Algebra I

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 or , are called rational numbers. Since a number such as 5 may be written as , all integers are rational numbers. All rational numbers can be written as fractions , 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 , with a being an integer and b being a natural number. 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.