problem 125

a. What type of problem is shown below? Explain the solution.
$$
\frac{1}{2}=\frac{1}{2} \cdot \frac{4}{4}=\frac{4}{8}
$$
b. What type of problem is shown below? Explain the solution.
$$
\frac{15}{35}=\frac{3 \cdot \frac{1}{8}}{8 \cdot 7}=\frac{3}{7}
$$

Amy Jiang
Amy Jiang
Numerade Educator
00:26

Problem 126

Explain the difference in the two approaches used to simplify $\frac{20}{28} .$ Are the results the same?
$$
\frac{4 \cdot 5}{4 \cdot 7} \text { and } \frac{2 \cdot 2 \cdot 5}{2 \cdot 2 \cdot 7}
$$

Amy Jiang
Amy Jiang
Numerade Educator
01:49

Problem 127

Gross pay is what a worker makes before deductions and net pay is what is left after taxes, health benefits, union dues, and other deductions are taken out. Suppose a worker's monthly gross pay is $\$ 3,575 .$ If deductions of $\$ 235$ $\$ 782, \$ 148,$ and $\$ 103$ are taken out of his check, what is his monthly net pay?

Ava Perkins
Ava Perkins
Numerade Educator
00:51

Problem 128

One day, a man bet on all eight horse races at Santa Anita Racetrack. He won $\$ 168$ on the first race and he won $\$ 105$ on the fourth race. He lost his $\$ 50$ -bets on each of the other races. Overall, did he win or lose money betting on the horses? How much?

James Kiss
James Kiss
Numerade Educator