Algebra (Mathematics Curriculum)
What Is Algebra?Algebra is a branch of mathematics that uses letters to represent numbers.
Dictionary DefinitionThe 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 AlgebraThe 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.
EquationAn equation is algebra has an equals sign (=). Here is an example of an equation:
ConstantsIn the equation below, the 2, 1, and 9 are constants. In algebra, constants have a fixed value.
VariableIn the equation below, the x is a variable. A variable is a letter that represents a number.
CoefficientThe 2 is a coefficient. A coefficient is a constant in front of a letter.
ExponentThe 2 is an exponent. An exponent tells you how many times the letter or number immediately to its left is multiplied by itself.
OperatorThe + is an operator. The operators include +, -, ×, and ÷.
TermsThe 2x2, 1 and 9 are terms. A terms is a collection of letters and/or numbers. (Note: Terms are separated by + or - operators.
ExpressionsThe 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 EquationsAlgebra 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 EquationsEquations 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 AlgebraAlgebra 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 AlgebraExponents 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 nth root of the base:
When the fraction is m over n
- Take the nth root and find the mth exponent, or
- Find the mth exponent and take the nth root:
Read more about how to multiply powers
Read more about how to divide powers
Read more about how to find a power of a power
Read more about how to find a power of an algebraic fraction
Read more about how to find a negative exponent
Read more about how to find fractional exponents in algebra
Like Terms in AlgebraA 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 FactoringExpanding 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 how to expand double brackets using the grid method
Read more about factors in algebra
Read more about the greatest common factor in algebra
Algebra LessonsHere 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 DefinitionsUnderstanding the definitions in algebra
Algebra EquationsUnderstanding linear equations
Understanding quadratic equations
Understanding simultaneous equations
Rearranging Algebraic EquationsSolving equations with addition
Solving equations with subtraction
Solving equations with multiplication
Solving equations with division
Arithmetic with AlgebraAdding letters
Exponents in AlgebraUnderstanding 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 AlgebraUnderstanding like terms
Collecting like terms
Adding like terms
Subtracting like terms
Expanding and FactoringExpanding brackets
Factoring an expression
Expanding brackets using the grid method
Understanding factors in algebra
Understanding the greatest common factor