Follow Us on Twitter

Algebra (Mathematics Curriculum)

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.

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.

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 coefficients
Read more about exponents
Read more about operators
Read more about terms in algebra
Read more about expressions in algebra

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 powers
Understanding dividing powers
Understanding powers of a power
Understanding powers of algebraic fractions
Understanding an exponent of -1
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