Lesson 1 - Purdue University
Lesson 1.1 (Part 1)
Examples:
Let n = a number
1) twelve less than twice some number
2) eight more than the ratio of twice a number and five
3) the difference of 45% of a number and one
Examples:
1) [pic]=
2) [pic]=
To EVALUATE an expression or formula, substitute the given value(s) for the variable(s) and follow the order of operations.
3) [pic]
4)
5) [pic]
6) [pic]
7) [pic] for [pic]
8) The base of a triangle is 10 feet and the height is 3.1 feet. Find the area of the triangle.
10
9) Find the area of a trapezoid if [pic]
[pic]
Sets of Numbers (Part 2 of lesson)
1. Natural Numbers: {1, 2, 3, ...} These are sometimes called the Counting Numbers.
2. Whole Numbers: {0, 1, 2, 3, ...} The Whole Numbers are the Natural Numbers plus zero.
3. Integers: {..., -3, -2, -1, 0, 1, 2, 3,...} The integers include all whole numbers and their opposites.
The set notation used in the above number sets is called roster set notation. Roster notation simply lists the numbers included.
4. Rational Numbers: [pic] This set of numbers includes any type of number that can be represented as a fraction. These types of number include the following
Fractions (proper, improper, or mixed)
Integers (denominator of 1)
Terminating Decimals
Repeating Decimals
Examples include the following: [pic]
The set notation used in the above number set is called Set-Builder Notation. The one above is read ‘all numbers of the form p over q such that p is an integer and q is a non-zero integer’. In this set notation a description is used. The vertical bar is read ‘such that’ or ‘where as’. There will be a variable or an expression with variables at the front.
5. Irrational Numbers: Irrational numbers include numbers that cannot be expressed as a fraction. Most of the irrational numbers you will encounter will be roots or the number pi (π). When written as a decimal, irrational numbers will not terminate or repeat. For example, an approximation for π is 3.14, but 3.14 does not exactly equal π.
6. Real Numbers: [pic]
Use this list of numbers and identify which numbers are in the following sets.
[pic]
Whole Numbers:
Integers:
Rational Numbers:
Irrational Numbers.
There is a good diagram found on the course web page or in your textbook that shows the relationship among the sets of numbers.
[pic]
Roster Notation: [pic]
Set-Builder Notation: [pic]
Ex) Write the following using roster notation.
[pic]
Ex) Write the following using set-builder notation.
[pic]
Elements & Subsets
[pic] The elements of set B are 1, 3, 5, and 7
[pic]
When all numbers of a first set A are members of a second set B, we can write [pic], which is read ‘A is a subset of B’.
[pic]
Use the following sets to determine if the statements below are true or false.
N = Natural Numbers
W = Whole Numbers
Z = Integers
Q = Rational Numbers
H = Irrational Numbers
R = Real Numbers
[pic]
-----------------------
Key Words
Translating to Algebraic Expressions
per
of
less than
more than
ratio
twice
decreased by
increased by
quotient of
times
minus
plus
divided by
product of
difference of
sum of
divide
multiply
subtract
add
Division
Multiplication
Subtraction
Addition
Exponential Notation
The expression an, in which n is a counting number means
[pic]
n factors
In an, a is called the base and n
$%-34?@ÒÓÔÕÚÛÝÞáëîï[?]
h (?h«I1EHöÿU[pic]j¥~aJ[pic]h«I1CJU[pic]V[pic]aJjh«I1U[pic]h«I15?CJaJ
h |I
h«I1h”KFh«I1CJ$aJ$
h«I1CJ$aJ$"jh«I1CJ$U[pic]aJ$mHnHu[pic]
h”KFh«I1 h«I16?h?Oh«I15?CJaJh«I1h(y[pic]h«I1CJ$aJ$hºuª5?CJ$aJ$h«I15?CJ$aJ$+jh™Dôh«I15?CJ$U[pic]aJ$mH is called the exponent, or power. When no exponent appears, it is assumed to be 1. Thus a1 = a.
Rules for Order of Operations
1. Simplify within any grouping symbols.
2. Simplify all exponential expressions.
3. Perform all multiplication and division working from left to right.
4. Perform all addition and subtraction working from left to right.
b1
h
b2
[pic]
3.1
[pic]
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