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Prealgebra & Introductory Algebra

Julie Miller, Molly O'Neill, Nancy Hyde

Chapter 4

Fractions and Mixed Numbers - all with Video Answers

Educators


Section 1

Introduction to Fractions and Mixed Numbers

00:39

Problem 1

a. When a whole unit is divided into parts, we call the parts ______of the whole unit.
b. Given a fraction $\frac{a}{b}$, where $a$ and $b$ are whole numbers and $b \neq 0$, the top number $a$ is called the ______ and the bottom number $b$ is called the _____.
c.A fraction whose numerator is an integer and whose denominator is a nonzero integer is called a ______ number.
d.A positive fraction whose numerator is less than its denominator (or the opposite of such a fraction) is called a _______ fraction.
e.A positive fraction whose numerator is greater than or equal to its denominator (or the opposite of such a fraction) is called an ______ fraction.
f. A ________ number is a sum of a whole number and a fractional part of a whole.

Amy Jiang
Amy Jiang
Numerade Educator
00:14

Problem 2

Identify the numerator and the denominator for each fraction.
$$
\frac{2}{3}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:06

Problem 3

Identify the numerator and the denominator for each fraction.
$$
\frac{8}{9}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:06

Problem 4

Identify the numerator and the denominator for each fraction.
$$
\frac{12 x}{11 y^{2}}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:06

Problem 5

Identify the numerator and the denominator for each fraction.
$$
\frac{7 p}{9 q}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:07

Problem 6

Write a fraction that represents the shaded area.

Erika Bustos
Erika Bustos
Numerade Educator
00:14

Problem 7

Write a fraction that represents the shaded area.

Erika Bustos
Erika Bustos
Numerade Educator
00:09

Problem 8

Write a fraction that represents the shaded area.

Erika Bustos
Erika Bustos
Numerade Educator
00:10

Problem 9

Write a fraction that represents the shaded area.

Erika Bustos
Erika Bustos
Numerade Educator
00:08

Problem 10

Write a fraction that represents the shaded area.

Erika Bustos
Erika Bustos
Numerade Educator
00:10

Problem 11

Write a fraction that represents the shaded area.

Erika Bustos
Erika Bustos
Numerade Educator
00:16

Problem 12

Write a fraction to represent the portion of gas in a gas tank represented by the gauge.

Erika Bustos
Erika Bustos
Numerade Educator
00:06

Problem 13

The scoreboard for a recent men's championship swim meet in Melbourne, Australia, shows the final standings in the event. What fraction of the finalists are from the USA?
$$
\begin{array}{l|l|l}
\hline \text { Name } & \text { Country } & \text { Time } \\
\hline \text { Maginni, Filippo } & \text { ITA } & 48.43 \\
\hline \text { Hayden, Brent } & \text { CAN } & 48.43 \\
\hline \text { Sullivan, Eamon } & \text { AUS } & 48.47 \\
\hline \text { Cielo Filho, Cesar } & \text { BRA } & 48.51 \\
\hline \text { Lezak, Jason } & \text { USA } & 48.52 \\
\hline \text { Van Den Hoogenband, Pieter } & \text { NED } & 48.63 \\
\hline \text { Schoeman, Roland Mark } & \text { RSA } & 48.72 \\
\hline \text { Neethling, Ryk } & \text { RSA } & 48.81 \\
\hline
\end{array}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:09

Problem 14

Refer to the scoreboard from Exercise $13 .$ What fraction of the finalists are from the Republic of South Africa (RSA)?

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:22

Problem 15

The graph categorizes a sample of people by blood type. What fraction of the sample represents people with type O blood?

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:49

Problem 16

Refer to the graph from Exercise $15 .$ What fraction of the sample represents people with type A blood?

Breanna Ollech
Breanna Ollech
Numerade Educator
00:07

Problem 17

A class has 21 children -11 girls and 10 boys. What fraction of the class is made up of boys?

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:12

Problem 18

In a neighborhood in Ft. Lauderdale, Florida, 10 houses are for sale and 53 are not for sale. Write a fraction representing the portion of houses that are for sale.

