Transcript 1.1 Variables in Algebra

1.1 Variables in Algebra
Algebra 1 Concepts and Skills
McDougal Littell
Linda Stamper
In Algebra, you can use letters to represent one or more
variables. When a letter is used to represent a range of
numbers, it is called a variable. The numbers are called
values of the variable.
An expression that represents a particular number is
called a numerical expression. Example 3 + 2
A variable expression consists of constants, variables
and operations.
constants - numbers
variables - letters
operations - addition, subtraction, multiplication and
division
State the meaning of the variable expression and
name the operation.
The problem.
State the meaning.
Word form
Name the operation.
16m
16 times m
multiplication
The multiplication symbol x is usually not used in algebra
because of its possible confusion with the variable x.
Example 1 State the meaning of the variable expression
and name the operation.
1. Write the problem.
2. State the meaning.
Word form
3. Name the operation.
k
4
k divided by 4
division
Example 2 State the meaning of the variable expression
and name the operation.
1. Write the problem.
y – 12
2. State the meaning.
y minus 12
12 subtracted from y
3. Name the operation.
12 less than y
subtraction
To evaluate a variable expression, you write the expression,
substitute a number for each variable, and simplify.
Evaluate the variable expression when b = 3.
The problem.
7b
Substitute.
7(3)
Simplify.
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When substituting a
value into an expression,
use parentheses.
In algebra work
downward in columns.
Skip one line after
the answer.
Highlight or circle
your answer. You
may find it helpful
to fold your paper in
half lengthwise to
create 2 columns.
Example 3 Evaluate the variable expression when b = 3.
1. Write the problem.
2. Substitute.
3. Simplify.
18
b
18
3
6
Get into the habit of using parentheses when you
substitute. It will help eliminate errors when the
problems are more complex!
Example 4 Evaluate the variable expression when b = 3.
1. Write the problem.
12  b
2. Substitute.
12  3
3. Simplify.
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A formula is an algebraic equation that relates two or
more quantities.
Distance
d  rt
Perimeter
P  a bc
triangle
P  l w l w
P  2l  2w
rectangle
A measure of the
distance around a
geometric figure.
Area
square units of the
interior region of a two
dimensional figure or
the surface of a three
dimensional figure.
A  lw
1
A  bh
2
distance = rate • time
rectangle
triangle
Example 5 Use a variable expression to find the distance
traveled by a truck moving at an average speed of 65 miles
per hour for 6 hours.
d = rt
1.Write the formula.
= (65)(6)
2. Substitute.
3. Simplify.
4. Write a sentence.
= 390
The truck traveled 390 miles.
Note: Include the label in your sentence.
Use one equal sign per line of work.
Keep the equal signs in a line!
Example 6 Find the perimeter of a triangle with two sides
5 miles long and one side 3 miles long.
What is the name of
this triangle according
to the angles and the
sides? triangle
acute isosceles
Example 6 Find the perimeter of a triangle with two sides
5 miles long and one side 3 miles long.
1. Write the formula.
2. Substitute.
3. Simplify.
4. Write a sentence.
P = a + b +c
= (5) + (5) + (3)
= 13
b
a
c
The triangle has a perimeter of 13 miles.
Check if you used one equal sign per line of work. Are
the equal signs in a line?
Example 7 Find the area of a triangle with base 15
centimeters and height 8 centimeters.
What is the name of
this triangle according
to the angles and the
sides?
right scalene triangle
Example 7 Find the area of a triangle with base 15
centimeters and height 8 centimeters.
1
A  bh
1. Write the formula.
2
2. Substitute.
 1 (15)(8)
2
3. Simplify.
= 60
4. Write a sentence.
The area of the triangle is
60 square centimeters.
You cannot
write 602
cm.
The area of the
triangle is 60 cm2.
1-A1 Pages 6-7, #17-46