Download 2.1 Integers and Rational Numbers.notebook

2.1 Integers and Rational Numbers.notebook
August 31, 2012
Practice Quiz
Write an expression, equation or inequality:
1. The sum of 24 and three times a number y is
equal to 56.
Find the unit rate.
2. The sum of five times a number b and 33 is at
least 55.
6. 8.5 pints
3 servings
7.
26 miles
8 minutes
Evaluate the following expressions
3. The product of 6 and a number w.
8.
Is the given number a solution?
9.
when
5.
4.
Aug 22­1:07 PM
Aug 29­10:28 AM
Natural Numbers
2.1 Integers and
Rational Numbers
Students will be able to
perform math
operations on rational
numbers.
Counting Numbers
1, 2, 3, 4, 5, ...
∞
Example of where you have seen Natural Numbers
used.
­5
­4
­2
­3
Aug 22­1:07 PM
­1
5
4
3
Aug 20­9:19 PM
Integers
Whole Numbers
All of the Whole Numbers + all of the opposites of the
Natural Numbers
0 + All of the Natural Number
0, 1, 2, 3, 4, 5, ...
2
1
0
∞
‐∞. . . , -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, . . . ∞
Example of where you have seen Whole Numbers used.
Positive Integers
­5
­4
­3
­2
­1
0
1
2
3
4
5
Negative Intege
­5
­4
­3
­2
­1
0
1
2
3
4
5
Example of where you have seen Integers used.
Aug 20­9:25 PM
What abou
Aug 20­9:28 PM
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2.1 Integers and Rational Numbers.notebook
August 31, 2012
Rationals
Irrationals
• All Natural, Whole, and Integers
a
• Any number you can write as a fraction b
• Any number that is NOT Rational
• Decimals that do not terminate AND do not repeat
• "CRAZY NUMBERS"
where a & b are integers with b ≠0
• Any terminating decimal (0.5, 7.13, -6.876,
• Square roots of non-perfect square numbers
-24.45)
• Any repeating decimal
(π, √2, √23, √30, √55)
• Can be positive or negative
(‐10., 2., 3.6262…, ‐2.12333…)
Example of where you have seen Irrational Numbers
used.
• Square roots of Perfect Square Numbers
(1, 4, 9, 16, 25, ...)
Example of where you have seen Rational
Numbers used.
Aug 20­9:33 PM
Aug 20­10:05 PM
Real Number System
RATIONALS
Order Numbers
IRRATIONALS
3
NATURAL
49
­4
8.3
WHOLE
0
π
¼
INTEGERS
½
12
7.12
1. 8.7
3. π
5. 7. 2. ­ 7.3
4.
6. 8. 2.3 0
­13
π
√11
7
√25
­5
1.9
­3.8989
15.32984902...
Aug 20­10:18 PM
Aug 22­9:13 AM
Real Number System Practice
Put the following numbers in order from least to
greatest. Classify each number by circling the
correct letter(s) below. More than one can apply.
N = Natural; W = Whole; I = Integer; R = Rational Irr = Irrational
IR
-5
R
R
8
2/3
√5
-5.3
π
6.9
____, _____, _____, ____, ____, ____, _____
NW I R Irr NW I R Irr NW I R Irr NW I R Irr NW I R Irr NW I RIrr
NW I R Irr
Absolute Value
- the distance between a and 0 on a number
line. The symbol a represents the absolute
value of a.
If a is positive then a = a ................. 2 = 2
If a is 0, then a = 0
...................
0=0
If a is negative, then a = a ............. - 4 = 4
R
Aug 21­12:35 PM
Aug 22­10:42 AM
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2.1 Integers and Rational Numbers.notebook
For the given value of a, find - a and a
August 31, 2012
Assignment
P67-68 #14-22 even #23, 24, 53, 61-64
means the opposite of a
1. a = - 5.7
2. a = 5
6
3. π
Aug 22­10:39 AM
Aug 29­3:51 PM
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