IT103 Algebra

Unit 2: Some Math Basics

R Batzinger

2025-07-31

Session 2: Math Prerequisites

1 Real Numbers: Algebra Essentials

Types of numbers

  • natural: 1 to infinity as whole numbers
  • whole: 0 plus all natural numbers
  • integer: positive and negative whole numbers
  • rational: fraction of integers
  • irrational number: all others that do not fit above patterns

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English reading of numbers

  • Set of 3 digits: Hundreds, Tens, Units
  • Trillions, Billions, Millions, Thousands, -
  • The decimal point is read as AND

Examples

123,456,789.001

3.14159

1,001

2,210.55

1,000,001.001

Perform calculations using order of operations.

Please excuse my dear aunt sally!

  • Parenthesis
  • Exponents
  • Multiplication
  • Division
  • Addition
  • Subtraction

\[3^2 - 8/2 + 4^2\]

Properties of real numbers:

  • commutative
  • associative
  • distributive
  • inverse
  • identity

Evaluate algebraic expressions.

Simplify algebraic expressions.

Given a mathematical expression, simplify it using the order of operations.

  1. Simplify any expressions within grouping symbols.
  2. Simplify any expressions containing exponents or radicals.
  3. Perform any multiplication and division in order, from left to right.
  4. Perform any addition and subtraction in order, from left to right.

2 Exponents and Scientific Notation

3 Radicals and Rational Exponents

4 Polynomials

5 Factoring Polynomials

6 Rational Expressions