Transcript 1-1 - rmartinmath

1.1
Expressions and Variables
Skill Check
Lesson Presentation
Lesson Quiz
1.1
Expressions and Variables
Skill Check
1. 16 + 8 = 24
2. 13  4 = 52
3. 34 – 9 = 15
4. 96  6 = 16
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
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).
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.
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.
1.1
EXAMPLE
Expressions and Variables
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
= 480
ANSWER
Substitute 120 for d.
Multiply.
A blue whale eats about 480 tons of food in 120 days.
1.1
Expressions and Variables
Study Strategy
When you write a variable expression involving
multiplication, avoid using the symbol
confused with the variable x.
. It may be
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
= 14
Substitute 10 for x and 4 for y.
Add.
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
= 14
xy = 10(4)
= 40
Substitute 10 for x and 4 for y.
Add.
Substitute 10 for x and 4 for y.
Multiply.
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
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
1.1
EXAMPLE
Expressions and Variables
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 teams
=
Number of players
in league

Number of players
on each team
= 120  p
ANSWER
120
The number of teams is 120  p, or p .
1.1
Expressions and Variables
Lesson Quiz
Evaluate the expression when x = 8, y = 2, and z = 6.
1. x + z 14
2.
3
3. z – y
4
4. xy 16
5. Write a variable expression to represent the amount
Stephan earns in w weeks if he earns $110 each week. 110w
6. Challenge A company makes inline skates that have 4
wheels on each skate. Suppose the company produces p
pairs of inline skates each hour and is in operation for h
hours each day. Write a variable expression for the number
of wheels the company uses each day. Evaluate the
expression for p = 40 and h = 16.
8ph; 5120