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Intermediate Algebra

Jerome E. Kaufmann, Karen L. Schwitters

Chapter 1

Basic Concepts and Properties - all with Video Answers

Educators


Section 0

Review of Fractions

00:23

Problem 1

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$26$$

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00:30

Problem 2

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$16$$

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00:31

Problem 3

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$36$$

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00:37

Problem 4

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$80$$

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00:23

Problem 5

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$49$$

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00:29

Problem 6

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$92$$

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00:26

Problem 7

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$56$$

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00:33

Problem 8

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$144$$

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00:33

Problem 9

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$120$$

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00:32

Problem 10

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$84$$

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00:37

Problem 11

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$135$$

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00:20

Problem 12

Factor each composite number into a product of prime numbers; for example, $18=2 \cdot 3 \cdot 3$.
$$98$$

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00:32

Problem 13

Find the least common multiple of the given numbers.
$$6 \text { and } 8$$

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00:25

Problem 14

Find the least common multiple of the given numbers.
$$8 \text { and } 12$$

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00:48

Problem 15

Find the least common multiple of the given numbers.
$$12 \text { and } 16$$

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00:26

Problem 16

Find the least common multiple of the given numbers.
$$9 \text { and } 12$$

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00:51

Problem 17

Find the least common multiple of the given numbers.
$$28 \text { and } 35$$

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02:20

Problem 18

Find the least common multiple of the given numbers.
$$42 \text { and } 66$$

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01:27

Problem 19

Find the least common multiple of the given numbers.
$$49 \text { and } 56$$

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00:32

Problem 20

Find the least common multiple of the given numbers.
$$18 \text { and } 24$$

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00:55

Problem 21

Find the least common multiple of the given numbers.
$$8,12, \text { and } 28$$

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00:39

Problem 22

Find the least common multiple of the given numbers.
$$\text { 6, } 10 \text { , and } 12$$

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00:42

Problem 23

Find the least common multiple of the given numbers.
$$9,15, \text { and } 18$$

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01:08

Problem 24

Find the least common multiple of the given numbers.
$$8,14, \text { and } 24$$

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00:29

Problem 25

Reduce each fraction to lowest terms.
$$\frac{8}{12}$$

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00:23

Problem 26

Reduce each fraction to lowest terms.
$$\frac{12}{16}$$

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00:37

Problem 27

Reduce each fraction to lowest terms.
$$\frac{16}{24}$$

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00:36

Problem 28

Reduce each fraction to lowest terms.
$$\frac{18}{32}$$

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00:28

Problem 29

Reduce each fraction to lowest terms.
$$\frac{15}{9}$$

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00:28

Problem 30

Reduce each fraction to lowest terms.
$$\frac{48}{36}$$

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00:29

Problem 31

Multiply or divide as indicated, and express answers in reduced form.
$$\frac{3}{4} \cdot \frac{5}{7}$$

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00:23

Problem 32

Multiply or divide as indicated, and express answers in reduced form.
$$\frac{4}{5} \cdot \frac{3}{11}$$

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00:20

Problem 33

Multiply or divide as indicated, and express answers in reduced form.
$$\frac{2}{7} \div \frac{3}{5}$$

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00:30

Problem 34

Multiply or divide as indicated, and express answers in reduced form.
$$\frac{5}{6} \div \frac{11}{13}$$

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00:40

Problem 35

Multiply or divide as indicated, and express answers in reduced form.
$$\frac{3}{8} \cdot \frac{12}{15}$$

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00:32

Problem 36

Multiply or divide as indicated, and express answers in reduced form.
$$\frac{4}{9} \cdot \frac{3}{2}$$

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00:31

Problem 37

A certain recipe calls for $\frac{3}{4}$ cup of milk. To make half of the recipe, how much milk is needed?

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00:38

Problem 38

John is adding a diesel fuel additive to his fuel tank, which is half full. The directions say to add $\frac{1}{3}$ of the bottle to a full fuel tank. What portion of the bottle should he add to the fuel tank?

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00:23

Problem 39

Mark shares a computer with his roommates. He has partitioned the hard drive in such a way that he gets $\frac{1}{3}$ of the disk space. His part of the hard drive is currently $\frac{2}{3}$ full. What portion of the computer's hard drive space 3 is he currently taking up?

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00:40

Problem 40

Angelina teaches $\frac{2}{3}$ of the deaf children in her local school. Her local school educates $\frac{1}{2}$ of the deaf children in the school district. What portion of the school district's deaf children is Angelina teaching?

