Preliminaries

Before you begin learning, relearning, or reviewing algebra, you need to feel comfortable with some pre-algebra terms and operations. The first items you should become familiar with are the different categories or types of numbers and the common math symbols.

Categories of numbers

In doing algebra, you work with several categories of numbers.

  • Natural or counting numbers. The numbers 1, 2, 3, 4, …are called natural or counting numbers.

  • Whole numbers. The numbers 0, 1, 2, 3, …are called whole numbers.

  • Integers. The numbers …–2, –1, 0, 1, 2, …are called integers.

  • Negative integers. The numbers …–3, –2, –1 are called negative integers.

  • Positive integers. The natural numbers are sometimes called the positive integers.

  • Rational numbers. Fractions, such as equation or equation, are called rational numbers. Since a number such as 5 may be written as equation, all integers are rational numbers. All rational numbers can be written as fractions equation, with a being an integer and b being a natural number. Terminating and repeating decimals are also rational numbers, because they can be written as fractions in this form.

  • Irrational numbers. Another type of number is an irrational number. Irrational numbers cannot be written as fractions equation, with a being an integer and b being a natural number. equation and π are examples of irrational numbers. An irrational number, when exactly expressed as a decimal, neither terminates nor has a repeating decimal pattern.

  • Even numbers. Even numbers are integers divisible by 2: … –6, –4, –2, 0, 2, 4, 6, …

  • Prime numbers. A prime number is a natural number that has exactly two different factors, or that can be perfectly divided by only itself and 1. For example, 19 is a prime number because it can be perfectly divided by only 19 and 1, but 21 is not a prime number because 21 can be perfectly divided by other numbers (3 and 7). The only even prime number is 2; thereafter, any even number may be divided perfectly by 2. Zero and 1 are not prime numbers or composite numbers. The first 10 prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

  • Odd numbers. Odd numbers are integers not divisible by 2: …–5, –3, –1, 1, 3, 5,….

  • Composite numbers. A composite number is a natural number divisible by more than just 1 and itself: …4, 6, 8, 9,…

  • Squares. Squares are the result when numbers are multiplied by themselves, that is, raised to the second power. 2 · 2 = 4; 3 · 3 = 9. The first six squares of natural numbers are 1, 4, 9, 16, 25, 36.

  • Cubes. Cubes are the result when numbers are multiplied by themselves and then again by the original number, that is, raised to the third power. 2 · 2 · 2 = 8; 3 · 3 · 3 = 27. The first six cubes of natural numbers are 1, 8, 27, 64, 125, 216.

Ways to show multiplication

There are several ways to show multiplication of a pair of numerical values.

  • When the two numerical values are known, you can show the multiplication of 4 with 3 as follows:

    equation
  • When one value is a number and the other value is a variable: show multiplication of 4 and a as follows:

    equation
  • When both values are variables: show the multiplication of a and b as follows:

    equation

Common math symbols

The following math symbols appear throughout algebra. Be sure to know what each symbol represents.

Symbol references:

  • = is equal to

  • ≠ is not equal to

  • > is greater than

  • < is less than

  • ≥ is greater than or equal to (also written equation)

  • ≤ is less than or equal to (also written equation)

  • equation is not greater than

  • equation is not less than

  • equation is not greater than or equal to

  • equation is not less than or equal to

  • ≈ is approximately equal to (also equation)