Algebra Basics Explained
Introduction to Algebra
From Numbers to Symbols
Arithmetic is great for working with numbers you already know. If you have 3 apples and you get 2 more, you know you have 5. But what if you don't know exactly how many apples you have? What if the number can change? That's where algebra comes in. It's a powerful way of doing math that uses symbols to represent unknown or changing values.
Variable
noun
A symbol, usually a letter, that represents an unknown number or a quantity that can change.
Think of a variable as a placeholder. Imagine you're baking cookies and the recipe calls for a certain number of chocolate chips, but you want to decide how many to add later. You could write down in your notes "add chocolate chips." The letter stands for the number of chips you'll eventually use. It could be 50, 100, or 200. The value can vary, which is where the name "variable" comes from.
Building with Expressions
Once we have variables, we can combine them with numbers and mathematical operations like addition, subtraction, multiplication, and division. When we do this, we create an algebraic expression. An expression is like a mathematical phrase; it's a set of instructions for a calculation, but it doesn't give a final answer because we don't know the value of the variable.
For example, if you get paid 💲20 an hour, and is the number of hours you work, the expression represents your total earnings. If you work 3 hours, your earnings are . If you work 8 hours, they're .
Expressions are made of a few key parts.
| Part | Description | In the expression 4x + 7 |
|---|---|---|
| Variable | The letter representing an unknown. | x |
| Coefficient | The number multiplied by the variable. | 4 |
| Constant | A number that stands alone. | 7 |
| Term | A single number, a variable, or numbers and variables multiplied together. | 4x and 7 are both terms. |
Notice that an expression doesn't have an equals sign. It's just a recipe for a value, waiting for you to plug in a number for the variable.
Making Mathematical Sentences
If an expression is a mathematical phrase, then an equation is a complete mathematical sentence. An equation sets two expressions equal to each other using an equals sign (=). It makes a statement of fact: the thing on the left side has the exact same value as the thing on the right side.
Think of an equation as a perfectly balanced scale. For the scale to stay level, both sides must have the same weight. For example, the equation states that "some unknown number plus 5" has the same value as "12".
This equation tells a story. It describes a relationship. It doesn't just list a calculation; it makes a claim that one quantity is equivalent to another. This is the fundamental idea that allows us to solve for the unknown values in algebra.
Now that you've got the basics of variables, expressions, and equations, let's test your knowledge.
What is the primary purpose of algebra, as distinct from arithmetic?
In the expression , what is the letter 'x' called?
Understanding these core building blocks is the first step. With them, you can start to describe the world in the language of algebra.