Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00 Edition
ISBN: 9780395977224
Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher: McDougal Littell
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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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Question
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Chapter 2.1, Problem 37WE

a.

To determine

To find: the values of (7−4)−2 and 7−(4−2) .

a.

Expert Solution
Check Mark

Answer to Problem 37WE

  (7−4)−2=1

  7−(4−2)=5

Explanation of Solution

Concept Used:

While solving the expressions, first perform the operations within the grouping symbol. Then start from the left and perform the multiplication or division as it appears in the expression on going towards right. After that again start from the left and perform the additions or subtractions as it appears in the expression on going towards right.

Consider the expression,

  (7−4)−2

First perform the subtraction within the parenthesis:

  (7−4)−2=3−2=1

Now consider the expression,

  7−(4−2)

First perform the subtraction within the parenthesis:

  7−(4−2)=7−2=5

b.

To determine

To explain: is the subtraction of real numbers associative.

b.

Expert Solution
Check Mark

Answer to Problem 37WE

No

Explanation of Solution

No, the subtraction of real numbers is not associative.

As for subtraction of real numbers to be associative, it must be true that for the real numbers a, b and c ,

  a−(b−c)=(a−b)−c

To prove the claim that the subtraction of real numbers is not associative, consider the counter example from part (a).

As shown in part (a),

  (7−4)−2=1

  7−(4−2)=5

So, clearly (7−4)−2≠7−(4−2)

Hence, subtraction of real numbers is not associative.

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Chapter 2.1, Problem 36WE
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Chapter 2.1, Problem 38WE

