Algebra Rules Flashcards

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Questions and Answers

What is algebra?

Algebra is based on the operations of arithmetic and on the concept of an unknown quantity, or variable.

How do you multiply an algebraic equation by another algebraic equation?

Multiply each term in one equation by each term in the other equation. E.g. FOIL - (x + 1)(x + 2) = x^2 + 3x + 2.

What is a term in algebra?

A term is either a constant, a variable, or the product of one or more constants and/or variables.

What is a constant?

Constants are known quantities represented by numerical expressions. Signup and view all the answers

What is an algebraic expression?

A combination of variables, constants, and arithmetical operations. Signup and view all the answers

What types of triangles does the Pythagorean Theorem apply to?

Pythagorean Theorem only works for right-angled triangles. Signup and view all the answers

What is a polynomial?

A polynomial is an expression that is a sum of terms with nonnegative integer powers. Signup and view all the answers

What are solutions (roots) in an algebraic equation?

The solutions are assignments of constant values to the equation's variables that make the equation true. Signup and view all the answers

What are equivalent equations?

Two equations with the same solution or solutions. Signup and view all the answers

What is a linear equation?

A linear equation has a linear polynomial on one side and either a linear polynomial or constant on the other. Signup and view all the answers

What is a linear equation with one unknown?

A linear equation with only one variable. Signup and view all the answers

What is a linear equation with two unknowns?

A linear equation with two variables. Signup and view all the answers

How do you solve a linear equation with one unknown?

Isolate the variable on one side of the equation. Signup and view all the answers

What is the difference between fractions and ratios?

Fractions are (Part / Whole), whereas ratios are (Part : Part). Signup and view all the answers

How do you solve two linear equations with two unknowns using substitution?

Express one unknown in terms of the other and substitute into the second equation. Signup and view all the answers

What is a coefficient?

A coefficient is a non-variable multiplying a variable or variables. Signup and view all the answers

How do you solve two linear equations with two unknowns using elimination?

Change the equations to eliminate one unknown and solve for the remaining unknown. Signup and view all the answers

Why does setting equations equal to zero help in finding solutions?

This approach helps identify the values of the variable that satisfy the equation. Signup and view all the answers

Study Notes

Algebra Fundamentals

Algebra combines arithmetic operations with the concept of variables, representing unknown quantities (e.g. 3x² + 3x + 3).
Numerical expressions symbolize known quantities called constants.

Operations in Algebra

Multiplication of algebraic equations involves distributing each term in one equation by each term in the other (e.g. FOIL method).
An algebraic expression consists of variables, constants, and arithmetic operations.

Components of Algebra

A term can be a constant, a variable, or a product of constants and/or variables, functioning as a single input in functions.
A polynomial is characterized by:
- Being a sum of terms,
- Having nonnegative integer powers for variables,
- Possibly containing multiple variables or a single term (monomial).

Equation Characteristics

Solutions or roots of an equation are value assignments to variables that satisfy the equation.
Equivalent equations share the same solutions, maintain their integrity despite algebraic manipulation.

Linear Equations

Linear equations feature linear polynomials, with variables having an exponent of 1.
Types include:
- One unknown: involves isolating the variable to find its value.
- Two unknowns: consist of linear equations with two variables, solvable through substitution or elimination methods.

Solving Linear Equations

Substitution method:
- Express one unknown in terms of another, substitute into the second equation, and solve for the unknown.
Elimination method:
- Adjust equations to align coefficients of one variable; add or subtract to eliminate it and solve for the other.

Ratios and Fractions

Fractions represent a part over a whole, while ratios compare parts against each other (e.g. part:part or part:whole).

Finding Solutions

Setting equations to zero allows for determining inputs that satisfy the equation, essential for solving algebraic representations.

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Description

Test your knowledge of basic algebra principles with these flashcards. Each card provides a definition or explanation about fundamental algebraic concepts. Perfect for students looking to strengthen their understanding of algebraic operations and equations.