Expression Math

6 Key excerpts on "Expression Math"

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  eBook - ePub

  Introductory Algebra

  • Chris Nord(Author)
  • 2021(Publication Date)
  • Chemeketa Press

    (Publisher)

  CHAPTER 4

  Expressions

  What is a Number?

  The English language is full of figures of speech — such as “beating around the bush” — that we use to explain ideas. These are phrases that have meaning beyond their literal, word-for-word interpretation. When we say we’re “beating around the bush,” we mean avoiding a major, important topic by addressing minor, unimportant topics instead. If someone asks us what we’re beating, we say something like “Oh, that’s just an expression,” a combination of words that work together to create meaning.

  In math, an expression is a combination of numbers, variables, and operation symbols that together have meaning. In math, the meaning of an expression is a number. In this chapter, we will distinguish between

  arithmetic expressions

  , which are expressions that don’t contain variables, and

  algebraic expressions

  , which do contain variables.

  4.1 Introduction to Expressions

  In this section, you will learn how to evaluate arithmetic and algebraic expressions. You will also learn how to represent and interpret measurements in scientific notation. Finally, we will officially introduce formulas and learn two important ones — the area formula for a rectangle and the area formula for a triangle.

  A. Arithmetic Expressions

  An arithmetic expression is a combination of numbers and operation symbols. This can be as simple as a single number, such as 23, or it can be a much more complicated combination of numbers and operation symbols, such as .

  An arithmetic expression can always be evaluated by performing each of the operations correctly and in the correct order. Once an arithmetic expression has been evaluated, it can then be replaced with its number value. Both the original expression and its evaluated form have the same meaning.

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  Technical Mathematics with Calculus

  • Michael A. Calter, Paul A. Calter, Paul Wraight, Sarah White(Authors)
  • 2016(Publication Date)
  • Wiley

    (Publisher)

  What is Algebra? Understanding the fundamental rules of algebra is important in order to calculate results for a wide variety of situations in science and technology. Algebra is a language of mathematics that is based on generalized arithmetic using letters to represent numbers in expressions, equations, or formulas. 2 ⋅ 2 ⋅ 2 ⋅ 2 = 2 4 translates to a ⋅ a ⋅ a ⋅ a = a 4 and more generally a a a a a a n n factors        ( )( )( )( ) ( ) = The material in this chapter is the foundation on which other later chapters in this book are built, so your understanding of the concepts in this chapter is important. 2 ◆◆◆ OBJECTIVES ◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆◆ When you have completed this chapter, you should be able to: • Identify and understand all the components (literal terms, constants, and variables) that make up algebra. • Add and subtract algebraic expressions and identify groups using symbols like parentheses and brackets. • Complete operations using integral exponents and remove groups of symbols in algebraic expressions. • Complete operations with algebraic expressions using multiplication. • Complete operations with algebraic expressions using division. Introduction to Algebra 2–1 Algebraic Expressions Mathematical Expressions A mathematical expression is a grouping of mathematical symbols, such as signs of operation, numbers, and letters. ◆◆◆ Example 1: The following are mathematical expressions: (a) x 2 - 2x + 3 (b) x 5 sin 3 ⋅ (c) + x e 5 log x 2 ◆◆◆ 41 Section 2–1 ◆ Algebraic Expressions Algebraic and Transcendental Expressions An algebraic expression is one containing algebraic symbols and operations (addition, subtrac- tion, multiplication, division, roots, and powers), such as in Example 1(a). A transcendental expression, such as in Examples 1(b) and (c), contains trigonometric, exponential, or logarith- mic functions. Equations None of the expressions in Example 1 contains an equal sign ( = ).

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  eBook - ePub

  Common Core Standards for Middle School Mathematics

  A Quick-Start Guide

  • Amitra Schwols, Kathleen Dempsey, John Kendall(Authors)
  • 2013(Publication Date)
  • ASCD

    (Publisher)

  Chapter 4

  Expressions and Equations

  . . . . . . . . . . . . . . . . . . . .

  The introduction to the Common Core standards' high school Algebra domain provides some useful definitions to help differentiate the two mathematical terms expression and equation:

  An expression is a record of a computation with numbers, symbols that represent numbers, arithmetic operations, exponentiation, and, at more advanced levels, the operation of evaluating a function…. An equation is a statement of equality between two expressions, often viewed as a question asking for which values of the variables the expressions on either side are in fact equal. These values are the solutions to the equation. (CCSSI, 2010c, p. 62)

  The middle school Expressions and Equations (EE) domain provides a critical bridge between content in the Operations and Algebraic Thinking domain in earlier grades and algebraic content students will encounter in high school. Figure 4.1 shows an overview of the Expressions and Equations domain's clusters and standards by grade level.

