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Developmental Mathematics

Elayn Martin-Gay

Chapter 3

Adding and Subtracting Fractions - all with Video Answers

Educators

Section 1

Adding and Subtracting Like Fractions

Problem 1

Add and simplify. See Examples I through 3.
$\frac{1}{7}+\frac{2}{7}$

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Problem 2

Add and simplify. See Examples I through 3.
$\frac{9}{17}+\frac{2}{17}$

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Problem 3

Add and simplify. See Examples I through 3.
$\frac{1}{10}+\frac{1}{10}$

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Problem 4

Add and simplify. See Examples I through 3.
$\frac{1}{4}+\frac{1}{4}$

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Problem 5

Add and simplify. See Examples I through 3.
$\frac{2}{9}+\frac{4}{9}$

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Problem 6

Add and simplify. See Examples I through 3.
$\frac{3}{10}+\frac{2}{10}$

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Problem 7

Add and simplify. See Examples I through 3.
$\frac{6}{20}+\frac{1}{20}$

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Problem 8

Add and simplify. See Examples I through 3.
$\frac{2}{8}+\frac{3}{8}$

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Problem 9

Add and simplify. See Examples I through 3.
$\frac{3}{14}+\frac{4}{14}$

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Problem 10

Add and simplify. See Examples I through 3.
$\frac{5}{24}+\frac{7}{24}$

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Problem 11

Add and simplify. See Examples I through 3.
$\frac{10}{11}+\frac{3}{11}$

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Problem 12

Add and simplify. See Examples I through 3.
$\frac{13}{17}+\frac{9}{17}$

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Problem 13

Add and simplify. See Examples I through 3.
$\frac{4}{13}+\frac{2}{13}+\frac{1}{13}$

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Problem 14

Add and simplify. See Examples I through 3.
$\frac{5}{11}+\frac{1}{11}+\frac{2}{11}$

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00:46

Problem 15

Add and simplify. See Examples I through 3.
$\frac{7}{18}+\frac{3}{18}+\frac{2}{18}$

Harsh Gadhiya
Harsh Gadhiya
Numerade Educator

Problem 16

Add and simplify. See Examples I through 3.
$\frac{7}{15}+\frac{4}{15}+\frac{1}{15}$

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Problem 17

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{10}{11}-\frac{4}{11}$

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Problem 18

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{9}{13}-\frac{5}{13}$

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Problem 19

Objective B Subtract and simplify. See Examples 4 and 5.
. $\frac{4}{5}-\frac{1}{5}$

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Problem 20

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{7}{8}-\frac{4}{8}$

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Problem 21

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{7}{4}-\frac{3}{4}$

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Problem 22

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{18}{5}-\frac{3}{5}$

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Problem 23

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{7}{8}-\frac{1}{8}$

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Problem 24

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{5}{6}-\frac{1}{6}$

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Problem 25

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{25}{12}-\frac{15}{12}$

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Problem 26

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{30}{20}-\frac{15}{20}$

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Problem 27

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{11}{10}-\frac{3}{10}$

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Problem 28

Objective B Subtract and simplify. See Examples 4 and 5.
. $\frac{14}{15}-\frac{4}{15}$

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Problem 29

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{86}{90}-\frac{85}{90}$

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Problem 30

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{74}{80}-\frac{73}{80}$

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Problem 31

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{27}{33}-\frac{8}{33}$

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Problem 32

Objective B Subtract and simplify. See Examples 4 and 5.
$\frac{37}{45}-\frac{18}{45}$

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Problem 33

Objectives A B Mixed Practice Perform the indicated operation See Examples I through 5.
$\frac{8}{21}+\frac{5}{21}$

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Problem 34

Objectives A B Mixed Practice Perform the indicated operation See Examples I through 5.
. $\frac{7}{37}+\frac{9}{37}$

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Problem 35

Objectives A B Mixed Practice Perform the indicated operation See Examples I through 5.
$\frac{99}{100}-\frac{9}{100}$

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Problem 36

Objectives A B Mixed Practice Perform the indicated operation See Examples I through 5.
$\frac{85}{200}-\frac{15}{200}$

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Problem 37

Objectives A B Mixed Practice Perform the indicated operation See Examples I through 5.
$\frac{13}{28}-\frac{13}{28}$

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Problem 38

Objectives A B Mixed Practice Perform the indicated operation See Examples I through 5.
$\frac{15}{26}-\frac{15}{26}$

