Nature of Mathematics (MindTap Course List)
Nature of Mathematics (MindTap Course List)
13th Edition
ISBN: 9781133947257
Author: karl J. smith
Publisher: Cengage Learning
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Concept explainers

Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
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Chapter 5.3, Problem 24PS
To determine

a)

To simplify:

The expression (−1)4.

To determine

b)

To simplify:

The expression 10(−8−2).

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Chapter 5.3, Problem 23PS
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Chapter 5 Solutions

Nature of Mathematics (MindTap Course List)

Ch. 5.1 - Level 1 IN YOUR OWN WORDS Explain each of the...Ch. 5.1 - Prob. 2PSCh. 5.1 - Prob. 3PSCh. 5.1 - Prob. 4PSCh. 5.1 - Prob. 5PSCh. 5.1 - Prob. 6PSCh. 5.1 - Prob. 7PSCh. 5.1 - Prob. 8PSCh. 5.1 - Prob. 9PSCh. 5.1 - Prob. 10PS
Ch. 5.1 - Prob. 11PSCh. 5.1 - Prob. 12PSCh. 5.1 - Prob. 13PSCh. 5.1 - Prob. 14PSCh. 5.1 - Prob. 15PSCh. 5.1 - Prob. 16PSCh. 5.1 - Prob. 17PSCh. 5.1 - Prob. 18PSCh. 5.1 - Prob. 19PSCh. 5.1 - Prob. 20PSCh. 5.1 - Prob. 21PSCh. 5.1 - Level 1 In Problems 15-26, classify each as an...Ch. 5.1 - Prob. 23PSCh. 5.1 - Prob. 24PSCh. 5.1 - Prob. 25PSCh. 5.1 - Prob. 26PSCh. 5.1 - Prob. 27PSCh. 5.1 - Prob. 28PSCh. 5.1 - Prob. 29PSCh. 5.1 - Level 1 Think of three nonassociative word triples...Ch. 5.1 - Prob. 31PSCh. 5.1 - Prob. 32PSCh. 5.1 - Prob. 33PSCh. 5.1 - Prob. 34PSCh. 5.1 - Prob. 35PSCh. 5.1 - Prob. 36PSCh. 5.1 - Prob. 37PSCh. 5.1 - Prob. 38PSCh. 5.1 - Prob. 39PSCh. 5.1 - Prob. 40PSCh. 5.1 - Prob. 41PSCh. 5.1 - Prob. 42PSCh. 5.1 - Prob. 43PSCh. 5.1 - Prob. 44PSCh. 5.1 - Prob. 45PSCh. 5.1 - Prob. 46PSCh. 5.1 - Prob. 47PSCh. 5.1 - Prob. 48PSCh. 5.1 - Prob. 49PSCh. 5.1 - Prob. 50PSCh. 5.1 - Prob. 51PSCh. 5.1 - Prob. 52PSCh. 5.1 - Prob. 53PSCh. 5.1 - Prob. 54PSCh. 5.1 - Prob. 55PSCh. 5.1 - Problem Solving Level 3 Consider a soldier facing...Ch. 5.1 - Prob. 57PSCh. 5.1 - Prob. 58PSCh. 5.1 - Prob. 59PSCh. 5.1 - Problem Solving Level 3 60. The Vanishing...Ch. 5.2 - IN YOUR OWN WORDS What is a prime number?Ch. 5.2 - Prob. 2PSCh. 