Download M84 Act 3 Number Line

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Math 84
Activity # 3
Your Name: _______________________
“Number Line”
Introduction to the Integers
 Real Numbers = All numbers, including positive and negative fractions, decimals, and zero.
 Whole Numbers: The numbers 0,1,2,3….
 Integers: A whole number (not a fraction or a decimal) that can be positive, negative or “0”
– whole numbers.
The set of numbers: {..., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6,...}
 Rational Numbers = numbers which can be represented as a/b
 Irrational #’s can not be represented as a/b such as the square root of 3, π ( “pi”).
Recall that the set of whole numbers is {0, 1, 2, 3, ...}. Each whole number has an opposite.
List the opposites of the set of whole numbers above
The set of whole numbers union the set of their opposites, forms the set of integers which is
{..., − 3, − 2, − 1, 0, 1, 2, 3, ...} .
Exercise. On the number line below, graph a point A with a coordinate of 4. Graph a point B at a
point which is nine units to the left of point A. Graph a point C which is a distance of three units
from point B.
←−
−
−5 




 2 
4 
→
7
6
−4
−3
−2
−1
0 1
3
5
Using Negative Numbers
1) How could negative integers be used in the following situations – in sentence form?
Elevation
Temperature
.
Banking
Body weight
.
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Translate the following using the “-“ symbol and numbers
2) The opposite of negative six. _________=___________
(and simplify)
3) Negative four subtract ten.
(do not simplify)
______________
4) Negative two subtract negative ten ______________ (do not simplify)
5) Does − x represent a negative number? Explain.
Absolute Value
The absolute value of a number, x, is denoted x and represents the distance of the number x
from zero on the number line.
Hint: Like distance, absolute value can never be negative as it is the distance from a given
point on the number line to the point “0”
Simplify the following.
6) − −5
7) − ( −5 )
8)
−9 + −5
9) − 9 − − 5
10)
− − (30 2 −
20
2
)
11) Ordering Integers and Inequality Symbols
A number x is less than a number y if x lies to the left of y on the number line.
Use the inequality symbols, < and >, on the following problems filling in the blank.
a) 5 ____ 3
b) 10 ____ 25
c) -1 ____ 2
d) -2 ____-4
The inequality symbol for “is less than or equal to” is __________
The inequality symbol for “is greater than or equal to” is ________
These two symbols are called the “weak” inequality symbols.
12) Translate.
Negative four is less than or equal to negative four. _________________
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Is this statement true or false? _______________
13) Simplify each expression and then insert either > or <.
− 55 − − ( −30 )
− ( −10 ) +
{ 80 − 4 }
3
Review. Show work on separate paper.
14) Simplify using the order of operations.
{
(
)
15 • ( 5 • 2 )2 − 2 • 22 + 23  110 + 32 • 10 − 10 




( )   ÷ −6
15) 2 + 4 •   8 ÷ 23 + 5 − −3

}
+ 10
16) Draw a number line and plot the following:
2
14,
-3 , -5,
-6,
6
a) The distance of -6 from zero is _______ and it is shown as _______.
b) What other number is the exact same distance from zero? _____
17) a) What is the distance between -204 and -144? b) What is the distance between -123 and 344?
18) Add or subtract and verify your answer using the number line.
a) − 6 + (−5)
b) − 4 + 4
c) 7 − 13
d) − 17 − (−9)
19) Write the correct symbol, < or > between the numbers below to make the statement true.
a) − 27
− 22
b) − 123
121
c)
-1
( −3)
2
In problems 20-21 write an expression corresponding to the given description and simplify it.
20) The opposite of negative eleven times opposite of five subtracted from nine.
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21) Five times the difference between negative seven and the quotient of negative forty two and negative
six.
Write your own review: Using at least two sets of parentheses, one absolute value, two
exponential expressions and three operations, create a problem.
{
(
)
}
Ex: 3 + 2 • 4 + 6 • −32 + 33 ÷ −32 + 2 • 5
Your problem: ________________________________
Your, step-by-step, solution:
Your solution:
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***EX (3 pts) Solve the ex problem above
{
}
3 + 2 • 4 + 6 • ( −32 + 33 ) ÷ −32 + 2 • 5
5