Download Algebra 1A Vocabulary 1-2

Algebra 1A Vocabulary 1-2
 Review
 Problem 5
 Suppose you draw a segment from any one vertex of a
regular polygon to the other vertices. A sample for a
regular hexagon is shown above. Use the table to find a
pattern. What is a rule for the number of nonoverlapping
triangles formed?
Problem 5
Number of Sides of Polygon
Number of Triangles

Give a rule in words to find the number of
nonoverlapping triangles in a polygon.

Write an algebraic expression for the number of
nonoverlapping triangles in a polygon that has n
sides.
Review
 What is a variable?
 What does a numerical expression contain?
 What does an algebraic expression contain?
 Give an example of an operation.
Exponents
An exponent is a shorthand notation for repeated
multiplication.
3•3•3•3•3
3 is a factor 5 times
Using an exponent, this product can be written as
exponent
5
base
3
Exponential Notation
exponent
5
base
3
Read as “three to the fifth power” or “the fifth power of three.”
This is called exponential notation. The exponent, 5,
indicates how many times the base, 3, is a factor.
3•3•3•3•3
3 is a factor 5 times
Simplify
 You simplify a numerical expression when you replace
it with its single numerical value.
 Example:
4 9 is 36,
 To simplify a power, you replace it with its simplest
name,
 For example,

3  3 3 3 3  81
4
 The simplest being 81.

Sample Problems
1. What is the simplest form of each expression?
7
A. 10
2
2 
B.  
5 
C.
0.4 
3
Order of Operations
 When simplifying algebraic expressions with more than
one operation, you have to make a decision about what
order to perform the operations.
 For example,
Could be
2 + 3 5
2 + 3 5


or 2 + 3 5
Rules for
Order of Operations
1. Perform all operations within parentheses
( ), brackets [ ], or other grouping
symbols such as fraction bars, starting
with the innermost set.
2. Simplify powers.
3. Multiply or divide in order from left to
right.
4. Add or subtract in order from left to right.
Sample Problems
1. What is the simplified form of each expression?
A.
6 - 2  2
2
2 1
B.
5
4
C. 75  3  2
3