5.2 - Prob. 3PSCh. 5.2 - Prob. 4PSCh. 5.2 - Prob. 5PSCh. 5.2 - Prob. 6PSCh. 5.2 - Prob. 7PSCh. 5.2 - Prob. 8PSCh. 5.2 - Prob. 9PSCh. 5.2 - Prob. 10PSCh. 5.2 - Prob. 11PSCh. 5.2 - Prob. 12PSCh. 5.2 - Prob. 13PSCh. 5.2 - Prob. 14PSCh. 5.2 - Find all the prime numbers less than or equal to...Ch. 5.2 - Determine the largest prime you need to consider...Ch. 5.2 - Prob. 17PSCh. 5.2 - Prob. 18PSCh. 5.2 - Prob. 19PSCh. 5.2 - Prob. 20PSCh. 5.2 - Prob. 21PSCh. 5.2 - Prob. 22PSCh. 5.2 - Prob. 23PSCh. 5.2 - Prob. 24PSCh. 5.2 - Prob. 25PSCh. 5.2 - Prob. 26PSCh. 5.2 - Prob. 27PSCh. 5.2 - Prob. 28PSCh. 5.2 - Prob. 29PSCh. 5.2 - Prob. 30PSCh. 5.2 - Prob. 31PSCh. 5.2 - Prob. 32PSCh. 5.2 - Prob. 33PSCh. 5.2 - Prob. 34PSCh. 5.2 - Prob. 35PSCh. 5.2 - Prob. 36PSCh. 5.2 - Prob. 37PSCh. 5.2 - Prob. 38PSCh. 5.2 - Prob. 39PSCh. 5.2 - Two movie theaters, UAI and UAII, start their...Ch. 5.2 - Prob. 41PSCh. 5.2 - Shannon is planning a party and wants to give each...Ch. 5.2 - Boxes that are 12 inches tall are stacked next to...Ch. 5.2 - Hot dogs come in packages of 10, while buns come...Ch. 5.2 - IN YOUR OWN WORDS We used a sieve of Eratosthenes...Ch. 5.2 - Prob. 46PSCh. 5.2 - Prob. 47PSCh. 5.2 - Prob. 48PSCh. 5.2 - Prob. 49PSCh. 5.2 - Prob. 50PSCh. 5.2 - Prob. 51PSCh. 5.2 - Prob. 52PSCh. 5.2 - Prob. 53PSCh. 5.2 - Prob. 54PSCh. 5.2 - Prob. 55PSCh. 5.2 - What is the smallest natural number that is...Ch. 5.2 - Prob. 57PSCh. 5.2 - Prob. 58PSCh. 5.2 - Prob. 59PSCh. 5.2 - Prob. 60PSCh. 5.3 - Prob. 1PSCh. 5.3 - Prob. 2PSCh. 5.3 - Prob. 3PSCh. 5.3 - Prob. 4PSCh. 5.3 - Prob. 5PSCh. 5.3 - Prob. 6PSCh. 5.3 - Prob. 7PSCh. 5.3 - Prob. 8PSCh. 5.3 - Prob. 9PSCh. 5.3 - Prob. 10PSCh. 5.3 - Prob. 11PSCh. 5.3 - Prob. 12PSCh. 5.3 - Prob. 13PSCh. 5.3 - Prob. 14PSCh. 5.3 - Prob. 15PSCh. 5.3 - Prob. 16PSCh. 5.3 - Prob. 17PSCh. 5.3 - Prob. 18PSCh. 5.3 - Prob. 19PSCh. 5.3 - Simplify the expressions in Problems 9-37. a....Ch. 5.3 - Prob. 21PSCh. 5.3 - Prob. 22PSCh. 5.3 - Prob. 23PSCh. 5.3 - Prob. 24PSCh. 5.3 - Prob. 25PSCh. 5.3 - Prob. 26PSCh. 5.3 - Prob. 27PSCh. 5.3 - Prob. 28PSCh. 5.3 - Prob. 29PSCh. 5.3 - Prob. 30PSCh. 5.3 - Prob. 31PSCh. 5.3 - Prob. 32PSCh. 5.3 - Prob. 33PSCh. 5.3 - Prob. 34PSCh. 5.3 - Prob. 35PSCh. 5.3 - Prob. 36PSCh. 5.3 - Prob. 37PSCh. 5.3 - Prob. 38PSCh. 5.3 - Prob. 39PSCh. 5.3 - Prob. 40PSCh. 5.3 - Prob. 41PSCh. 5.3 - Prob. 42PSCh. 5.3 - Prob. 43PSCh. 5.3 - Prob. 44PSCh. 5.3 - Prob. 45PSCh. 5.3 - Prob. 46PSCh. 5.3 - Prob. 47PSCh. 5.3 - Prob. 48PSCh. 5.3 - Prob. 49PSCh. 5.3 - Prob. 50PSCh. 5.3 - Prob. 51PSCh. 5.3 - Prob. 52PSCh. 5.3 - Perform the indicated operations. Let k be a...Ch. 5.3 - Perform the indicated operations. Let k be a...Ch. 5.3 - a. State the commutative property. b. Is ...Ch. 5.3 - Prob. 56PSCh. 5.3 - Prob. 57PSCh. 5.3 - Prob. 58PSCh. 5.3 - Multiply 1,234,5679,999,999 a. using a calculator...Ch. 5.3 - Prob. 60PSCh. 5.4 - IN YOUR OWN WORDS What does it mean for a fraction...Ch. 5.4 - IN YOUR OWN WORDS Describe the process for...Ch. 5.4 - Prob. 3PSCh. 5.4 - Prob. 4PSCh. 5.4 - IN YOUR OWN WORDS Use algebra to show where the...Ch. 5.4 - IN YOUR OWN WORDS Use algebra to show where the...Ch. 5.4 - Completely reduce the fractions in Problems 7-18....Ch. 5.4 - Completely reduce the fractions in Problems 7-18....Ch. 5.4 - Completely reduce the fractions in Problems 7-18....Ch. 5.4 - Completely reduce the fractions in Problems 7-18....Ch. 5.4 - Completely reduce the fractions in problem 7-18....Ch. 5.4 - Completely reduce the fractions in problem 7-18....Ch. 5.4 - Completely reduce the fractions in problem 7-18....Ch. 5.4 - Completely reduce the fractions in problem 7-18....Ch. 5.4 - Completely reduce the fractions in problem 7-18....Ch. 5.4 - Completely reduce the fractions in problem 7-18....Ch. 5.4 - Completely reduce the fractions in problem 7-18....Ch. 5.4 - Completely reduce the fractions in problem 7-18....Ch. 5.4 - Perform the indicated operations in problems...Ch. 5.4 - Perform the indicated operations in problems...Ch. 5.4 - Perform the indicated operations in problems...Ch. 5.4 - Perform the indicated operations in problems...Ch. 5.4 - Perform the indicated operations in problems...Ch. 5.4 - Prob. 24PSCh. 5.4 - Prob. 25PSCh. 5.4 - Prob. 26PSCh. 5.4 - Prob. 27PSCh. 5.4 - Prob. 28PSCh. 5.4 - Prob. 29PSCh. 5.4 - Prob. 30PSCh. 5.4 - Prob. 