Download 2. integer numbers

2. INTEGER NUMBERS
The set of integers, denoted Z, is formally defined as follows:
Z = { ..., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ... }
So, integers can be:
negative integers {-1, -2,-3, -4, -5, ... }
positive integers {1, 2, 3, 4, 5, ... }
or zero {0}
0 is neither positive nor negative. Notice that 0 together with the positive integers are natural
numbers.
Any natural number is also an integer. To get integers, we just add all the negative numbers to all
natural numbers.
The set of natural numbers is contained in the set of integers. It looks something like this
Integers are an “extension” of natural numbers. All rules that are established for natural numbers
(order of operations, properties of addition and multiplication, the fact that multiplication and
division as well as addition and subtraction are opposite operations) are also true for integers.
The set of the integer numbers doesn't have a beginning or an ending and it has infinite elements.
ORDER AND COMPARISON OF INTEGERS
The number line is a line labelled with the integers in increasing order from left to right, that
extends in both directions:
For any two different places on the number line, the integer on the right is greater than the integer
on the left.
In particular, that line tells you that the negatives are getting smaller as they move off to the left.
That is, –5 < –4 ; – 5 is less than –4.
9 > 4 ; nine is greater than four
–7 < 9 ; negative seven is less than nine.
You can see this video about negative numbers:
https://www.youtube.com/watch?v=OAoLCXpao6s
ABSOLUTE VALUE AND OPPOSITE OF AN INTEGER
The absolute value of x, denoted |x| is the distance of x from zero. This is why absolute value is
never negative; absolute value only asks "how far?", not "in which direction?" This means not only
that | 3 | = 3, because 3 is three units to the right of zero, but also that | –3 | = 3, because –3 is three
units to the left of zero.
Warning: The absolute-value notation is bars, not parentheses or brackets. Use the proper notation;
the other notations do not mean the same thing.
If two numbers are at the same distance from 0 as in the case of 10 and -10 they are called
opposites. Opposites have the same absolute value since they are both at the same distance from 0.
10   10  10
ORDERING INTEGER NUMBERS
1) Write each set of numbers in the correct order from least to greatest
a)
–16
–45
33
7
–9
b)
23
–78
–2
18
–5
c)
44
–56
28
32
–19
d)
–25
–6
–74
–69
–8
e)
78
66
–2
4
–12
2) The following average temperatures have been recorded across eight cities in the state of
Michigan for the month of January from 1981 - 2010
Houghton Benton
City
Mt.Pleasant
Lake
Temperature (˚C)
–11
–13
Iron
Harbor Mountain
1
–15
Battle
Creek
6
Detroit Cadillac Dearborn
2
–9
–1
Answer the following questions based on the data given above:
a)
b)
c)
d)
e)
f)
Which city recorded the warmest average temperature for the month of January?
Which city recorded a cooler average temperature in January?
List three cities that recorded relatively warmer average temperature in January
The cities that recorded average temperatures between –9º C and 6º C are ......
Which cities recorded subzero temperatures?
Houghton Lake recorded the lowest average temperature in January. True or False? If false,
support your answer.
OPPOSITE AND ABSOLUTE VALUE OF INTEGER
NUMBERS
1) Write the opposite of each integer:
a) Opposite of –51
b) Opposite of 9
c) Opposite of 32
d) Opposite of –6
e) Opposite of 20
f) Opposite of 83
g) Opposite of –18
2) Write the absolute value of each integer:
a)
 13
b)  37
c)
91
d)
52
e) –  88
f) – 20
3) Compare using the symbols <, > or =
a)
Absolute value of –34
b)
Opposite of –25
c)
Opposite of 11
d)
Absolute value of 40
Opposite of 17
Absolute value of –25
Opposite of 14
Absolute value of –85