# Introduction to Algebraic Expressions

An algebraic expression say 2 × x + y ÷ 2 – 3 cannot be evaluated to a definite number as values of x and y are unknown. x and y may be given any values and the resulting value of the expression would differ as a result.

The expression is written in a more compact form as

2x + y / 2 – 3

This expression has three algebraic terms. Terms of an algebraic expression are separated by + or – signs. 2x, y / 2 and 3 are the three terms in the given algebraic expression. 2 and x are factors of the term 2xy / 2 has factors 1 / 2 and y.

An algebraic expression is where algebra begins and there is a lot to it.

Two expressions may be joined by a sign of equality or inequality. An equal relationship gives rise to an equation. An unequal relationship gives rise to an inequality. Read more about equations in the blog article Great Importance of Algebra Learning.

Example 1

Michel has x dollars. His friend Rajesh has y dollars. They have lunch together in a restaurant. Each of them spend 10 dollars on the lunch. How much money are they left with individually? What is the total amount of money they are left with?

Solution

Michel has x – 10 dollars after paying for the lunch

Rajesh has– 10 dollars after paying for the lunch

Total amount they are left with in dollars is

x – 10 + y – 10

x + y – 10 – 10

x + y – 20

Example 2

Reconsider example 1 given above. Find the total amount of money Michel and Rajesh have after paying for the lunch if

a) Michel has 120 dollars and Rajesh has 145 dollars before payment

b) Michel has 205 dollars and Rajesh has 201 dollars before payment

Solution

a)

x + y – 20

120 + 145 – 20 =  245

They have a total amount of \$245 after payment.

b)

x + y – 20

205 + 201 – 20 =  386

They have a total amount of \$386 after payment.

Example 3

John wants to sell his used mobile phone. He sets its price to 80% of the price at which he bought it. If he bought the mobile at a price p dollars, write the expression for the reduced price at which he sells his mobile.

Solution

80% of p

80% x p

80 ÷ 100 × p

4 ÷ 5 × p

4p / 5

Thinking about math is like exercising your mind. As physical exercise develops body, math thinking develops mind. A real world situation is translated into pure symbols of an expression using logic. The expression is then manipulated using logic rules of math. This is independent of the given real world situation.

Example 1 of this article at its end derives an algebraic expression. It is like a short-cut formula for the situation given in example 2. It helps ease calculating total sum of money left to Michel and Rajesh for all possible amounts of money they may have.

The problem given here is simple. This quality of algebraic expressions becomes very useful when the problem is more complicated and the general result obtained for a situation needs to be used repeatedly.

Translating a real world problem into an algebraic expression is not difficult. You are required to logically translate the given situation into just two things. They are

1. Numbers both known and unknown. Unknown numbers are written as alphabets.
2. Algebraic operations like addition, subtraction, multiplication, division etc. They are simple operations.

To know more about algebraic expressions and their use watch these excellent videos at KhanAcademy