Chapter 2 Solutions

Algebra: Structure And Method, Book 1

Ch. 2.1 - Prob. 1OECh. 2.1 - Prob. 2OECh. 2.1 - Prob. 3OECh. 2.1 - Prob. 4OECh. 2.1 - Prob. 5OECh. 2.1 - Prob. 6OECh. 2.1 - Prob. 7OECh. 2.1 - Prob. 8OECh. 2.1 - Prob. 9OECh. 2.1 - Prob. 10OE
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Prob. 59WECh. 2.4 - Prob. 60WECh. 2.4 - Prob. 61WECh. 2.4 - Prob. 62WECh. 2.4 - Prob. 1PCh. 2.4 - Prob. 2PCh. 2.4 - Prob. 3PCh. 2.4 - Prob. 4PCh. 2.4 - Prob. 5PCh. 2.4 - Prob. 6PCh. 2.4 - Prob. 7PCh. 2.4 - Prob. 8PCh. 2.4 - Prob. 9PCh. 2.4 - Prob. 10PCh. 2.4 - Prob. 11PCh. 2.4 - Prob. 12PCh. 2.4 - Prob. 1MRECh. 2.4 - Prob. 2MRECh. 2.4 - Prob. 3MRECh. 2.4 - Prob. 4MRECh. 2.4 - Prob. 5MRECh. 2.4 - Prob. 6MRECh. 2.4 - Prob. 7MRECh. 2.4 - Prob. 8MRECh. 2.4 - Prob. 9MRECh. 2.4 - Prob. 10MRECh. 2.4 - Prob. 11MRECh. 2.4 - Prob. 12MRECh. 2.4 - Prob. 1STCh. 2.4 - Prob. 2STCh. 2.4 - Prob. 3STCh. 2.4 - Prob. 4STCh. 2.4 - Prob. 5STCh. 2.4 - Prob. 6STCh. 2.4 - Prob. 7STCh. 2.4 - Prob. 8STCh. 2.4 - Prob. 9STCh. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.5 - Prob. 1OECh. 2.5 - Prob. 2OECh. 2.5 - Prob. 3OECh. 2.5 - Prob. 4OECh. 2.5 - Prob. 5OECh. 2.5 - Prob. 6OECh. 2.5 - Prob. 7OECh. 2.5 - Prob. 8OECh. 2.5 - Prob. 9OECh. 2.5 - Prob. 10OECh. 2.5 - Prob. 11OECh. 2.5 - 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Prob. 10MRECh. 2.5 - Prob. 11MRECh. 2.5 - Prob. 12MRECh. 2.6 - Prob. 1OECh. 2.6 - Prob. 2OECh. 2.6 - Prob. 3OECh. 2.6 - Prob. 4OECh. 2.6 - Prob. 5OECh. 2.6 - Prob. 6OECh. 2.6 - Prob. 7OECh. 2.6 - Prob. 8OECh. 2.6 - Prob. 9OECh. 2.6 - Prob. 10OECh. 2.6 - Prob. 11OECh. 2.6 - Prob. 12OECh. 2.6 - Prob. 13OECh. 2.6 - Prob. 14OECh. 2.6 - Prob. 15OECh. 2.6 - Prob. 16OECh. 2.6 - Prob. 17OECh. 2.6 - Prob. 18OECh. 2.6 - Prob. 19OECh. 2.6 - Prob. 20OECh. 2.6 - Prob. 21OECh. 2.6 - Prob. 22OECh. 2.6 - Prob. 23OECh. 2.6 - Prob. 24OECh. 2.6 - Prob. 25OECh. 2.6 - Prob. 26OECh. 2.6 - Prob. 27OECh. 2.6 - Prob. 28OECh. 2.6 - Prob. 29OECh. 2.6 - Prob. 30OECh. 2.6 - Prob. 1WECh. 2.6 - Prob. 2WECh. 2.6 - Prob. 3WECh. 2.6 - Prob. 4WECh. 2.6 - Prob. 5WECh. 2.6 - Prob. 6WECh. 2.6 - Prob. 7WECh. 2.6 - Prob. 8WECh. 2.6 - Prob. 9WECh. 2.6 - Prob. 10WECh. 2.6 - Prob. 11WECh. 2.6 - Prob. 12WECh. 2.6 - Prob. 13WECh. 2.6 - Prob. 14WECh. 2.6 - Prob. 15WECh. 2.6 - Prob. 16WECh. 2.6 - Prob. 17WECh. 2.6 - Prob. 18WECh. 2.6 - 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Prob. 3STCh. 2.7 - Prob. 4STCh. 2.7 - Prob. 5STCh. 2.7 - Prob. 6STCh. 2.7 - Prob. 7STCh. 2.7 - Prob. 8STCh. 2.7 - Prob. 9STCh. 2.7 - Prob. 10STCh. 2.8 - Prob. 1OECh. 