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  eBook - PDF

  Elementary Algebra

  • Alan Tussy, R. Gustafson(Authors)
  • 2012(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  Since problems in algebra are often presented in words, the ability to interpret what you read is important. In this section, we will introduce several strategies that will help you translate English words into algebraic expressions. Identify Terms and Coefficients of Terms. Recall that variables and/or numbers can be combined with the operations of arithmetic to create algebraic expressions. Addition symbols separate expressions into parts called terms. For example, the expression has two terms. 8 First term Second term x x 8 Write each expression in simpler form. Identify each of the following expressions as either a sum, difference, product, or quotient. Copyright 201 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. Since subtraction can be written as addition of the opposite, the expression has three terms. First term Second term Third term In general, a term is a product or quotient of numbers and/or variables. A single number or variable is also a term. Examples of terms are: 4, , , , , , The numerical factor of a term is called the coefficient of the term. For instance, the term has a coefficient of 6 because . The coefficient of is because . More examples are shown below. A term such as 4, that consists of a single number, is called a constant term. 15 ab 2 15 ab 2 15 15 ab 2 6 r 6 r 6 r 15 ab 2 3 n 3.7 x 5 w 3 6 r y ( 9) ( 3 a ) a 2 a 2 3 a 9 a 2 3 a 9 1.8 Algebraic Expressions 69 Term Coefficient 8 1 27 27 1 t x 1 6 x 6 3 4 3 4 b 0.9 0.9 pq 8 y 2 This term also could be written as .

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  eBook - PDF

  PreStatistics

  • Donald Davis, William Armstrong, Mike McCraith, , Donald Davis, William Armstrong, Mike McCraith(Authors)
  • 2018(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  55 r.nagy/Shutterstock.com Chapter 2 CHAPTER CONTENTS Section 2.1 Translating English to Algebra: Expressions, Equations, and Inequalities Section 2.2 Order of Operations and Evaluating Numerical Expressions Section 2.3 Basics of Solving Linear Equations Algebraic Expressions Used in Statistics and Basics of Solving Equations 56 CHAPTER 2 • Algebraic Expressions Used in Statistics and Basics of Solving Equations SECTION 2.1 Translating English to Algebra: Expressions, Equations, and Inequalities When most people think of arithmetic and algebra, what comes to mind is a page full of numbers and letters, with very few words or sentences associated with them. Statistics is a bit different. Many applications in statistics are based on situations that are presented in narrative form, with our task being to translate that narrative into mathematics. In this section, we learn how to translate English into algebra. OBJECTIVE 1 Differentiate between an Expression and an Equation What differentiates arithmetic from algebra is that algebra is the part of mathematics in which letters are used to represent numbers that are either unknown or change from time to time. These letters are known as variables . Commonly used variables include x , y , z , n , t , and so on. In statistics, some variables are denoted by lower case Greek letters such as m (pronounced “mu”), s (pronounced “sigma”), l (pronounced “lambda”), and x (pronounced “kai”). If we place a real number in front or behind a variable, we call that number a coefficient . For our purposes, many of the coefficients will be represented by rational numbers. Together, variables and coefficients make up algebraic terms . Terms that are separated with addition and subtraction signs are called algebraic expressions .

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  eBook - PDF

  Mathematics for Machine Technology

  • John Peterson, Robert Smith(Authors)
  • 2019(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  244 Fundamentals of Algebra 4 UNIT 39 Symbolism and Algebraic Expressions OBJECTIVES After studying this unit you should be able to ● ● Express word statements as algebraic expressions. ● ● Express diagram dimensions as algebraic expressions. ● ● Evaluate algebraic expressions by substituting numbers for symbols. Algebra is a branch of mathematics in which letters are used to represent numbers. By the use of letters, general rules called formulas can be stated mathematically. Algebra is an extension of arithmetic; therefore, the rules and procedures that apply to arithmetic also apply to algebra. Many problems that are difficult or impossible to solve by arithmetic can be solved by algebra. The basic principles of algebra discussed in this text are intended to provide a practical background for machine shop applications. A knowledge of algebraic fundamentals is essential in the use of trade handbooks and for the solutions of many geometric and trigonometric problems. SYMBOLISM Symbols are the language of algebra. Both arithmetic numbers and literal numbers are used in algebra. Arithmetic numbers are numbers that have definite numerical values, such as 4, 5.17, and 7 8 . Literal numbers are letters that represent arithmetic numbers, such as a, x, V, and P . Depending on how it is used, a literal number can represent one particular arith-metic number, a wide range of numerical values, or all numerical values. Customarily, the multiplication sign s 3 d is not used in algebra, because it can be misin-terpreted as the letter x . When a literal number is multiplied by a numerical value, or when two or more literal numbers are multiplied, no sign of operation is required. SECTION FOUR UNIT 39 SYMBOLISM AND ALGEBRAIC EXPRESSIONS 245 Examples 1. 5 times a is written 5 a 2. 17 times c is written 17 c 3.

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