Algebra 2
1.1 REAL NUMBERS & NUMBER OPERATIONS
Set Notation : {…numbers listed in a pattern…}
Real Numbers : the numbers found on the number line.
Whole Numbers : { 0 , 1 , 2 , 3 , …}
Natural Numbers (also called “Counting Numbers”):
{ 1 , 2 , 3 , 4 , …}
Integers:
{…, -3 , -2 , -1 , 0 , 1 , 2 , 3 ,…}
Rational Numbers : numbers that can be written as the ratio
of two integers.
Irrational Numbers : numbers that are not Rational (duh!).
Ex.1 Draw a Venn Diagram to show the real number system.
Approximating Square Roots: Find the 2 perfect squares the
number under the radical is between and take the square root of both.
Symbols :  means “approximately”
> means “greater than”
< means “less than”
Definitions :
Opposite: The opposite of the number a is –a.
Reciprocal: The reciprocal of a is 1 .
a
Sum : Adding
Difference : Subtracting
Product : Multiplying
Quotient : Dividing
Section 1.1
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Algebra 2
Ex.2 Which number is larger?
5
9
a.)
8
14
c.) 11
3.1
b.) 0.73
0.731
d.) 5.1
5.13
Ex.3 Graph the numbers on the number line and write the numbers
form least to greatest.
5
a.) 1.8, 3,
2
b.) 1.75,  5,
5 12
,  ,  10
3
5
REAL NUMBER PROPERTIES USING ADDITION AND
MULTIPLICATION
CLOSURE: If you add any 2 real numbers the sum will be a real
number.
If you multiply any 2 real numbers the product will be a real number.
We say that the set of numbers is “closed under” that operation.
Ex.4 Are the odd integers closed under…
a.) addition
b.) subtraction
c.) multiplication
d.) division
Ex.5 Are the irrational numbers closed under multiplication?
Section 1.1
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Algebra 2
COMMUTATIVE: You can switch the order of the numbers you are
adding (or multiplying) and the result will be the same.
ASSOCIATIVE: You can group the numbers you are adding (or
multiplying) and the result will be the same.
IDENTITY: 0 is the “additive identity” because it is the real number
that can be added to any number and not change the number’s value.
1 is the “multiplicative identity” because it is the real number that can
be multiplied by any number and not change the number’s value.
INVERSE: When adding, a number’s inverse is its opposite because
when you add a number and its opposite the result is 0(the additive
identity).
When multiplying, a number’s inverse is its reciprocal because when
you multiply a number and its inverse the result is 1(the multiplicative
identity).
DISTRIBUTIVE:
Section 1.1
for any real numbers a, b, and c
a( b  c )  ab  ac
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Algebra 2
Ex.6 What property is being used?
8 3
a.)

3 8
b.) (2  3)  8  8  (2  3)
c.) 10  0  10
Ex.7 What is the difference of 3 and 15 ?
1
Ex.8 What is the quotient of 8 and  ?
2
Unit Analysis is used to convert between different units of measurement.
Ex.9 a.) 12 ft =
yds
b.) If there are 6 francs in one dollar, how many francs will
you receive for $500?
c.)
Section 1.1
60
mi

hr
ft
sec
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