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```Properties of Real Numbers
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N:
W:
Z:
Q:
I:
R:
Natural (1,2,3, …)
Whole (0,1,2,3,…)
Integers (… -2,-1,0,1,2,…)
Rationals (m/n; m,n integers)
Irrational ( 2,  , 7 , 3.45978)
Real (all rational and irrational)
Real Numbers, R
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M
A
G
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N
A
R
Y
Q
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Z
W
N
Properties of Real Numbers
For any real numbers a, b, and c
Commutative
a b  ba
Multiplication
a *b  b * a
Associative
(a  b)  c  a  (b  c) (a * b)* c  a *(b * c)
Identity
a+0=a=0+a
a *1  a  1* a
a  (a )  0  ( a)  a
If a is not zero,
1 then 1
Inverse
a*
a
1
a
*a
Properties of Real Numbers
 Distributive property
 For all real numbers a, b, and c
a(b+c) = ab + ac and (b+c)a = ba + ca
Solving Equations;
5 Properties of Equality
Reflexive
For any real number a, a=a
Symmetric
Property
For all real numbers a and b,
if a=b, then b=a
Transitive
Property
For all reals, a, b, and c,
if a=b and b=c, then a=c
Solving Equations;
5 Properties of Equality
Subtraction
For any reals a, b, and c, if
a=b then a+c=b+c and ac=b-c
Multiplication
and Division
For any reals a, b, and c, if
a=b then a*c=b*c, and, if c is
not zero, a/c=b/c
Comparing 2 Real Numbers
1. Approximate Irrational Numbers & fractions
as a decimal (Remember: a fraction is just
division)
2. Determine the larger of two numbers and
place the appropriate inequality between
them
Comparing 2 Real Numbers
Compare
17 and 3.8 using < or >
17  4.123
17  3.8
or
3.8  17
Comparing 3 Real Numbers
1. Approximate Irrational Numbers & fractions
as a decimal (Remember: a fraction is just
division)
2. Rewrite them left to right in ascending order
3. Put a less than symbol (<) between them
Comparing 3 Real Numbers
Compare
17 , 5, and 4 using < or >
17  4.123
4 
17  5
```
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