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:05

Problem 19

Simplify if possible.
$$
\frac{-13}{1}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:05

Problem 20

Simplify if possible.
$$
\frac{-14}{1}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:05

Problem 21

Simplify if possible.
$$
\frac{2}{2}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:03

Problem 22

Simplify if possible.
$$
\frac{8}{8}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:04

Problem 23

Simplify if possible.
$$
\frac{0}{-3}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:03

Problem 24

Simplify if possible.
$$
\frac{0}{7}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:08

Problem 25

Simplify if possible.
$$
\frac{-3}{0}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:09

Problem 26

Simplify if possible.
$$
\frac{-11}{0}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:05

Problem 27

Simplify if possible.
$$
\frac{-9}{-10}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:05

Problem 28

Simplify if possible.
$$
\frac{-13}{-6}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:14

Problem 29

Which expressions are equivalent to $\frac{-9}{10} ?$
a. $\frac{9}{10}$
b. $-\frac{9}{10}$
c. $\frac{9}{-10}$
d. $\frac{-9}{-10}$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:11

Problem 30

Which expressions are equivalent to $-\frac{4}{5} ?$
a. $\frac{-4}{5}$
b. $\frac{-4}{-5}$
c. $\frac{4}{-5}$
d. $-\frac{5}{4}$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:17

Problem 31

Which expressions are equivalent to $\frac{-4}{1} ?$
a. $\frac{4}{-1}$
b. -4
c. $-\frac{4}{1}$
d. $\frac{1}{-4}$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:14

Problem 32

Which expressions are equivalent to $\frac{-9}{1} ?$
a. $\frac{-9}{-1}$
b. $\frac{9}{-1}$
c. -9
d. $-\frac{9}{1}$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:08

Problem 33

Label the fraction as proper or improper.
$$
\frac{7}{8}
$$

Erika Bustos
Erika Bustos
Numerade Educator
00:04

Problem 34

Label the fraction as proper or improper.
$$
\frac{2}{3}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:04

Problem 35

Label the fraction as proper or improper.
$$
\frac{10}{10}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:04

Problem 36

Label the fraction as proper or improper.
$$
\frac{3}{3}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:06

Problem 37

Label the fraction as proper or improper.
$$
\frac{7}{2}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:04

Problem 38

Label the fraction as proper or improper.
$$
\frac{21}{20}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:14

Problem 39

Write an improper fraction for the shaded portion of each group of figures.

Erika Bustos
Erika Bustos
Numerade Educator
00:11

Problem 40

Write an improper fraction for the shaded portion of each group of figures.

Erika Bustos
Erika Bustos
Numerade Educator
00:11

Problem 41

Write an improper fraction for the shaded portion of each group of figures.

Erika Bustos
Erika Bustos
Numerade Educator
00:20

Problem 42

Write an improper fraction for the shaded portion of each group of figures.

Erika Bustos
Erika Bustos
Numerade Educator
00:16

Problem 43

Write an improper fraction to represent the length of the objects shown in the figure.

Erika Bustos
Erika Bustos
Numerade Educator
00:14

Problem 44

Write an improper fraction to represent the length of the objects shown in the figure.

Erika Bustos
Erika Bustos
Numerade Educator
00:12

Problem 45

Write an improper fraction and a mixed number for the shaded portion of each group of figures.

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:12

Problem 46

Write an improper fraction and a mixed number for the shaded portion of each group of figures.

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:16

Problem 47

Write an improper fraction and a mixed number to represent the length of the nail.

Erika Bustos
Erika Bustos
Numerade Educator
01:26

Problem 48

Write an improper fraction and a mixed number for the number of cups of sugar indicated in the figure.

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
00:11

Problem 49

Convert the mixed number to an improper fraction.
$$
1 \frac{3}{4}
$$

Erika Bustos
Erika Bustos
Numerade Educator
00:07

Problem 50

Convert the mixed number to an improper fraction.
$$
6 \frac{1}{3}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:10

Problem 51

Convert the mixed number to an improper fraction.
$$
-4 \frac{2}{9}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:06

Problem 52

Convert the mixed number to an improper fraction.
$$
-3 \frac{1}{5}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:08

Problem 53

Convert the mixed number to an improper fraction.
$$
-3 \frac{3}{7}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:06

Problem 54

Convert the mixed number to an improper fraction.
$$
-8 \frac{2}{3}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:07

Problem 55

Convert the mixed number to an improper fraction.
$$
6 \frac{3}{4}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:05

Problem 56

Convert the mixed number to an improper fraction.
$$
10 \frac{3}{5}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:07

Problem 57

Convert the mixed number to an improper fraction.
$$
11 \frac{5}{12}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:05

Problem 58

Convert the mixed number to an improper fraction.
$$
12 \frac{1}{6}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:13

Problem 59

Convert the mixed number to an improper fraction.
$$
-21 \frac{3}{8}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:07

Problem 60

Convert the mixed number to an improper fraction.
$$
-15 \frac{1}{2}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:11

Problem 61

How many thirds are in $10 ?$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:10

Problem 62

How many sixths are in $2 ?$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:18

Problem 63

How many eighths are in $2 \frac{3}{8} ?$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:13

Problem 64

How many fifths are in $2 \frac{3}{5} ?$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:12

Problem 65

How many fourths are in $1 \frac{3}{4}$ ?

