Download LESSON 1-2 NOTES: PROPERTIES OF REAL NUMBERS So far in

LESSON 1-2 NOTES:
PROPERTIES OF REAL NUMBERS
So far in your math studies you have focused on the real numbers and its subsets. The two main subsets of
the real numbers are the rational and irrational numbers. You will study imaginary numbers in the future.
REAL NUMBERS
Rational Numbers:
Irrational Numbers:
...-5, -½, 0, 0.222, 1, 2, ¼, 0.75, ⅚, 2.5,...
Integers: ...-3, -2, -1, 0, 1, 2, 3, ...
Whole Numbers: 0, 1, 2, 3, ...
Natural Numbers: 1, 2, 3, ...
Rational Numbers: All numbers you can write as a quotient of integers , b ≠ 0; include terminating
decimals ( = 0.125) and repeating decimals ( = 0. ).
Irrational Numbers: All numbers that cannot be written as quotients of integers; include decimal
representations that neither terminate nor repeat; example:
= 1.414213...
EXAMPLE/PRACTICE: Graph the numbers on the number line. - ,
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0
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, and 2.
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EXAMPLE/PRACTICE: Classify each variable according to the set of numbers that best describes its
values. [natural, whole, integers, rational, irrational]
1. the area of the circle A found by using the formula πr2
2. the air temperature t in Saint Paul, MN, measured to the nearest degree Fahrenheit
3. the last four digits s of a Social Security number
4. the number n of equal slices in a pizza; the portion p of the pizza in one slice
EXAMPLES/PRACTICE: Write each set of numbers in increasing order
4 5
5. 2 2, ,  ,0.9, 1
5 4
6.
5
2
, 6, ,  , 0.5
8
3
EXAMPLES/PRACTICE:
7.  2, 2
Compare the two numbers. Use > or < to write an inequality.
8. 4, 17
9.
29,5
10.
50,6.8
11. 7 ,
PROPERTIES OF REAL NUMBERS
* The opposite or additive inverse of any number a is -a. The sum of a number and its opposite is 0.
The number 0 is called the additive identity for the real numbers.
Examples:
12 + (−12) = 0,
−7 + 7 = 0
* The reciprocal or multiplicative inverse of any nonzero number a is . The product of a number
and its reciprocal is 1. The number 1 is called the multiplicative identity.
Examples: 5( ) = 1,
−3(
)=1
* The property of real numbers excludes a single number, zero. Zero has no multiplicative inverse.
Let a, b, and c represent real numbers.
PROPERTY
ADDITION
MULTIPLICATION
Closure
Commutative
Associative
Identity
Inverse
Distributive
EXAMPLES/PRACTICE: Name the property of real numbers illustrated by each equation.
12.
2 3
 1
3 2
13. 6(2 + x) = 6 · 2 + 6 · x
14. 2 · 20 = 20 · 2
15. 8 + (−8) = 0
16. 2(0.5 · 4) = (2 · 0.5) · 4
17. −11 + 5 = 5 + (−11)