# 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."# 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

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

^{2}# Operator

**+**is an operator. The operators include

**+**,

**-**,

**×**, and

**÷**.

# Terms

The**2x**,

^{2}**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:

- Linear equations

- Quadratic equations

- Simultaneous equations contain several equations:

Read more about quadratic equations

Read more about simultaneous equations

# Rearranging Algebraic Equations

Equations can be rearranged in order to solve problems.- If an algebraic equation contains addition, the added term can be subtracted from both sides:

The term has changed sides, and changed signs. - If an algebraic equation contains subtraction, the subtracted term can be added to both sides:

The term has changed sides, and changed signs. - If an algebraic equation contains multiplication, the multiplied term can be divided from both sides:

The term has swapped sides, and swapped from top to bottom. - If an algebraic equation contains division, the dividedterm can be multiplied by both sides:

The term has swapped sides, and swapped from bottom to top.

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 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.

- Terms can be added:.

- Terms can be subtracted:

- Terms can be multiplied. The coefficients are multiplied, and each letter must appear in the result as many times as they appear in the multiplication.

- Terms can be divided.

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:

- When exponents of the same base are multiplied together, the exponents can be added:

- When exponents of the same base are divided, the exponents can be subtracted:

- When an exponent is raised to another exponent, the exponents can be multiplied:

- When a fraction has an exponent, the exponents can be applied to both the numerator and denominator of the fraction:

- When a exponent is negative, calculate the positive exponent then find the reciprocal:

- Exponents can be fractions. There are two varieties:

When the fraction is**1 over n**, take the**n**of the base:^{th}root

When the fraction is**m over n**

- Take the
**n**and find the^{th}root**m**, or^{th}exponent - Find the
**m**and take the^{th}exponent**n**:^{th}root

- Take the

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.

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 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 algebraUnderstanding constants

Understanding coefficients

Understanding equations

Understanding exponents

Understanding expressions

Understanding operators

Understanding terms

Understanding variables

# Algebra Equations

Understanding linear equationsUnderstanding quadratic equations

Understanding simultaneous equations

# Rearranging Algebraic Equations

Solving equations with additionSolving equations with subtraction

Solving equations with multiplication

Solving equations with division

# Arithmetic with Algebra

Adding lettersSubtracting letters

Multiplying letters

Dividing letters

Adding terms

Subtracting terms

Multiplying terms

Dividing terms

# Exponents in Algebra

Understanding the laws of exponentsUnderstanding multiplying exponents

Understanding dividing exponents

Understanding raising exponents

Understanding exponents of fractions

Understanding negative exponents

Understanding fractional exponents

# Like Terms in Algebra

Understanding like termsCollecting like terms

Adding like terms

Subtracting like terms

# Expanding and Factoring

Expanding bracketsFactoring an expression

Expanding brackets using the grid method

Understanding factors in algebra

Understanding the greatest common factor