Writing Algebraic Expressions

Writing Algebraic Expressions

Problem:	Ms. Jensen likes to divide her class into groups of 2. Use mathematical symbols to represent all the students in her class.
Solution:	Let g represent the number of groups in Ms. Jensen's class.
	Then 2 · g, or 2g can represent "g groups of 2 students".

In the problem above, the variable g represents the number of groups in Ms. Jensen's class. A variable is a symbol used to represent a number in an expression or an equation. The value of this number can vary (change). Let's look at an example in which we use a variable.

Example 1:	Write each phrase as a mathematical expression.
	Phrase Expression the sum of nine and eight 9 + 8 the sum of nine and a number x 9 + x

The expression 9 + 8 represents a single number (17). This expression is a numerical expression, (also called an arithmetic expression). The expression 9 + x represents a value that can change. If x is 2, then the expression 9 + x has a value of 11. If x is 6, then the expression has a value of 15. So 9 + x is an algebraic expression. In the next few examples, we will be working solely with algebraic expressions.

Example 2:	Write each phrase as an algebraic expression.
	Phrase Expression nine increased by a number x 9 + x fourteen decreased by a number p 14 - p seven less than a number t t - 7 the product of 9 and a number n 9 · n   or   9n thirty-two divided by a number y 32 ÷ y   or

In Example 2, each algebraic expression consisted of one number, one operation and one variable. Let's look at an example in which the expression consists of more than one number and/or operation.

Example 3:	Write each phrase as an algebraic expression using the variable n.
	Phrase Expression five more than twice a number 2n + 5 the product of a number and 6 6n seven divided by twice a number 7 ÷ 2n   or    three times a number decreased by 11 3n - 11

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Example 4:	A small company has $1000 to distribute to its employees as a bonus. How much money will each employee get?
Solution:	Let e represent the number of employees in the company. The amount of money each employee will get is represented by the following algebraic expression:

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Example 5:	An electrician charges $45 per hour and spends $20 a day on gasoline. Write an algebraic expression to represent his earnings for one day.
Solution:	Let x represent the number of hours the electrician works in one day. The electrician's earnings can be represented by the following algebraic expression:
Solution:	45x - 20

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Summary:

A variable is a symbol used to represent a number in an expression or an equation. The value of this number can change. An algebraic expression is a mathematical expression that consists of variables, numbers and operations. The value of this expression can change.