Follow Us on Twitter

What is Algebra? (Mathematics Lesson)

What Is Algebra?

Algebra is a branch of mathematics that uses letters to represent numbers.

Dictionary Definition

The Oxford English Dictionary defines algebra as "the part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations."
Here is an example of an algebraic equation. In this example, the letter x represents a number. Our job is find the value of x. Later on this page, we'll talk about what algebra is used for.



Where Does the Word Algebra Come From?

Algebra comes from the Arabic word al-jebr, which means "reunion of broken parts".

Albert Einstein and Algebra

The famous scientist Albert Einstein learned algebra from a young age.

The famous scientist Albert Einstein learned algebra from a young age.

His Uncle Jakob gave him books on the subject and called algebra "a merry science".

He compared algebra to hunting a little animal. You didn't know the name of the animal, so you called it "x". When you finally caught the animal you gave it the correct name.

Algebra Terminology

Equation

An equation is algebra has an equals sign (=). Here is an example of an equation:

Constants

In the equation below, the 2, 1, and 9 are constants. In algebra, constants have a fixed value.

Variable

In the equation below, the x is a variable. A variable is a letter that represents a number.

Coefficient

The 2 is a coefficient. A coefficient is a constant in front of a letter.

Exponent

  • The 2 is an exponent. An exponent tells you how many times the letter or number immediately to its left is multiplied by itself.

    Operator

  • The + is an operator. The operators include +, -, ×, and ÷.

    Terms

    The 2x2, 1 and 9 are terms. A terms is a collection of letters and/or numbers. (Note: Terms are separated by + or - operators.

    Expressions

    The 2x + 1 and 5 are expressions. An expression is one term or several terms that are added (+) or subtracted (-) together. (Note: The = separates expressions.)



    Read more about definitions in algebra
    Read more about equations
    Read more about constants
    Read more about variables
    Read more about co-efficients
    Read more about exponents
    Read more about operators
    Read more about terms in algebra
    Read more about expressions in algebra

    Why Is Algebra Useful?

    Algebra is useful because it can describe relationships and lets us solve puzzles.

    Many things in the world are described by mathematical relationships; like the sizes of shapes, or the movement of objects. Algebra lets us write these relationships down in a very precise way.

    Algebraic Equations

    Algebra is used to describe equations.

    There are different forms of equations:

    Read more about linear equations
    Read more about quadratic equations
    Read more about simultaneous equations

    Rearranging Algebraic Equations

    Equations can be rearranged in order to solve problems.

    Read more about algebraic equations that contain addition
    Read more about algebraic equations that contain subtraction
    Read more about algebraic equations that contain multiplication
    Read more about algebraic equations that contain division

    Arithmetic with Algebra

    Algebra uses letters to represent numbers.

    Letters can be added, subtracted, multiplied and divided; just like numbers.

    • Adding letters works when the letter is added to numbers, other letters and the same letter.


    • Subtracting letters works when the letter is subtracted by numbers, other letters and the same letter.


    • Multiplying letters works when the letter is multiplied by numbers, other letters and the same letter.


    • Dividing letters works when the letter is divided by numbers, other letters and the same letter.

    Read more about how to add letters
    Read more about how to subtract letters
    Read more about how to multiply letters
    Read more about how to divide letters

    Terms can also be added, subtract, multiplied and divided.

    Read more about how to add terms
    Read more about how to subtract terms
    Read more about how to multiply terms
    Read more about how to divide terms

    Exponents in Algebra

    Exponents notation indicates that a quantity is multiplied by itself a number of times.



    There are laws of exponents:

    Read more about the laws of exponents
    Read more about how to multiply exponents with the same base
    Read more about how to divide exponents with the same base
    Read more about how to raise one exponent to another exponent
    Read more about how to find the exponent where the base is a fraction
    Read more about how to find a negative exponent
    Read more about how to find a fractional exponent

    Like Terms in Algebra

    A like term is a term with the same combination of letters and exponents. The only difference between like terms is their coefficients.



    Expressions can be simplified by collecting like terms.

    • Identify the like terms:


    • Add and/or subtract the like terms together:

    Read more about like terms in algebra
    Read more about how to collect like terms
    Read more about how to add like terms
    Read more about how to subtract like terms

    Expanding and Factoring

    Expanding and factoring are methods for simplifying algebraic expressions. They are opposites of each other.



    • Expanding takes out brackets from an expression. The term outside the bracket multiplies each term inside the brackets.



      Expanding brackets can be done using a visual method called the grid method.



    • Factoring simplifies an expression by putting in a bracket, so the expression is a product of factors.



      The method works by taking the greatest common factor outside of the bracket.
    Read more about how to expand brackets
    Read more about how to factor an expression
    Read more about how to expand brackets using the grid method
    Read more about factors in algebra
    Read more about the greatest common factor in algebra

  • Curriculum

    Algebra Lessons

    Here is a handy list of our algebra lessons. The lessons and tests on these pages are designed to take a beginner through the basics of algebra. By the end of this curriculum, students will be solving some pretty daunting-looking equations by themselves.

    Algebra Definitions

    Understanding the definitions in algebra
    Understanding constants
    Understanding coefficients
    Understanding equations
    Understanding exponents
    Understanding expressions
    Understanding operators
    Understanding terms
    Understanding variables

    Algebra Equations

    Understanding linear equations
    Understanding quadratic equations
    Understanding simultaneous equations

    Rearranging Algebraic Equations

    Solving equations with addition
    Solving equations with subtraction
    Solving equations with multiplication
    Solving equations with division

    Arithmetic with Algebra

    Adding letters
    Subtracting letters
    Multiplying letters
    Dividing letters
    Adding terms
    Subtracting terms
    Multiplying terms
    Dividing terms

    Exponents in Algebra

    Understanding the laws of exponents
    Understanding multiplying exponents
    Understanding dividing exponents
    Understanding raising exponents
    Understanding exponents of fractions
    Understanding negative exponents
    Understanding fractional exponents

    Like Terms in Algebra

    Understanding like terms
    Collecting like terms
    Adding like terms
    Subtracting like terms

    Expanding and Factoring

    Expanding brackets
    Factoring an expression
    Expanding brackets using the grid method
    Understanding factors in algebra
    Understanding the greatest common factor