2.8 - Prob. 2OECh. 2.8 - Prob. 3OECh. 2.8 - Prob. 4OECh. 2.8 - Prob. 5OECh. 2.8 - Prob. 6OECh. 2.8 - Prob. 7OECh. 2.8 - Prob. 8OECh. 2.8 - Prob. 9OECh. 2.8 - Prob. 10OECh. 2.8 - Prob. 11OECh. 2.8 - Prob. 12OECh. 2.8 - Prob. 13OECh. 2.8 - Prob. 14OECh. 2.8 - Prob. 15OECh. 2.8 - Prob. 16OECh. 2.8 - Prob. 17OECh. 2.8 - Prob. 18OECh. 2.8 - Prob. 19OECh. 2.8 - Prob. 20OECh. 2.8 - Prob. 21OECh. 2.8 - Prob. 22OECh. 2.8 - Prob. 23OECh. 2.8 - Prob. 24OECh. 2.8 - Prob. 25OECh. 2.8 - Prob. 1WECh. 2.8 - Prob. 2WECh. 2.8 - Prob. 3WECh. 2.8 - Prob. 4WECh. 2.8 - Prob. 5WECh. 2.8 - Prob. 6WECh. 2.8 - Prob. 7WECh. 2.8 - Prob. 8WECh. 2.8 - Prob. 9WECh. 2.8 - Prob. 10WECh. 2.8 - Prob. 11WECh. 2.8 - Prob. 12WECh. 2.8 - Prob. 13WECh. 2.8 - Prob. 14WECh. 2.8 - Prob. 15WECh. 2.8 - Prob. 16WECh. 2.8 - Prob. 17WECh. 2.8 - Prob. 18WECh. 2.8 - Prob. 19WECh. 2.8 - Prob. 20WECh. 2.8 - Prob. 21WECh. 2.8 - Prob. 22WECh. 2.8 - Prob. 23WECh. 2.8 - Prob. 24WECh. 2.8 - Prob. 25WECh. 2.8 - Prob. 26WECh. 2.8 - Prob. 27WECh. 2.8 - Prob. 28WECh. 2.8 - Prob. 29WECh. 2.8 - Prob. 30WECh. 2.8 - Prob. 31WECh. 2.8 - Prob. 32WECh. 2.8 - Prob. 33WECh. 2.8 - Prob. 34WECh. 2.8 - Prob. 35WECh. 2.8 - Prob. 36WECh. 2.8 - Prob. 1MRECh. 2.8 - Prob. 2MRECh. 2.8 - Prob. 3MRECh. 2.8 - Prob. 4MRECh. 2.8 - Prob. 5MRECh. 2.8 - Prob. 6MRECh. 2.8 - Prob. 7MRECh. 2.8 - Prob. 8MRECh. 2.8 - Prob. 9MRECh. 2.8 - Prob. 10MRECh. 2.9 - Prob. 1OECh. 2.9 - Prob. 2OECh. 2.9 - Prob. 3OECh. 2.9 - Prob. 4OECh. 2.9 - Prob. 5OECh. 2.9 - Prob. 6OECh. 2.9 - Prob. 7OECh. 2.9 - Prob. 8OECh. 2.9 - Prob. 9OECh. 2.9 - Prob. 10OECh. 2.9 - Prob. 11OECh. 2.9 - Prob. 12OECh. 2.9 - Prob. 13OECh. 2.9 - Prob. 14OECh. 2.9 - Prob. 15OECh. 2.9 - Prob. 16OECh. 2.9 - Prob. 17OECh. 2.9 - Prob. 18OECh. 2.9 - Prob. 19OECh. 2.9 - Prob. 20OECh. 2.9 - Prob. 21OECh. 2.9 - Prob. 22OECh. 2.9 - Prob. 23OECh. 2.9 - Prob. 24OECh. 2.9 - Prob. 1WECh. 2.9 - Prob. 2WECh. 2.9 - Prob. 3WECh. 2.9 - Prob. 4WECh. 2.9 - Prob. 5WECh. 2.9 - Prob. 6WECh. 2.9 - Prob. 7WECh. 2.9 - Prob. 8WECh. 2.9 - Prob. 9WECh. 2.9 - Prob. 10WECh. 2.9 - Prob. 11WECh. 2.9 - Prob. 12WECh. 2.9 - Prob. 13WECh. 2.9 - Prob. 14WECh. 2.9 - Prob. 15WECh. 2.9 - Prob. 16WECh. 2.9 - Prob. 17WECh. 2.9 - Prob. 18WECh. 2.9 - Prob. 19WECh. 2.9 - Prob. 20WECh. 2.9 - Prob. 21WECh. 2.9 - Prob. 22WECh. 2.9 - Prob. 23WECh. 2.9 - Prob. 24WECh. 2.9 - Prob. 25WECh. 2.9 - Prob. 26WECh. 2.9 - Prob. 27WECh. 2.9 - Prob. 28WECh. 2.9 - Prob. 29WECh. 2.9 - Prob. 30WECh. 2.9 - Prob. 31WECh. 2.9 - Prob. 32WECh. 2.9 - Prob. 33WECh. 2.9 - Prob. 34WECh. 2.9 - Prob. 35WECh. 2.9 - Prob. 1MRECh. 