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Problem 39

Objectives A B Mixed Practice Perform the indicated operation See Examples I through 5.
$\frac{3}{16}+\frac{7}{16}+\frac{2}{16}$

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Problem 40

Objectives A B Mixed Practice Perform the indicated operation See Examples I through 5.
$\frac{5}{18}+\frac{1}{18}+\frac{6}{18}$

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Problem 41

Objective C Find the perimeter of each figure.
(Figure Can't Copy)

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Problem 42

Objective C Find the perimeter of each figure.
(Figure Can't Copy)

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Problem 43

Objective C Find the perimeter of each figure.
(Figure Can't Copy)

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Problem 44

Objective C Find the perimeter of each figure.
(Figure Can't Copy)

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01:22

Problem 45

A railroad inspector must inspect $\frac{19}{20}$ of a mile of railroad track. If she has already inspected $\frac{5}{20}$ of a mile, how much more does she need to inspect?

Emma Parzyck
Emma Parzyck
Numerade Educator
01:33

Problem 46

Scott Davis has run $\frac{11}{8}$ miles already and plans to complete $\frac{16}{8}$ miles. To do this, how much farther must he run?

Ernest Castorena
Ernest Castorena
Numerade Educator
03:36

Problem 47

Emil Vasquez, a bodybuilder, worked out $\frac{7}{8}$ of an hour one morning before school and $\frac{5}{8}$ of an hour that evening. How long did he work out that day?

Nick Johnson
Nick Johnson
Numerade Educator
01:05

Problem 48

A recipe for Heavenly Hash cake calls for $\frac{3}{4}$ cup of sugar and later $\frac{1}{4}$ cup of sugar. How much sugar is needed to make the recipe?

Luke P
Luke P
Numerade Educator
06:03

Problem 49

The circle graph below shows full-time U.S. college students’ time use on an average weekday. Use this graph for Exercises 49–52. Write your answers in simplest form.
What fraction of a full-time U.S. college student's weekday is spent on eating and drinking, grooming, and sleeping?

Sheryl Ezze
Sheryl Ezze
Numerade Educator
07:28

Problem 50

The circle graph below shows full-time U.S. college students’ time use on an average weekday. Use this graph for Exercises 49–52. Write your answers in simplest form.
What fraction of a full-time U.S. college student's weekday is spent on working and related activities and educational activities?

Gus Steppen
Gus Steppen
Numerade Educator
07:28

Problem 51

The circle graph below shows full-time U.S. college students’ time use on an average weekday. Use this graph for Exercises 49–52. Write your answers in simplest form.
How much greater is the fractional part of a college student's weekday that is spent on leisure and sports than on traveling?

Gus Steppen
Gus Steppen
Numerade Educator
06:02

Problem 52

The circle graph below shows full-time U.S. college students’ time use on an average weekday. Use this graph for Exercises 49–52. Write your answers in simplest form.
How much greater is the fractional part of a college student's weekday that is spent on sleeping than on educational activities?

Anna Jones
Anna Jones
Numerade Educator

Problem 53

Road congestion can be caused by a variety of problems. Approximately $\frac{3}{20}$ of all road congestion in the United States is caused by weather, while $\frac{5}{20}$ of all road congestion in the United States is caused by incidents such as accidents and disabled vehicles. What fraction of U.S. road congestion is caused by weather or incidents?

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02:13

Problem 54

In $2015, \frac{5}{20}$ of Target's total retail sales were in the health, beauty, and houschold essentials category, and $\frac{4}{20}$ of Target's total retail sales were in the food and pet supplies category. What fraction of Target's total retail sales were made in these two categories combined?

Cheryl Glor
Cheryl Glor
Numerade Educator
01:49

Problem 55

As of March 2017 , the fraction of states in the United States with maximum interstate highway speed limits up to and including 70 mph was $\frac{34}{50}$. The fraction of states with 70 mph speed limits was $\frac{21}{50}$. What fraction of states had speed limits that were less than 70 mph ?

Lauren Shelton
Lauren Shelton
Numerade Educator
04:29

Problem 56

When people take aspirin, $\frac{31}{50}$ of the time it is used to treat some type of pain. Approximately $\frac{7}{50}$ of all aspirin use is for treating headaches. What fraction of aspirin use is for treating pain other than headaches?

