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Blue Whales During its summer feeding season, a blue whale eats about 4 tons of food every day. To find about how many tons of food a blue whale eats in a given number of days, you can multiply the number of days by 4, as shown in the table.

Expressions and Variables

Days Tons of food eaten

1 4 • 1

2 4 • 2

10 4 • 10

d 4 • d

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A numerical expression consists of numbers and operations. In the table,

the expression 4 • 10 is a numerical expression. It can also be written as 4 10 or 4(10).

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A variable is a letter used to represent one or more numbers. A variable expression consists of numbers, variables, and operations.

A numerical expression consists of numbers and operations. In the table,

the expression 4 • 10 is a numerical expression. It can also be written as 4 10 or 4(10).

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A numerical expression consists of numbers and operations. In the table,

the expression 4 • 10 is a numerical expression. It can also be written as 4 10 or 4(10).

To evaluate a variable expression, substitute a number for each variable and evaluate the resulting numerical expression.

A variable is a letter used to represent one or more numbers. A variable expression consists of numbers, variables, and operations.

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Evaluating a Variable ExpressionEXAMPLE 1

= 480

ANSWER A blue whale eats about 480 tons of food in 120 days.

Multiply.

SOLUTION

4 • d = 4 • 120 Substitute 120 for d.

Evaluate the expression 4 • d when d = 120 to find out about how many tons of food a blue whale eats in a feeding season of 120 days.

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Study Strategy

When you write a variable expression involving

multiplication, avoid using the symbol . It may be confused with the variable x.

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Evaluating Expressions with Two VariablesEXAMPLE 2

Evaluate the expression when x = 10 and y = 4.

x + y = Substitute 10 for x and 4 for y.

= 14

10 + 4

Add.

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Evaluating Expressions with Two VariablesEXAMPLE 2

Evaluate the expression when x = 10 and y = 4.

Substitute 10 for x and 4 for y.

xy = Substitute 10 for x and 4 for y.

= 40

10(4)

Add.

Multiply.

x + y =

= 14

10 + 4

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Writing Variable Expressions You can solve a real-world problem by creating a verbal model and using it to write a variable expression. A verbal model describes a problem using words as labels and using math symbols to relate the words. The table shows common words and phrases that indicate mathematical operations.

Expressions and Variables

Common Words and Phrases that Indicate Operations

Addition Subtraction Multiplication Division

plus

the sum of

increased by

total

more than

added to

minus

the difference of

decreased by

fewer than

less than

subtracted from

times

the product of

multiplied by

of

divided by

divided into

the quotient of

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Evaluating a Variable ExpressionEXAMPLE 3

Baseball You plan to divide the 120 players in a baseball league into teams with the same number of players. Use a verbal model to write a variable expression for the number of teams if you know the number of players on each team.

= 120 p

ANSWER

Expressions and Variables

SOLUTION

Let p represent the number of players on each team. The word divide indicates division.

Number of teams =Number of players

in league Number of playerson each team

The number of teams is 120 p, or .120

p

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