Download -1 Natural Numbers Integers Whole Numbers Rational Numbers

Venn Diagram of the Real Numbers
Algebra I
Name: ______________________________
Date: __________________ Hour: ________
Place each number below in the smallest set in which it belongs. For example, -1 is
a real number, a rational number, and an integer, so we place it in the “Integers” box
but not inside the whole numbers box or the natural numbers box.
Directions:
8
-1.3
ð
2.175
-7
1000
0.00005
-1
Natural Numbers
Integers
Whole Numbers
Rational Numbers
Irrational Numbers
Real Numbers
Questions:
1) Given all possible real numbers, name at least one number that is a whole number but not
a natural number: __________
2) Can a number be both rational and irrational? __________ If yes, name one: __________
3) Can a number be both rational and an integer? __________ If yes, name one: __________
4) Given all possible real numbers, name at least one number that is an integer but not a whole
number: __________
Side note:
Just for the record, this diagram in no way conveys the actual sizes of the sets. In mathematics, the number
of elements that belong to a set is called the cardinality of the set. Technically (and with a lot more
mathematics behind you), it can be proven that the cardinality of the irrational numbers (uncountable
infinity) is actually larger than the cardinality (size) of the rational numbers (countable infinity). Another
interesting fact is that the cardinality (size) of the rational numbers, integers, whole numbers, and natural
numbers are all equal. This type of mathematics is studied in a course called Real Analysis (that comes
after the Calculus sequence).
Solving Equations Pre-Test
Algebra I
Name: _______________________________
Form A
Date: _____________________ Hour: ______
SHOW ALL WORK to receive credit!
For each of the questions below, solve the equation.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)