This document discusses expressions and variables. It provides examples of: 1) A numerical expression representing how many tons of food a blue whale eats in a given number of days. 2) Definitions of numerical expressions, variable expressions, and how to evaluate variable expressions by substituting values for variables. 3) An example of evaluating a variable expression for how many tons of food a blue whale eats in 120 days.

1. LESSON
1.1 Expressions and Variables
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.
Days Tons of food eaten
1 4•1
2 4•2
10 4 • 10
d 4•d
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2. LESSON
1.1 Expressions and Variables
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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3. LESSON
1.1 Expressions and Variables
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).
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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4. LESSON
1.1 Expressions and Variables
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).
A variable is a letter used to represent one or more numbers. A variable
expression consists of numbers, variables, and operations.
To evaluate a variable expression, substitute a number for each variable and
evaluate the resulting numerical expression.
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5. LESSON
1.1 Expressions and Variables
EXAMPLE 1 Evaluating a Variable Expression
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.
SOLUTION
4 • d = 4 • 120 Substitute 120 for d.
= 480 Multiply.
ANSWER A blue whale eats about 480 tons of food in 120 days.
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6. LESSON
1.1 Expressions and Variables
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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7. LESSON
1.1 Expressions and Variables
EXAMPLE 2 Evaluating Expressions with Two Variables
Evaluate the expression when x = 10 and y = 4.
x + y = 10 + 4 Substitute 10 for x and 4 for y.
= 14 Add.
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8. LESSON
1.1 Expressions and Variables
EXAMPLE 2 Evaluating Expressions with Two Variables
Evaluate the expression when x = 10 and y = 4.
x + y = 10 + 4 Substitute 10 for x and 4 for y.
= 14 Add.
xy = 10(4) Substitute 10 for x and 4 for y.
= 40 Multiply.
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9. LESSON
1.1 Expressions and Variables
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.
Common Words and Phrases that Indicate Operations
Addition Subtraction Multiplication Division
plus minus times divided by
the sum of the difference of the product of divided into
increased by decreased by multiplied by the quotient of
total fewer than of
more than less than
added to subtracted from
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10. LESSON
1.1 Expressions and Variables
EXAMPLE 3 Evaluating a Variable Expression
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.
SOLUTION
Let p represent the number of players on each team. The word divide
indicates division.
Number of players Number of players
Number of teams = in league
÷ on each team
= 120 ÷ p
120
ANSWER The number of teams is 120 ÷ p, or p .
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