31PSCh. 5.4 - Prob. 32PSCh. 5.4 - Prob. 33PSCh. 5.4 - Prob. 34PSCh. 5.4 - Prob. 35PSCh. 5.4 - Prob. 36PSCh. 5.4 - Prob. 37PSCh. 5.4 - Prob. 38PSCh. 5.4 - Prob. 39PSCh. 5.4 - Prob. 40PSCh. 5.4 - Prob. 41PSCh. 5.4 - Prob. 42PSCh. 5.4 - Prob. 43PSCh. 5.4 - Prob. 44PSCh. 5.4 - Perform the indicated operations in problems...Ch. 5.4 - Perform the indicated operations in problems...Ch. 5.4 - Prob. 47PSCh. 5.4 - Prob. 48PSCh. 5.4 - Prob. 49PSCh. 5.4 - Prob. 50PSCh. 5.4 - Prob. 51PSCh. 5.4 - Prob. 52PSCh. 5.4 - Prob. 53PSCh. 5.4 - Prob. 54PSCh. 5.4 - Prob. 55PSCh. 5.4 - Prob. 56PSCh. 5.4 - Prob. 57PSCh. 5.4 - Prob. 58PSCh. 5.4 - Prob. 59PSCh. 5.4 - Prob. 60PSCh. 5.5 - Prob. 1PSCh. 5.5 - Prob. 2PSCh. 5.5 - Prob. 3PSCh. 5.5 - Prob. 4PSCh. 5.5 - Prob. 5PSCh. 5.5 - Prob. 6PSCh. 5.5 - Prob. 7PSCh. 5.5 - Prob. 8PSCh. 5.5 - Prob. 9PSCh. 5.5 - Prob. 10PSCh. 5.5 - Prob. 11PSCh. 5.5 - Prob. 12PSCh. 5.5 - Prob. 13PSCh. 5.5 - Prob. 14PSCh. 5.5 - Prob. 15PSCh. 5.5 - Prob. 16PSCh. 5.5 - Prob. 17PSCh. 5.5 - Prob. 18PSCh. 5.5 - Prob. 19PSCh. 5.5 - Prob. 20PSCh. 5.5 - Prob. 21PSCh. 5.5 - Prob. 22PSCh. 5.5 - Prob. 23PSCh. 5.5 - Prob. 24PSCh. 5.5 - Prob. 25PSCh. 5.5 - Prob. 26PSCh. 5.5 - Prob. 27PSCh. 5.5 - Prob. 28PSCh. 5.5 - Prob. 29PSCh. 5.5 - Prob. 30PSCh. 5.5 - Prob. 31PSCh. 5.5 - Prob. 32PSCh. 5.5 - Prob. 33PSCh. 5.5 - Prob. 34PSCh. 5.5 - Prob. 35PSCh. 5.5 - Prob. 36PSCh. 5.5 - Prob. 37PSCh. 5.5 - Prob. 38PSCh. 5.5 - If a carpenter wants to make sure that the corner...Ch. 5.5 - Prob. 40PSCh. 5.5 - An antenna is to be erected and held by guy wires....Ch. 5.5 - Prob. 42PSCh. 5.5 - Prob. 43PSCh. 5.5 - Prob. 44PSCh. 5.5 - Prob. 45PSCh. 5.5 - Prob. 46PSCh. 5.5 - Prob. 47PSCh. 5.5 - Prob. 48PSCh. 5.5 - Prob. 49PSCh. 5.5 - Prob. 50PSCh. 5.5 - Prob. 51PSCh. 5.5 - Prob. 52PSCh. 5.5 - Prob. 53PSCh. 5.5 - Prob. 54PSCh. 5.5 - Prob. 55PSCh. 5.5 - Prob. 56PSCh. 5.5 - Prob. 57PSCh. 5.5 - Prob. 58PSCh. 5.5 - Prob. 59PSCh. 5.5 - Prob. 60PSCh. 5.6 - Prob. 1PSCh. 5.6 - Prob. 2PSCh. 5.6 - Prob. 3PSCh. 5.6 - Prob. 4PSCh. 5.6 - Prob. 5PSCh. 5.6 - Prob. 6PSCh. 5.6 - Prob. 7PSCh. 5.6 - Tell whether each number is an element of N a...Ch. 5.6 - Prob. 9PSCh. 5.6 - Prob. 10PSCh. 5.6 - Express each of the numbers in Problems 9-12 as a...Ch. 5.6 - Prob. 12PSCh. 5.6 - Prob. 13PSCh. 5.6 - Prob. 14PSCh. 5.6 - Prob. 15PSCh. 5.6 - Prob. 16PSCh. 5.6 - Prob. 17PSCh. 5.6 - Prob. 18PSCh. 5.6 - Prob. 19PSCh. 5.6 - Prob. 20PSCh. 5.6 - Prob. 21PSCh. 5.6 - Prob. 22PSCh. 5.6 - Prob. 23PSCh. 5.6 - Prob. 24PSCh. 5.6 - Prob. 25PSCh. 5.6 - Carry out the operations with decimal forms in...Ch. 5.6 - Prob. 27PSCh. 5.6 - Prob. 28PSCh. 5.6 - Prob. 29PSCh. 5.6 - Prob. 30PSCh. 5.6 - Prob. 31PSCh. 5.6 - Prob. 32PSCh. 5.6 - Prob. 33PSCh. 5.6 - Prob. 34PSCh. 5.6 - Prob. 35PSCh. 5.6 - Prob. 36PSCh. 5.6 - Prob. 37PSCh. 5.6 - Prob. 38PSCh. 5.6 - Prob. 39PSCh. 5.6 - Prob. 40PSCh. 5.6 - Prob. 41PSCh. 5.6 - Prob. 42PSCh. 5.6 - Prob. 43PSCh. 5.6 - Prob. 44PSCh. 5.6 - Prob. 45PSCh. 5.6 - Prob. 46PSCh. 5.6 - Prob. 47PSCh. 5.6 - Prob. 48PSCh. 5.6 - Prob. 49PSCh. 5.6 - Prob. 50PSCh. 5.6 - Prob. 51PSCh. 5.6 - Prob. 52PSCh. 5.6 - Prob. 53PSCh. 5.6 - Prob. 54PSCh. 5.6 - Prob. 55PSCh. 5.6 - Let be an arbitrary operation in Problems 52-59....Ch. 5.6 - Let be an arbitrary operation in Problems 52-59....Ch. 5.6 - Prob. 58PSCh. 5.6 - Prob. 59PSCh. 5.6 - Prob. 60PSCh. 5.7 - Level 1. IN YOUR OWN WORDS. What do we mean by...Ch. 5.7 - Prob. 2PSCh. 5.7 - Prob. 3PSCh. 5.7 - Prob. 4PSCh. 5.7 - Prob. 5PSCh. 5.7 - Prob. 6PSCh. 5.7 - Level 1. Perform the indicated operations in...Ch. 5.7 - Prob. 8PSCh. 5.7 - Prob. 9PSCh. 5.7 - Prob. 10PSCh. 5.7 - Prob. 11PSCh. 5.7 - Prob. 12PSCh. 5.7 - Prob. 13PSCh. 5.7 - Prob. 14PSCh. 5.7 - Prob. 15PSCh. 5.7 - Prob. 16PSCh. 5.7 - Prob. 17PSCh. 5.7 - Prob. 18PSCh. 5.7 - Prob. 19PSCh. 5.7 - Prob. 20PSCh. 5.7 - Prob. 21PSCh. 5.7 - Prob. 22PSCh. 5.7 - Prob. 23PSCh. 5.7 - Prob. 24PSCh. 5.7 - Prob. 25PSCh. 5.7 - Prob. 26PSCh. 5.7 - Prob. 27PSCh. 5.7 - Prob. 28PSCh. 5.7 - Prob. 29PSCh. 5.7 - Prob. 30PSCh. 5.7 - Prob. 31PSCh. 5.7 - Prob. 32PSCh. 5.7 - Prob. 33PSCh. 5.7 - Prob. 34PSCh. 5.7 - Prob. 35PSCh. 5.7 - Level 2. If you know that your aunt in Problem 34...Ch. 5.7 - Prob. 37PSCh. 5.7 - Prob. 38PSCh. 5.7 - Prob. 39PSCh. 5.7 - Prob. 40PSCh. 5.7 - Prob. 41PSCh. 5.7 - Prob. 42PSCh. 5.7 - Prob. 43PSCh. 5.7 - Prob. 44PSCh. 5.7 - Prob. 45PSCh. 5.7 - Prob. 46PSCh. 5.7 - Prob. 47PSCh. 5.7 - Prob. 48PSCh. 5.7 - Prob. 49PSCh. 5.7 - Prob. 50PSCh. 5.7 - Prob. 51PSCh. 5.7 - Prob. 52PSCh. 5.7 - Prob. 53PSCh. 5.7 - Prob. 54PSCh. 5.7 - Prob. 55PSCh. 5.7 - Prob. 56PSCh. 5.7 - Prob. 57PSCh. 5.7 - Prob. 58PSCh. 5.7 - Prob. 59PSCh. 5.7 - Prob. 60PSCh. 5.8 - Prob. 1PSCh. 5.8 - Prob. 2PSCh. 5.8 - Prob. 3PSCh. 5.8 - Prob. 4PSCh. 5.8 - Prob. 5PSCh. 5.8 - Prob. 6PSCh. 5.8 - Prob. 7PSCh. 5.8 - Prob. 8PSCh. 5.8 - Prob. 9PSCh. 5.8 - Number the letters of the alphabet from 1 to 26;...Ch. 5.8 - Prob. 11PSCh. 5.8 - Prob. 12PSCh. 5.8 - Prob. 13PSCh. 5.8 - Prob. 14PSCh. 5.8 - Prob. 15PSCh. 5.8 - Prob. 16PSCh. 5.8 - Prob. 17PSCh. 5.8 - Prob. 18PSCh. 5.8 - Prob. 19PSCh. 5.8 - Prob. 20PSCh. 5.8 - Prob. 21PSCh. 5.8 - Prob. 22PSCh. 5.8 - Prob. 23PSCh. 5.8 - Prob. 24PSCh. 5.8 - Prob. 25PSCh. 5.8 - Prob. 26PSCh. 5.8 - Prob. 27PSCh. 5.8 - Prob. 28PSCh. 5.8 - Prob. 29PSCh. 5.8 - Prob. 30PSCh. 5.8 - Prob. 31PSCh. 5.8 - Give the decoding key for the encoding keys in...Ch. 5.8 - Prob. 33PSCh. 5.8 - Prob. 34PSCh. 5.8 - Prob. 35PSCh. 5.8 - Prob. 36PSCh. 5.8 - Prob. 37PSCh. 5.8 - Prob. 38PSCh. 5.8 - Prob. 39PSCh. 5.8 - Use Figure 5.25 to encode or decode the messages...Ch. 5.8 - Prob. 41PSCh. 5.8 - Prob. 42PSCh. 5.8 - Prob. 43PSCh. 5.8 - Prob. 44PSCh. 5.8 - Prob. 45PSCh. 5.8 - Prob. 46PSCh. 5.8 - Prob. 47PSCh. 5.8 - Prob. 48PSCh. 5.8 - Prob. 51PSCh. 5.8 - Prob. 52PSCh. 5.8 - Prob. 53PSCh. 5.8 - Prob. 54PSCh. 5.8 - Prob. 55PSCh. 5.8 - Prob. 56PSCh. 5.8 - Prob. 57PSCh. 5.8 - Prob. 58PSCh. 5.8 - Prob. 59PSCh. 5.8 - Prob. 60PSCh. 5.CR - Prob. 1CRCh. 5.CR - Prob. 2CRCh. 5.CR - Prob. 3CRCh. 5.CR - Prob. 4CRCh. 5.CR - Reduce each fraction. If it is reduced, so state....Ch. 5.CR - Prob. 6CRCh. 5.CR - Prob. 7CRCh. 5.CR - Prob. 8CRCh. 5.CR - Prob. 9CRCh. 5.CR - Prob. 10CRCh. 5.CR - Prob. 11CRCh. 5.CR - Prob. 12CRCh. 5.CR - Prob. 13CRCh. 5.CR - Prob. 14CRCh. 5.CR - Prob. 15CRCh. 5.CR - Prob. 16CRCh. 5.CR - Prob. 17CRCh. 5.CR - Do You Weigh Too Much? In the United States, an...Ch. 5.CR - Prob. 19CRCh. 5.CR - Prob. 20CR
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