Download Chapter 1.1—Introduction to Integers Chapter 1.1-

Chapter 1.1—Introduction to Integers
Chapter 1.1--Introduction to Integers
Our real numbers consist of several classes of numbers that can be grouped as in the
following diagram.
Natural Numbers
Irrational
Numbers
Whole Numbers
Integers
Rational Numbers (Fractions)
Natural numbers are those you learned before going to school: {1, 2, 3, 4, 5, 6, 7, 8, 9,
10, ...}
Numerals
1
2
3
4
5
6
7
8
9
10
English
one
two
three
four
five
six
seven
eight
nine
ten
Spanish
uno
dos
tres
cuatro
cinco
seis
siete
ocho
nueve
diez
German
eins
zwei
drei
vier
fünf
sechs
sieben
acht
neun
zehn
French
un
deux
trois
quatre
cinq
six
sept
uit
nouf
dix
Chinese
yi
er
san
si
wu
liu
qi
ba
jiu
shi
Swahili
moja
mbili
tatu
nne
tano
sita
saba
nane
tisa
kumi
Language?
Whole numbers include all of the natural numbers and zero.
Integers contain all of the natural numbers, zero and all of their negatives.
Rational Numbers consist of fractions where the numerator and denominator are integers.
The denominator is never zero! The decimal expansion of a rational number either
1
 0. 5 or repeats like 13  0. 3333. . .
terminates like
2
The set of Irrational Numbers is infinitely bigger than any of the above sets. Numbers
like 2 , 3 , and  are all irrational.
All real numbers can be place on a number line. We usually write the number line with 0
somewhere in the middle and positive integers spaced evenly to the right and negative
© W Clarke
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Chapter 1.1—Introduction to Integers
integers spaced evenly to the left.
We use the symbols:
a  b if " a is less than b " when a lies to the left of b on the number line.
a  b if " a is greater than b " when a lies to the right of b on the number line.
Two numbers are called "opposites" if one number is the same as another except that they
have differing signs. I personally dislike the term opposite when used to describe
numbers and will not use it very often.
The "absolute value" of a number is its positive distance from the origin 0 .
|−5|  5 and |5|  5.
Question 13: Place the correct symbol < or >, between the two numbers: 21 -34.
21  −34
Question 28: Given C  −33, −24, −10, 0 which elements of the set C are less than
−10 ?
−24, −33
Question 42: Find the opposite number: 45
−45
Question 43: Find the opposite number: −31
31
Question 50: Evaluate
−−30  30
Question 55: Evaluate
|−12|  12
Question 60: Evaluate
−|−18|  −18
Question 76: Write the given numbers in order from least to greatest −4, |−15|, −|−7|, 0
−|−7|, −4, 0, |−15|
Question 84: On the number line, the two points that are five units form −3 are
________ and ________.
−8, 2
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