Page 169 - ArithBook5thEd ~ BCC

Chapter 6

Toward Algebra

6.1 Evaluating Expressions

Amathematical expression is any meaningful combination of numbers, letters, operation symbols (such
as +, −, ×, ÷, √ ), and grouping symbols (such as parentheses, brackets, fraction bars and the extended
square root symbol like √ ). For example, the expression

x + y
x − y
indicates a fraction whose numerator is the sum of two unspecified numbers, x and y,and whose
denominator is their difference. Letters in a mathematical expression are called variables because they
represent unspecified numbers that can take various different values. Expressions can be evaluated
(assigned a numerical value) if numerical values are assigned to all the variables appearing in the
expression.
x + y
Example 206. Evaluate the expression if x =2 and y = −6.
x − y
Solution. We replace each letter by its assigned numerical value, enclosed in parentheses,

x + y (2) + (−6)
= ,
x − y (2) − (−6)
and simplify the resulting expression
(2) + (−6) −4 1
= = − .
(2) − (−6) 8 2

Assigning different values to the letters in an expression usually changes the value of the expression.
x + y
Example 207. Evaluate the expression if x = −3and y =3.
x − y
Solution. Replacing x and y by their assigned values,
x + y (−3) + (3) 0
= = =0.
x − y (−3) − (3) −6

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