Transcript Variable Expressions - Northside Middle School

1. 3
Variables and Expressions
In the Real World
Hot Air Balloons You are riding in a hot air
balloon. After traveling 5 miles, the balloon
speed changes to 6 miles per hour. What is
the total distance you travel if the balloon
stays at this speed for 1 hour? for 2 hours?
You will find the answer in Example 1.
1. 3
Variables and Expressions
In the Real World
Hot Air Balloons You are riding in a hot air
balloon. After traveling 5 miles, the balloon
speed changes to 6 miles per hour. What is
the total distance you travel if the balloon
stays at this speed for 1 hour? for 2 hours?
You will find the answer in Example 1.
Variable Expressions A variable is a symbol, usually a letter, that
represents one or more numbers.
A variable expression consists of numbers, variables, and operations.
To evaluate a variable expression, substitute a number for each
variable. Then find the value of the numerical expression.
1. 3
Variables and Expressions
In the Real World
Hot Air Balloons You are riding in a hot air
balloon. After traveling 5 miles, the balloon
speed changes to 6 miles per hour. What is
the total distance you travel if the balloon
stays at this speed for 1 hour? for 2 hours?
You will find the answer in Example 1.
Variable Expressions A variable is a symbol, usually a letter, that
represents one or more numbers.
A variable expression consists of numbers, variables, and operations.
To evaluate a variable expression, substitute a number for each
variable. Then find the value of the numerical expression.
You can write the product of a number and a variable by writing the
number next to that variable. For example, you can write 5 • n as 5 n.
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EXAMPLE
Variables and Expressions
1
Using a Variable Expression
To answer the questions about distance traveled, let t represent the time
in hours that the balloon travels at 6 miles per hour. So, the total
distance traveled is original distance + speed • time, which is 5 + 6t.
1
Write hours
traveled, t.
1
2
Substitute for t in the
expression 5 + 6t.
5 + 6t(1)
3
Evaluate to find the
total distance.
11
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EXAMPLE
Variables and Expressions
1
Using a Variable Expression
To answer the questions about distance traveled, let t represent the time
in hours that the balloon travels at 6 miles per hour. So, the total
distance traveled is original distance + speed • time, which is 5 + 6t.
1
Write hours
traveled, t.
2
Substitute for t in the
expression 5 + 6t.
3
Evaluate to find the
total distance.
1
5 + 6t(1)
11
2
5 + 6t(2)
17
ANSWER
If the balloon travels at 6 miles per hour for 1 hour, you travel a
total of 11 miles. After 2 hours you travel a total of 17 miles.
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EXAMPLE
Variables and Expressions
2
Evaluating Variable Expressions
Evaluate the expression when x = 8 and y = 2.
7x + 15 = 7x
(8) + 15
Substitute 8 for x.
= 56 + 15
Multiply.
= 71
Add.
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EXAMPLE
Variables and Expressions
2
Evaluating Variable Expressions
Evaluate the expression when x = 8 and y = 2.
7x + 15 = 7x
(8) + 15
Substitute 8 for x.
= 56 + 15
Multiply.
= 71
Add.
3x – 5y = 3x
(8) – 5y(2)
Substitute 8 for x and 2 for y.
= 24 – 10
Multiply.
= 14
Subtract.
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Variables and Expressions
Writing Expressions Many words and phrases suggest mathematical
operations. The following common words and phrases indicate addition,
subtraction, multiplication, and division.
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
the quotient of
per
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EXAMPLE
Variables and Expressions
3
Translating Verbal Phrases
Verbal Phrase
Variable Expression
The sum of a number and 9
n+9
The difference of a number and 21
n – 21
The product of 6 and a number
6n
The quotient of 48 and a number
48
n
1
n
3
One third of a number