# Introduction to algebra

Contents

This topic covers:
- Evaluating algebraic expressions
- Manipulating algebraic expressions & equivalent expressions
- Seeing structure in expressions
- Irrational numbers
- Division by zero

20 exercises available

Did you realize that the word "algebra" comes from Arabic (just like "algorithm" and "al jazeera" and "Aladdin")? And what is so great about algebra anyway?
This tutorial doesn't explore algebra so much as it introduces the history and ideas that underpin it.

Wait, why are we using letters in math? How can an 'x' represent a number? What number is it? This tutorial is great if you're just beginning to delve into the world of variables and expressions.

Learn how to substitute (or "plug in") values for variables and evaluate algebraic expressions.

Learn how to plug in values to evaluate real-world expressions.

Learn the basics of writing expressions with variables.

Learn to tell whether or not two algebraic expressions are equivalent by combining like terms and using the distributive property.

Sometimes one variable depends on another. For example, the amount of money you make might depend on how many hours you work.

Learn how to combine like terms (with negative numbers and variables), including more complex problems involving the distributive property.

Any expression (mathematical or otherwise) has meaning. Help us match the linear expression to the meaning options given. In some cases, more than one meaning may apply.

Learn how to evaluate expressions with variables whose values are unknown, by using another information about those variables. For example, given that a+b=3, evaluate 4a+4b.

Learn how to rewrite expressions with variables whose values are unknown, by using another information about those variables. For example, given that a+b=0, express a*b in terms of b alone.

Learn how to study algebraic expressions containing variables whose values are unknown, and how to derive new facts about those expression by using other information. For example, given two positive integers b and c where b>c, determine which expression is greater: b/(b+c) or 0.5.

Learn what irrational numbers are. Also learn how to classify numbers as whole, integer, rational, and irrational.

Learn some proofs about the existence of irrational numbers.

Determine whether various combinations of rational and irrational numbers are rational or irrational themselves.

Sal uses algebraic reasoning to tackle the problems of dividing by zero.

Most of us are use to using the digits 0-9 to represent numbers in the base-10 (decimal)number system. In this tutorial, we'll see that is just one of many (really infinite) number systems. In particular, we will focus on the binary (base-2) and hexadecimal (base-16) systems.