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Math 64
2.1 "Introduction to Integers"
Objectives:
*
Represent real-life situations with integers.
*
Compare integers and graph integers on a number line.
*
Find the absolute value of a number.
*
Find the opposite of a number
*
Read bar graphs containing integers.
Preliminaries:
Thus far in this text, all numbers have been 0 or greater than 0. Numbers greater that 0 are called positive numbers.
However, sometimes situations exist than cannot be represented by a number greater that 0. For example:
Negative
Temperatures are recorded as:
Zero
Positive
below zero
zero
above zero
The stock market will show as:
a loss
no change
a gain
Altitude can be measured as:
below sea level
sea level
above sea level
Business will report:
losses
no gain
pro…ts
Extending the number line to the left of 0 allows us to picture negative numbers, which are numbers that are less
than 0.
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Graphing Integers
Graphing Points on a Number Line:
1: Draw a horizontal line and choose some point on the line. Label this point as 0.
2: Using 0 as reference label all the integers.
3: For each point (number) that must be graphed draw a solid circle on the number line
that corresponds to the required point.
Example 1: (Graphing sets of Integers)
Graph the following sets of integers on a number line.
a) A = f 3; 1; 1; 3g
b) B = f 5; 2; 0; 3; 8g
Comparing Integers
We can compare integers by using a number line. For any two numbers graphed on a number line, the number to the
right is the greater number and the number to the left is the smaller number.
Page: 1
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
2.1
Symbols for Order:
Symbol
Meaning
Symbol
<
Meaning
>
Example 2: (Using > and <)
Insert the appropriate symbol in the blank to make each statement true.
a) 3
e)
0
0
1
b)
5
f)
7
2
4
c) 6
6
g) 8
10
d)
9
15
h) 10
20
Example 3: (True or false statements )
Determine whether each statement is true or false.
a) 0 =
0
b)
9<
10
c) 5
5
d) 11
12
Finding the Absolute Value of a Number
De…nition:
"Absolute Value"
The absolute value ( j j ) of a number is the number’s distance from 0 on the number line.
Example 4: (Finding absolute value of integers)
Find the following absolute values.
a) j+3j
b) j 1j
c) j0j
d) j 8j
Example 5: (Using >, < and = )
Insert the appropriate symbol in the blank to make each statement true.
a) j 5j
5
b) j2j
2
c)
12
j 12j
d) j 9j
j9j
Example 6: (Finding absolute value of integers)
Mark each statement as true or false.
a)
15 = j15j
b) j 2j = j2j
c) j 20j
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20
d) 16 > j 16j
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
2.1
Finding Opposites
De…nition:
"Opposites"
If a is a number, then
( a) = a:
Note: The opposite of 0 is 0 (itself !)
Example 7: (Finding opposites of integers)
Find the opposite of:
a)
10
b) +12
c)
7
Reading Bar Graphs Containing Integers
Example 8: (Application)
The graph below shows the average temperature (in Fahrenheit) of the eight planets, excluding the newly classi…ed "dwarf
planet," Pluto. Notice that a negative temperature is illustrated by a bar below the horizontal line representing 0 F; and a
positive temperature is illustrated by a bar above the horizontal line representing 0 F:
a) Which planet has the lowest average temperature?
b) Which planet has the highest average temperature?
Page: 3
Notes by Bibiana Lopez