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:06

Problem 66

Convert the mixed number to an improper fraction.
How many thirds are in $5 \frac{2}{3}$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:22

Problem 67

Convert the improper fraction to a mixed number.
$$
\frac{37}{8}
$$

Erika Bustos
Erika Bustos
Numerade Educator
00:09

Problem 68

Convert the improper fraction to a mixed number.
$$
\frac{13}{7}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:09

Problem 69

Convert the improper fraction to a mixed number.
$$
-\frac{39}{5}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:14

Problem 70

Convert the improper fraction to a mixed number.
$$
-\frac{19}{4}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:12

Problem 71

Convert the improper fraction to a mixed number.
$$
-\frac{27}{10}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:13

Problem 72

Convert the improper fraction to a mixed number.
$$
-\frac{43}{18}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:11

Problem 73

Convert the improper fraction to a mixed number.
$$
\frac{52}{9}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:53

Problem 74

Convert the improper fraction to a mixed number.
$$
\frac{67}{12}
$$

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
00:13

Problem 75

Convert the improper fraction to a mixed number.
$$
\frac{133}{11}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:09

Problem 76

Convert the improper fraction to a mixed number.
$$
\frac{51}{10}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:13

Problem 77

Convert the improper fraction to a mixed number.
$$
-\frac{23}{6}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:13

Problem 78

Convert the improper fraction to a mixed number.
$$
-\frac{115}{7}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:19

Problem 79

Divide. Write the quotient as a mixed number.
$7) \overline{ 3 0 9 }$

Erika Bustos
Erika Bustos
Numerade Educator
00:20

Problem 80

Divide. Write the quotient as a mixed number.
$4 )\overline { 9 2 1 }$

Erika Bustos
Erika Bustos
Numerade Educator
00:15

Problem 81

Divide. Write the quotient as a mixed number.
$$
5281 \div 5
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:15

Problem 82

Divide. Write the quotient as a mixed number.
$$
7213 \div 8
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:12

Problem 83

Divide. Write the quotient as a mixed number.
$$
8913 \div 11
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:13

Problem 84

Divide. Write the quotient as a mixed number.
$$
4257 \div 23
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:15

Problem 85

Divide. Write the quotient as a mixed number.
$1 5 )\overline { 1 8 7 }$

Erika Bustos
Erika Bustos
Numerade Educator
00:13

Problem 86

Divide. Write the quotient as a mixed number.
$3 4 )\overline { 6 9 5 }$

Erika Bustos
Erika Bustos
Numerade Educator
00:15

Problem 87

Plot the fraction on the number line.
$$
\frac{3}{4}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:15

Problem 88

Plot the fraction on the number line.
$$
\frac{1}{4}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:11

Problem 89

Plot the fraction on the number line.
$$
\frac{1}{5}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:07

Problem 90

Plot the fraction on the number line.
$$
\frac{1}{3}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:09

Problem 91

Plot the fraction on the number line.
$$
-\frac{2}{3}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:09

Problem 92

Plot the fraction on the number line.
$$
-\frac{2}{3}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:15

Problem 93

Plot the fraction on the number line.
$$
\frac{7}{6}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:14

Problem 94

Plot the fraction on the number line.
$$
\frac{7}{5}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:15

Problem 95

Plot the fraction on the number line.
$$
-\frac{4}{3}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:12

Problem 96

Plot the fraction on the number line.
$$
-\frac{3}{2}
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:08

Problem 97

Simplify.
$$
\left|-\frac{3}{4}\right|
$$

Erika Bustos
Erika Bustos
Numerade Educator
00:07

Problem 98

Simplify.
$$
\left|-\frac{8}{7}\right|
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:05

Problem 99

Simplify.
$$
\left|\frac{1}{10}\right|
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:06

Problem 100

Simplify.
$$
\left|\frac{3}{20}\right|
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:07

Problem 101

Simplify.
$$
-\left|-\frac{7}{3}\right|
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:05

Problem 102

Simplify.
$$
-\left|-\frac{1}{4}\right|
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:07

Problem 103

Simplify.
$$
-\left(-\frac{7}{3}\right)
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:05

Problem 104

Simplify.
$$
-\left(-\frac{1}{4}\right)
$$

Michelle Nguyen
Michelle Nguyen
Numerade Educator
00:38

Problem 105

True or false? Whole numbers can be written both as proper and improper fractions.

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
00:26

Problem 106

True or false? Suppose $m$ and $n$ are nonzero numbers, where $m>n$. Then $\frac{m}{n}$ is an improper fraction.

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
00:28

Problem 107

True or false? Suppose $m$ and $n$ are nonzero numbers, where $m>n$. Then $\frac{n}{m}$ is a proper fraction.

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator
00:58

Problem 108

True or false? Suppose $m$ and $n$ are nonzero numbers, where $m>n$. Then $\frac{n}{3 m}$ is a proper fraction.

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator