Download Aim 2 - What are Integers

Aim 2 ­ What are Integers
Aim 2: What are Integers?
Do Now: a) Write down an example of a whole number. b) Write down an example of a number that is not a whole number. Whole Numbers Non­Whole numbers
7, -12, 0, -97, 100
2
1
3.2, , 6 , -0.39
2 3
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Aim 2 ­ What are Integers
List the set of Counting (natural) Numbers:
{1, 2, 3, 4, 5, ...}
List the set of Whole Numbers:
{0, 1, 2, 3, 4, 5, ...}
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Aim 2 ­ What are Integers
Integers: Positive and negative whole numbers
List the set of Integers:
{...-3, -2, -1, 0, 1, 2, 3...}
Give an example of a real number that is not an integer.
3 5
16.7, , 1 , -0.25
4 8
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Aim 2 ­ What are Integers
Give a real life examples of an integer in each category below:
o
Temperature: 8 F
Money: spending $15
Football: losing 6 yards
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Aim 2 ­ What are Integers
Place the set of integers on the number line below:
5
Aim 2 ­ What are Integers
Which integer is larger, -5 or 3?
-5
­5
3
­4
­3
­2
­1
0
1
2
3
4
5
6
Aim 2 ­ What are Integers
Inequality Symbols
less than <
less than or equal to <
greater than > greater than or equal to >
not equal to =
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Aim 2 ­ What are Integers
Place the appropriate inequality symbol between
the two integers below.
a) 3 > -4
b) -2 < 5
c) 0 < 6
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Aim 2 ­ What are Integers
Place the following integers in order from least to greatest.
{50, -32, -53, 82, 11, -7, 0, 17}
-53, -32, -7, 0, 11, 17, 50, 82
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Aim 2 ­ What are Integers
Opposites
What is the opposite of earning $5?
What is the opposite of an eight yard gain?
Spending $5
An eight yard loss
Definition:
Opposites:
Numbers with the same digit but different sign.
Examples: 8 and -8, 16 and -16
Which property of real numbers can be associated for the definition of opposites?
Additive Inverse
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Aim 2 ­ What are Integers
Absolute Value
Definition:
Absolute Value: The distance from zero on a number line.
|K|
is the symbol for the absolute value of K.
Examples:
|4| = 4 and |­4|= 4
Why is the absolute value of ­4 and 4 equal to 4?
Both 4 and ­4 are 4 hops away from zero
­5
­4
­3
­2
­1
0
1
2
3
4
5
For all values of K is the |K| always positive? Explain why or why not
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Aim 2 ­ What are Integers
Practice:
1. Given the set of numbers {­4, 6, 0.8, 0, 5, 2/3, ­9.4}
a) List the integers {­4, 6, 0, 5}
b) List the whole numbers {6, 0, 5}
2. Which is larger, ­50, or 8?
3. Which is larger, |­35|, or |12|? Why?
= 35
= 12
4. State whether or not the statement is true or false? false
a. |­5| = 5 ______ b. |­5| < 4 _____ c. |10| = ­10 ______
false
true
5=5
5<4
10 = -10
5. Find the absolute value of each expression below:
a. |­3| _____
3
b. |7| ______
7
c. ­|5| ______
d. |­7| – |3| ________
4
-5
7-3
12
Aim 2 ­ What are Integers
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Aim 2 ­ What are Integers
-24
15
30
5+2
20 - 5
7
15
>
>
-4
=
-37, -23, -12, 0, 45, 55
-7, -6, I5I, I-6I, 8
6
5
Loihi
true
12, 0, 8.0
12, -5, 0, 8.0
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