KR
Kimberly Robertson
Numerade Educator
01:23

Problem 57

Find the fractional part of the world's land area within the continents of North America and South America.

Nicholas Bondra
Nicholas Bondra
Numerade Educator
01:34

Problem 58

Find the fractional part of the world's land area within the continents of Asia and Africa.

Nicholas Bondra
Nicholas Bondra
Numerade Educator

Problem 59

How much greater is the fractional part of the continent of Antarctica than the fractional part of the continent of Europe?

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Problem 60

How much greater is the fractional part of the continent of Asia than the continent of Australia?

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01:31

Problem 61

The theater industry is shifting away from analog movie screens toward digital and digital 3-D movie screens. Use the circle graph to answer Exercises 61 and 62. Write your answers in simplest form.
What fraction of U.S. theater screens are either digital 3-D or analog?

Erika Bustos
Erika Bustos
Numerade Educator
01:31

Problem 62

The theater industry is shifting away from analog movie screens toward digital and digital 3-D movie screens. Use the circle graph to answer Exercises 61 and 62. Write your answers in simplest form.
How much greater is the fraction of screens that are digital 3-D than the fraction of screens that are analog?

Erika Bustos
Erika Bustos
Numerade Educator

Problem 63

Write the prime factorization of each number. See Section 2.2.
10

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Problem 64

Write the prime factorization of each number. See Section 2.2.
12

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Problem 65

Write the prime factorization of each number. See Section 2.2.
8

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Problem 66

Write the prime factorization of each number. See Section 2.2.
20

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Problem 67

Write the prime factorization of each number. See Section 2.2.
55

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Problem 68

Write the prime factorization of each number. See Section 2.2.
28

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05:25

Problem 69

Perform each indicated operation.
$\frac{3}{8}+\frac{7}{8}-\frac{5}{8}$

Noraney Ocampo
Noraney Ocampo
Numerade Educator
00:23

Problem 70

Perform each indicated operation.
$\frac{12}{20}-\frac{1}{20}-\frac{3}{20}$

Erika Bustos
Erika Bustos
Numerade Educator
00:20

Problem 71

Perform each indicated operation.
$\frac{4}{11}+\frac{5}{11}-\frac{3}{11}+\frac{2}{11}$

Jodi Folley
Jodi Folley
Numerade Educator
00:29

Problem 72

Perform each indicated operation.
$\frac{9}{12}+\frac{1}{12}-\frac{3}{12}-\frac{5}{12}$

James Kiss
James Kiss
Numerade Educator
00:44

Problem 73

Find and correct the error. See the Concept Check in this section.
$\frac{2}{7}+\frac{9}{7}=\frac{11}{14}$

Emily Himsel
Emily Himsel
Numerade Educator
00:14

Problem 74

Find and correct the error. See the Concept Check in this section.
$\frac{3}{4}-\frac{1}{4}=\frac{2}{8}=\frac{1}{4}$

Amy Jiang
Amy Jiang
Numerade Educator
01:08

Problem 75

Find and correct the error. See the Concept Check in this section.
In your own words, explain how to add like fractions.

Emily Himsel
Emily Himsel
Numerade Educator
01:08

Problem 76

Find and correct the error. See the Concept Check in this section.
In your own words, explain how to subtract like fractions.

Emily Himsel
Emily Himsel
Numerade Educator
00:42

Problem 77

Use the circle graph for Exercises 49 through 52 and find the sum of all the daily time-use fractions. Explain your answer.

Yujie Wang
Yujie Wang
College of San Mateo

Problem 78

Use the map of the world for Exercises 57 through 60 and find the sum of all the continents' fractions. Explain your answer.

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03:14

Problem 79

Mike Cannon jogged $\frac{3}{8}$ of a mile from home and then rested. Then he continued jogging farther from home for another $\frac{3}{8}$ of a mile until he discovered his watch had fallen off. He walked back along the same path for $\frac{4}{8}$ of a mile until he found his watch. Find how far he was from his home.

Nick Johnson
Nick Johnson
Numerade Educator

Problem 80

A trim carpenter needs the following lengths of boards: $\frac{5}{4}$ feet, $\frac{15}{4}$ feet, $\frac{9}{4}$ feet, and $\frac{13}{4}$ feet. Is a 10 -foot board long enough for the carpenter to cut these lengths? If not, how much more length is needed?

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