Properties of Real Numbers and The Number Line.

Have you wonder what is the difference between a rational number and an irrational one? What is the difference between a whole number and a natural one? In this lesson you may learn to differenciate all the sets of real numbers. Learn the properties of real numbers and apply them to simplify algebraic expressions.

Lesson's Content

Lesson's Glossary

Real number:  Any number which can be negative, positive, or zero.

Additive inverses: The opposite of a number.

Identity element for addition:  Zero (0).

Identity element for multiplication: One (1).

Integers: All numbers in the set containing positive integers, negative integers, and zero.

Irrational numbers: Any number that is impossible to write it as a fraction. A decimal number that doesn’t end or keeps repeating.

Negative integers: The numbers -1,-2,-3,-4, and so on.

Negative number: The opposite of a positive number.

Negative side: The side situated at the left of the origin in a horizontal number line.

Positive integers:  Natural numbers: 1, 2, 3, 4, 5, ...

Positive number: The opposite of a negative number.

Positive side:  The side situated to the right of the origin in a horizontal number line.

Real number:  Any number which can be negative, positive, or zero.

Reciprocals:  Any two numbers which multiplied give 1; also known as multiplicative inverse.

Whole numbers:  All numbers in the set containing zero and all positive integers.

Interactive Algebraic Applets

The properties of real numbers are additive, associative,

commutative, distributive, and others. This interactive algebraic applet

offers the possibility to change values for a, b, and c; by dragging

the point in the sliders. You may see how the listed properties

update their values.

Vocabulary Puzzle

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