Pre-algebra contents: algebraic methods in arithmetic

The database of the EMTeachline Mathematics Software contains approximately 5 000 000 of math problems. Math problems are graded in 11 difficulty classes and cover all skill levels from basic through advanced. The software modules are organized by subject. Covered subject areas are Arithmetic, Pre-algebra, Algebra I and II, Trigonometry and Hyperbolic Trigonometry. The Arithmetic and Pre-Algebra modules offer tasks on simplification and evaluation of numeric expressions, including fractional expressions, computational problems, proofs of numeric equalities. The Algebra modules offer simplification and evaluation problems, proofs of algebraic identities and inequalities, solutions of algebraic equations and inequalities; included are linear, quadratic, cubic, reciprocal, biquadratic and fractional expressions. The Trigonometry and Hyperbolic Trigonometry modules offer simplification and evaluation problems, proofs of trigonometric and hyperbolic identities, and solutions of trigonometric and hyperbolic equations; included are all the basic and inverse trigonometric and hyperbolic functions. All problems are solved or proved in full detail. Each module allows employing the database for development of math tests, quizzes, exams, revision exercises and homeworks. Currently available themes, chapters and sections, together with those in preparation, are listed below. Our free online demos allow viewing math examples online.

• Simplify and evaluate expressions reduced to linear expressions. Integers.Elementary linear expressions

• Simplify and evaluate expressions reduced to linear expressions. Integers.Elementary linear expressions containing fractions

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Distributive law

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Formulas of short multiplication

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Formulas of short multiplication. Cubes

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Properties of powers

• Simplify and evaluate expressions reduced to linear expressions. Integers.Expressions reduced to linear expressions

• Simplify and evaluate expressions reduced to linear expressions. Integers.Fractional expressions. Properties of fractions. Rational coefficients

• Simplify and evaluate expressions reduced to linear expressions. Integers.Fractional expressions. Properties of fractions. Integer coefficients

• Simplify and evaluate expressions reduced to linear expressions. Integers.Fractional expressions. Method of substitution. Integer coefficients

• Simplify and evaluate expressions reduced to linear expressions. Integers.Fractional expressions. Method of substitution. Rational coefficients

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Factorization of quadratic trinomial

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Method of substitution. Distributive law

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Method of substitution. Formulas of short multiplication

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Method of substitution. Properties of powers

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Method of substitution. Factorization of quadratic trinomial

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Properties of fractions. Distributive law

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Properties of fractions. Formulas of short multiplication

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Properties of fractions. Properties of powers

• Simplify and evaluate expressions reduced to linear expressions. Integers.Linear expressions. Properties of fractions. Factorization of quadratic trinomial

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Elementary quadratic expressions

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions containing fractions

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Distributive law. Integer coefficients

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Formulas of short multiplication

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Distributive law. Rational coefficients

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Factorization of quadratic trinomial

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Properties of powers

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Fractional algebraic expression

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Grouping method

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Distributive law. Integer coefficients

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Distributive law. Rational coefficients

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Grouping method

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Factorization of quadratic trinomial

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Fractional expressions. Method of substitution. Distributive law. Integer coefficients

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Fractional expressions. Method of substitution. Distributive law. Rational coefficients

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Fractional expressions. Method of substitution. Formulas of short multiplication. Integer coefficients

• Simplify and evaluate expressions reduced to quadratic expressions. Integers.Fractional expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Bezout theorem. Integer roots. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Bezout theorem. Irrational roots. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Bezout theorem. Integer roots. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Grouping method. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Perfect square. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Bezout theorem. Irrational roots. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Formulas of short multiplication. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Difference of squares. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Factorization of quadratic trinomial. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Properties of fractions. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Difference and sum of cubes. Integers

• Simplify and evaluate high-degree expressions. Integers.Simplify and evaluate algebraic high-degree expressions. Method of substitution. Integers

• Simplify and evaluate fractional expressions. Integers.Elementary fractional algebraic expressions. Simplify and evaluate

• Simplify and evaluate fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with linear expression in numerator. Simplify and evaluate

• Simplify and evaluate fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator. Simplify and evaluate

• Simplify and evaluate fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with cubic expression in numerator. Simplify and evaluate

• Simplify and evaluate fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator. Simplify and evaluate

• Simplify and evaluate fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Simplify and evaluate

• Simplify and evaluate fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution. Simplify and evaluate

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Elementary linear expressions

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Elementary linear expressions containing fractions

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Distributive law

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Formulas of short multiplication

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Formulas of short multiplication. Cubes

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Properties of powers

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Expressions reduced to linear expressions

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Fractional expressions. Properties of fractions. Rational coefficients

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Fractional expressions. Properties of fractions. Integer coefficients

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Fractional expressions. Method of substitution. Integer coefficients

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Fractional expressions. Method of substitution. Rational coefficients

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Factorization of quadratic trinomial

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Method of substitution. Distributive law

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Method of substitution. Formulas of short multiplication

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Method of substitution. Properties of powers

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Method of substitution. Factorization of quadratic trinomial

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Properties of fractions. Distributive law

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Properties of fractions. Formulas of short multiplication

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Properties of fractions. Properties of powers

• Transform, evaluate and compare values of expressions reduced to linear expressions. Integers.Linear expressions. Properties of fractions. Factorization of quadratic trinomial

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Elementary quadratic expressions

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions containing fractions

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Distributive law. Integer coefficients

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Formulas of short multiplication

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Distributive law. Rational coefficients

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Factorization of quadratic trinomial

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Properties of powers

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Fractional algebraic expression

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Grouping method

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Distributive law. Integer coefficients

