Download Properties of real numbers

Applied Algebra II
Ch. 1.1-1.5 (Algebra Review)
Name: _____________________
Keep for your notes please!!
1.) For each of the following mathematical terms there are a set of numbers that demonstrate
that term correctly. Your task is to clearly define each of the terms based on the set of
numbers given for each term.
Real numbers { 10, -7, 5.2, 1.971123…,
Definition of real numbers :
8 , 6.33 }
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Whole numbers { 0, 1, 2, 3, 4, . . . }
Definition of whole numbers :
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6
3
Rational numbers { 9, , 1.5, }
2
4
Definition of rational numbers :
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Integer numbers {. . . , -3, -2, -1, 0, 1, 2, 3, . . .}
Definition of integer numbers :
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Natural numbers {1, 2, 3, 4, . . . }
Definition of natural numbers :
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2  29
Irrational numbers { 8 ,
,  , 1.971123…}
4
Definition of irrational numbers :
Term
Whole numbers
Examples
Definition
Integers
Rational numbers
Irrational numbers
Write down where the values would fit in the number line below and write these values in the
appropriate categories in the table above.
4
2, 4,  ,
3
1.2 ,
36 ,
2.562491...... , 9 ,
1 ,
5
 , 1.25 , .6666..... , 0 ,
1
Inequality symbols
 3  2 , which is stated as __________________________________________.
Is 3  2 a true statement? If not, explain below.

1.5  2 , which is stated as __________________________________________.
Is 1.5  2 a true statement? If not, explain below.

Properties of real numbers
Explanation of the additive inverse of a number:
 The sum of a number and its additive inverse equals 0.
Name the additive inverse of:
A.) -8
B.)
2
3
C.) Write down a second way of explaining the additive inverse or how to find it.
Explanation of the multiplicative inverse of a number:
 The product of a number and its multiplicative inverse equals 1.
Name the multiplicative inverse of:
2
3
C.) Write down a second way to explain the multiplicative inverse or how to find it.
A.) -8
B.)
Term
Operations with real numbers
Example
Meaning
Sum
Quotient
Difference
Product
Numerical Expression
Example: 5 + 12
Algebraic Expression
Example: 5x + 12

Explain the difference between a numerical expression and an algebraic expression.

What’s the difference between an expression and an equation?

2
Evaluate 2  3  6   4 11



How did you know what to do first? Second? Third?

The answer from above is a unique solution. What is a unique solution?
Mean, Median and Mode are three well known measures of central tendency.
1. Find the mean of the set of values {2,3,1,3,5,10}. Explain how to find the mean.
2. The median of the set of values {1,2,3,4,5,10} is 3.5. Explain how to find the median.
3. The mode of the set of values {2,3,1,3,5,10} is 3. Explain how to find the mode.
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 Solve 2x 1  11 . What am I asking you to do?

What does it mean to solve an equation?

Solve 2 x  1  3( x  4) .
Solve for h:
2h  8
 6g
5
For problems 4-6, be sure to define the variable, write an equation, solve the problem, and
check your work. For these problems to be considered complete, you need to show all of these
components on your paper.
4.) Enrique Romero bought a refrigerator for $50 more than half its original price. He paid
$525 for the refrigerator. What was the original price of the refrigerator?
Define the variable:
Equation:
Solve the problem:
Check your work.
5.) The high school principal has given Mrs. Diaz $420 to buy tickets to Phantom of the Opera
for her English class and chaperones. The school requires that there be one adult chaperone
for every five students on such a trip. How many $15 student tickets and $30 adult tickets can
she order?
Define the variable:
Equation:
Solve the problem:
Check your work.
6.) Two designs for a tuna can produced by the company Cat Munch are shown below. If each
can holds the same amount of tuna, what is the height of can A?
r = 1 in
r = 3 in
h = 1 in
Can B
Can A
Define the variable:
Equation:
Solve the problem:
Check your work.