2.9 - Prob. 2MRECh. 2.9 - Prob. 3MRECh. 2.9 - Prob. 4MRECh. 2.9 - Prob. 5MRECh. 2.9 - Prob. 6MRECh. 2.9 - Prob. 7MRECh. 2.9 - Prob. 8MRECh. 2.9 - Prob. 9MRECh. 2.9 - Prob. 10MRECh. 2.9 - Prob. 11MRECh. 2.9 - Prob. 12MRECh. 2.9 - Prob. 1STCh. 2.9 - Prob. 2STCh. 2.9 - Prob. 3STCh. 2.9 - Prob. 4STCh. 2.9 - Prob. 5STCh. 2.9 - Prob. 6STCh. 2.9 - Prob. 7STCh. 2.9 - Prob. 8STCh. 2.9 - Prob. 1ECh. 2.9 - Prob. 2ECh. 2.9 - Prob. 3ECh. 2.9 - Prob. 4ECh. 2.9 - Prob. 5ECh. 2.9 - Prob. 6ECh. 2.9 - Prob. 7ECh. 2.9 - Prob. 8ECh. 2 - Prob. 1CRCh. 2 - Prob. 2CRCh. 2 - Prob. 3CRCh. 2 - Prob. 4CRCh. 2 - Prob. 5CRCh. 2 - Prob. 6CRCh. 2 - Prob. 7CRCh. 2 - Prob. 8CRCh. 2 - Prob. 9CRCh. 2 - Prob. 10CRCh. 2 - Prob. 11CRCh. 2 - Prob. 12CRCh. 2 - Prob. 13CRCh. 2 - Prob. 14CRCh. 2 - Prob. 15CRCh. 2 - Prob. 16CRCh. 2 - Prob. 1CTCh. 2 - Prob. 2CTCh. 2 - Prob. 3CTCh. 2 - Prob. 4CTCh. 2 - Prob. 5CTCh. 2 - Prob. 6CTCh. 2 - Prob. 7CTCh. 2 - Prob. 8CTCh. 2 - Prob. 9CTCh. 2 - Prob. 10CTCh. 2 - Prob. 11CTCh. 2 - Prob. 12CTCh. 2 - Prob. 13CTCh. 2 - Prob. 14CTCh. 2 - Prob. 15CTCh. 2 - Prob. 16CTCh. 2 - Prob. 17CTCh. 2 - Prob. 18CTCh. 2 - Prob. 19CTCh. 2 - Prob. 20CTCh. 2 - Prob. 21CTCh. 2 - Prob. 22CTCh. 2 - Prob. 23CTCh. 2 - Prob. 24CTCh. 2 - Prob. 25CTCh. 2 - Prob. 1CLRCh. 2 - Prob. 2CLRCh. 2 - Prob. 3CLRCh. 2 - Prob. 4CLRCh. 2 - Prob. 5CLRCh. 2 - Prob. 6CLRCh. 2 - Prob. 7CLRCh. 2 - Prob. 8CLRCh. 2 - Prob. 9CLRCh. 2 - Prob. 10CLRCh. 2 - Prob. 11CLRCh. 2 - Prob. 12CLRCh. 2 - Prob. 13CLRCh. 2 - Prob. 14CLRCh. 2 - Prob. 15CLRCh. 2 - Prob. 16CLRCh. 2 - Prob. 17CLRCh. 2 - Prob. 18CLRCh. 2 - Prob. 19CLRCh. 2 - Prob. 20CLRCh. 2 - Prob. 21CLRCh. 2 - Prob. 22CLRCh. 2 - Prob. 23CLRCh. 2 - Prob. 24CLRCh. 2 - Prob. 25CLRCh. 2 - Prob. 26CLRCh. 2 - Prob. 27CLRCh. 2 - Prob. 28CLRCh. 2 - Prob. 29CLRCh. 2 - Prob. 30CLRCh. 2 - Prob. 31CLRCh. 2 - Prob. 32CLRCh. 2 - Prob. 33CLRCh. 2 - Prob. 34CLRCh. 2 - Prob. 35CLRCh. 2 - Prob. 1MSCh. 2 - Prob. 2MSCh. 2 - Prob. 3MSCh. 2 - Prob. 4MSCh. 2 - Prob. 5MSCh. 2 - Prob. 6MSCh. 2 - Prob. 7MSCh. 2 - Prob. 8MSCh. 2 - Prob. 9MSCh. 2 - Prob. 10MSCh. 2 - Prob. 11MSCh. 2 - Prob. 12MSCh. 2 - Prob. 13MSCh. 2 - Prob. 14MSCh. 2 - Prob. 15MSCh. 2 - Prob. 16MSCh. 2 - Prob. 17MSCh. 2 - Prob. 18MSCh. 2 - Prob. 19MSCh. 2 - Prob. 20MSCh. 2 - Prob. 21MSCh. 2 - Prob. 22MSCh. 2 - Prob. 23MSCh. 2 - Prob. 24MSCh. 2 - Prob. 25MSCh. 2 - Prob. 26MSCh. 2 - Prob. 27MSCh. 2 - Prob. 28MSCh. 2 - Prob. 29MSCh. 2 - Prob. 30MSCh. 2 - Prob. 31MSCh. 2 - Prob. 32MSCh. 2 - Prob. 33MSCh. 2 - Prob. 34MS

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