MATHEMATICS FOR ALL, grade 8: TOPIC 6: ALGEBRA

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A)Algebraic representation and formulae

OBJECTIVES: Learners will: understand and apply algebraic symbols and notation

Writing algebra

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

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: