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Order of Operations

Evaluating Algebraic Expressions

The basis of algebra is the use of letters, or other symbols, to represent numbers.

Something like

3x + 5y

is called an algebraic expression and means "three times the number x plus five times the number y". The expression will, of course, also represent a number - its value will depend on the values of x and y. For example:

If x = 3 and y = 4 then 3x + 5y = 3(3) + 5(4) = 9 + 20 = 29

In general, an algebraic expression is made up of numbers and letters (representing numbers whose value has not yet been specified), combined using arithmetical operations such as addition, subtraction, multiplication, division, square root, and so on. Here are some more examples of algebraic expressions:

x² + 5x + 7

(a + 3)²

Such expressions represent numbers whose value depends on the values we assign to the letters in the expressions. As shown previously, we can evaluate algebraic expressions for certain values of their variable by simply plugging the value of the variable into the expression. For example, consider the expression x + 2y. If x = 1 and y = 2, then x + 2y = 1 + 2(2) = 1 + 4 = 5. If x = 5 and y = 3, then x + 2y = 5 + 2(3) = 5 + 6 = 11.

Exercise

Let a =3 and b =7. Evaluate each of the expressions below.
Click on the question marks to see these examples step-by-step.

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