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Chapter Summary #1 (Adv. Algebra)
Real numbers.
The natural numbers, whole numbers, integers numbers, rational numbers and irrational numbers are all subsets of the real numbers. Each real number corresponds to a point on the number line. A real numbers distance from zero on the number line its absolute value.
-Natural Numbers. ( )
Natural numbers are the numbers used for counting.
Example: 1, 2, 3, 4, 5…
-Negative Numbers. ( )
Then man thought about numbers between 0 and 1. To give us fractions and decimals.
Example:
-Whole Numbers. ( )
Whole numbers are the natural numbers and 0.
Example: …-3, -2, -1, 0, 1, 2, 3..
-Integers.
The integers are the naturals numbers (also called positive integres), their opposites (also called negative integers), and zero.
-Rational numbers.
Rational numbers are all the numbers that can be written as quotients of integers. Each quotients must have a nonzero denominator.
Some rational numbers can be written as terminating decimals.
For example:
All other rational numbers can be written as repeating decimals.
For example:
-Irrational Numbers.
Irrational numbers are numbers that cannot be written as quotients of intergers.
Their decimal representations neither terminate nor repeat.
If a positive rational number is not a perfect square such as 25 or , then its square root is irrational.
“If we put all the numbers system together, then we have the Real Numbers”
Properties of Real Numbers.
The opposite or additive inverse of any number a is –a. The sum of opposite is 0.
Example:
The reciprocal or multiplicative inverse of any nonzero number a is .
The product of reciprocals is 1.
Examples:
Absolutes Values.
The absolute value of a real number it’s the distance from zero on the number line.
(Distance is always positive.)
Example:
Algebraic Expressions.
A variable is a symbol, usually a letter that represents one
Real numbers.
The natural numbers, whole numbers, integers numbers, rational numbers and irrational numbers are all subsets of the real numbers. Each real number corresponds to a point on the number line. A real numbers distance from zero on the number line its absolute value.
-Natural Numbers. ( )
Natural numbers are the numbers used for counting.
Example: 1, 2, 3, 4, 5…
-Negative Numbers. ( )
Then man thought about numbers between 0 and 1. To give us fractions and decimals.
Example:
-Whole Numbers. ( )
Whole numbers are the natural numbers and 0.
Example: …-3, -2, -1, 0, 1, 2, 3..
-Integers.
The integers are the naturals numbers (also called positive integres), their opposites (also called negative integers), and zero.
-Rational numbers.
Rational numbers are all the numbers that can be written as quotients of integers. Each quotients must have a nonzero denominator.
Some rational numbers can be written as terminating decimals.
For example:
All other rational numbers can be written as repeating decimals.
For example:
-Irrational Numbers.
Irrational numbers are numbers that cannot be written as quotients of intergers.
Their decimal representations neither terminate nor repeat.
If a positive rational number is not a perfect square such as 25 or , then its square root is irrational.
“If we put all the numbers system together, then we have the Real Numbers”
Properties of Real Numbers.
The opposite or additive inverse of any number a is –a. The sum of opposite is 0.
Example:
The reciprocal or multiplicative inverse of any nonzero number a is .
The product of reciprocals is 1.
Examples:
Absolutes Values.
The absolute value of a real number it’s the distance from zero on the number line.
(Distance is always positive.)
Example:
Algebraic Expressions.
A variable is a symbol, usually a letter that represents one