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00:19

Problem 41

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{2}{7}+\frac{3}{7}$$

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00:27

Problem 42

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{3}{11}+\frac{5}{11}$$

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00:23

Problem 43

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{7}{9}-\frac{2}{9}$$

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00:21

Problem 44

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{11}{13}-\frac{6}{13}$$

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00:25

Problem 45

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{3}{4}+\frac{9}{4}$$

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00:25

Problem 46

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{5}{6}+\frac{7}{6}$$

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00:29

Problem 47

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{11}{12}-\frac{3}{12}$$

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00:34

Problem 48

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{13}{16}-\frac{7}{16}$$

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00:25

Problem 49

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{5}{24}+\frac{11}{24}$$

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00:23

Problem 50

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{7}{36}+\frac{13}{36}$$

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00:26

Problem 51

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{1}{3}+\frac{1}{5}$$

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00:28

Problem 52

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{1}{6}+\frac{1}{8}$$

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00:23

Problem 53

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{15}{16}-\frac{3}{8}$$

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00:21

Problem 54

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{13}{12}=\frac{1}{6}$$

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00:35

Problem 55

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{7}{10}+\frac{8}{15}$$

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00:31

Problem 56

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{7}{10}+\frac{8}{15}$$

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00:37

Problem 57

Add or subtract as indicated, and express answers in lowest terms.
$$\frac{11}{24}+\frac{5}{32}$$

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00:40

Problem 58

Alicia and her brother Jeff shared a pizza. Alicia ate $\frac{1}{8}$ of the pizza, while Jeff ate $\frac{2}{3}$ of the pizza. How much of the pizza has been eaten?

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00:29

Problem 59

Rosa has $\frac{1}{3}$ pound of blueberries, $\frac{1}{4}$ pound of strawberries, and $\frac{1}{2}$ pound of raspberries. If she combines these for a fruit salad, how many pounds of these berries will be in the salad?

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00:39

Problem 60

A chemist has $\frac{11}{16}$ of an ounce of dirt residue to perform crime lab tests. He needs $\frac{3}{8}$ of an ounce to perform a test for iron content. How much of the dirt residue will
be left for the chemist to use in other testing?

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00:24

Problem 61

Simplify each numerical expression, expressing answers in reduced form.
$$\frac{1}{4}-\frac{3}{8}+\frac{5}{12}-\frac{1}{24}$$

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00:40

Problem 62

Simplify each numerical expression, expressing answers in reduced form.
$$\frac{1}{4}-\frac{3}{8}+\frac{5}{12}-\frac{1}{24}$$

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00:45

Problem 63

Simplify each numerical expression, expressing answers in reduced form.
$$\frac{5}{6}+\frac{2}{3} \cdot \frac{3}{4}-\frac{1}{4} \cdot \frac{2}{5}$$

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00:38

Problem 64

Simplify each numerical expression, expressing answers in reduced form.
$$\frac{3}{4}+\frac{2}{3}-\frac{1}{6}+\frac{5}{12}$$

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01:00

Problem 65

Simplify each numerical expression, expressing answers in reduced form.
$$\frac{3}{4} \cdot \frac{6}{9}-\frac{5}{6} \cdot \frac{8}{10}+\frac{2}{3} \cdot \frac{6}{8}$$

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00:33

Problem 66

Simplify each numerical expression, expressing answers in reduced form.
$$\frac{3}{5} \cdot \frac{5}{7}+\frac{2}{3} \cdot \frac{3}{5}-\frac{1}{7} \cdot \frac{2}{5}$$

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00:26

Problem 67

Simplify each numerical expression, expressing answers in reduced form.
$$\frac{7}{13}\left(\frac{2}{3}-\frac{1}{6}\right)$$

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00:42

Problem 68

Simplify each numerical expression, expressing answers in reduced form.
$$48\left(\frac{5}{12}-\frac{1}{6}+\frac{3}{8}\right)$$

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00:41

Problem 69

Blake Scott leaves $\frac{1}{4}$ of his estate to the Boy Scouts, 2 $\frac{-}{5}$ to the local cancer fund, and the rest to his church. What fractional part of the estate does the church receive?

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00:33

Problem 70

Franco has $\frac{7}{8}$ of an ounce of gold. He wants to give $\frac{3}{16}$ of an ounce to his friend Julie. He plans to divide the remaining amount of his gold in half to make two rings.
How much gold will he have for each ring?

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