Mixed Expressions

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  eBook - ePub

  Years 6 - 8 Maths For Students

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  What good is algebra? That question is a common one, and it deserves a decent answer. Algebra is used for solving problems that are just too difficult for ordinary arithmetic. And because number crunching is so much a part of the modern world, algebra is everywhere (even if you don’t see it): Architecture, engineering, medicine, statistics, computers, business, chemistry, physics, biology, and, of course, higher math. Anywhere numbers are useful, algebra is there.

  In this chapter, I introduce (or reintroduce) you to that elusive little fellow, Mr x, in a way that’s bound to make him seem a little friendlier. Then I show you how algebraic expressions are similar to and different from the arithmetic expressions that you’re used to working with. (For a refresher on arithmetic expressions, see Chapters 2 and 3 .)

  Expressing Yourself with Algebraic Expressions

  In this chapter, I introduce you to a new type of mathematical expression: The algebraic expression. An algebraic expression is any string of mathematical symbols that can be placed on one side of an equation and that includes at least one variable.

  Here are a few examples of algebraic expressions:

  2x + 3y

  14p − 7 + 2c

  8px2 + 9abc3

  The difference between arithmetic and algebraic expressions is simply that an algebraic expression includes at least one variable.

  In this section, I show you how to work with algebraic expressions. First, I show you how to separate an algebraic expression into one or more terms, and I walk through how to identify the coefficient and the variable part of each term.

  Coming to algebraic terms

  A term in an algebraic expression is any chunk of symbols set off from the rest of the expression by either addition or subtraction. As algebraic expressions get more complex, they begin to string themselves out in more terms. Here are some examples:

  Expression	Number of Terms	Terms
  5x	One	5x
  −5x + 2	Two	−5x and 2
  	Four	x2 y, , −xyz, and 8

  No matter how complicated an algebraic expression gets, you can always separate it out into one or more terms.

  When separating an algebraic expression into terms, group the plus or minus sign with the term that it immediately precedes.

  When a term has a variable, it’s called an algebraic term. When it doesn’t have a variable, it’s called a constant. For example, look at the following expression:

  The first three terms are algebraic terms and the last term is a constant. As you can see, in algebra, constant is just a fancy word for number.

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