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Distributive law. Rational coefficients

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Grouping method

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Quadratic expressions. Method of substitution. Factorization of quadratic trinomial

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Fractional expressions. Method of substitution. Distributive law. Integer coefficients

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Fractional expressions. Method of substitution. Distributive law. Rational coefficients

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Fractional expressions. Method of substitution. Formulas of short multiplication. Integer coefficients

• Transform, evaluate and compare values of expressions reduced to quadratic expressions. Integers.Fractional expressions. Method of substitution. Formulas of short multiplication. Rational coefficients

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Bezout theorem. Integer roots. Transform, evaluate and compare

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Bezout theorem. Irrational roots. Transform, evaluate and compare

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Bezout theorem. Integer roots. Transform, evaluate and compare

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Grouping method. Transform, evaluate and compare

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Bezout theorem. Irrational roots. Transform, evaluate and compare

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Formulas of short multiplication. Transform, evaluate and compare

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Difference of squares. Transform, evaluate and compare

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Factorization of quadratic trinomial. Transform, evaluate and compare

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Properties of fractions. Transform, evaluate and compare

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Difference and sum of cubes. Transform, evaluate and compare

• Transform, evaluate and compare values of high-degree expressions. Integers.Algebraic high-degree expressions. Method of substitution. Transform, evaluate and compare

• Transform, evaluate and compare values of fractional expressions. Integers.Elementary fractional algebraic expressions. Transform, evaluate and compare

• Transform, evaluate and compare values of fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with linear expression in numerator. Transform, evaluate and compare

• Transform, evaluate and compare values of fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator. Transform, evaluate and compare

• Transform, evaluate and compare values of fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with cubical expression in numerator. Transform, evaluate and compare

• Transform, evaluate and compare values of fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator. Transform, evaluate and compare

• Transform, evaluate and compare values of fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Transform, evaluate and compare.

• Transform, evaluate and compare values of fractional expressions. Integers.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution. Transform, evaluate and compare

• Test the validity of equalities reduced to linear equalities. Integers.Elementary linear expressions

• Test the validity of equalities reduced to linear equalities. Integers.Elementary linear expressions containing fractions

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Distributive law

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Formulas of short multiplication

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Formulas of short multiplication. Cubes

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Properties of powers

• Test the validity of equalities reduced to linear equalities. Integers.Expressions reduced to linear expressions

• Test the validity of equalities reduced to linear equalities. Integers.Fractional expressions. Properties of fractions. Rational coefficients

• Test the validity of equalities reduced to linear equalities. Integers.Fractional expressions. Properties of fractions. Integer coefficients

• Test the validity of equalities reduced to linear equalities. Integers.Fractional expressions. Method of substitution. Integer coefficients

• Test the validity of equalities reduced to linear equalities. Integers.Fractional expressions. Method of substitution. Rational coefficients

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Factorization of quadratic trinomial

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Method of substitution. Distributive law

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Method of substitution. Formulas of short multiplication

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Method of substitution. Properties of powers

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Method of substitution. Factorization of quadratic trinomial

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Properties of fractions. Distributive law

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Properties of fractions. Formulas of short multiplication

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Properties of fractions. Properties of powers

• Test the validity of equalities reduced to linear equalities. Integers.Linear expressions. Properties of fractions. Factorization of quadratic trinomial

• Test the validity of equalities reduced to quadratic equalities. Integers.Elementary quadratic expressions. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions containing fractions. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Distributive law. Integer coefficients. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Formulas of short multiplication. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Distributive law. Rational coefficients. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Factorization of quadratic trinomial. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Properties of powers. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Fractional algebraic expression. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Grouping method. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Method of substitution. Distributive law. Integer coefficients. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Method of substitution. Distributive law. Rational coefficients. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Method of substitution. Formulas of short multiplication. Integer coefficients. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Method of substitution. Formulas of short multiplication. Rational coefficients. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Method of substitution. Grouping method. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Quadratic expressions. Method of substitution. Factorization of quadratic trinomial. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Fractional expressions. Method of substitution. Distributive law. Integer coefficients. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Fractional expressions. Method of substitution. Distributive law. Rational coefficients. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Fractional expressions. Method of substitution. Formulas of short multiplication. Integer coefficients. Simplify

• Test the validity of equalities reduced to quadratic equalities. Integers.Fractional expressions. Method of substitution. Formulas of short multiplication. Rational coefficients. Simplify

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Bezout theorem. Integer roots. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Bezout theorem. Irrational roots. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Bezout theorem. Integer roots. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Grouping method. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Perfect square. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Bezout theorem. Irrational roots. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Formulas of short multiplication. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Difference of squares. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Factorization of quadratic trinomial. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Properties of fractions. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Difference and sum of cubes. Test the validity of equality

• Test the validity of high-degree equalities. Integers.Algebraic high-degree expressions. Method of substitution. Test the validity of equality

• Test the validity of fractional equalities. Integers.Elementary fractional algebraic expressions. Test the validity of equality

• Test the validity of fractional equalities. Integers.Fractional algebraic expressions reduced to a fraction with linear expression in numerator. Test the validity of equality

• Test the validity of fractional equalities. Integers.Fractional algebraic expressions reduced to a fraction with quadratic expression in numerator. Test the validity of equality

• Test the validity of fractional equalities. Integers.Fractional algebraic expressions reduced to a fraction with cubical expression in numerator. Test the validity of equality

• Test the validity of fractional equalities. Integers.Fractional algebraic expressions reduced to a fraction with biquadratic expression in numerator. Test the validity of equality

• Test the validity of fractional equalities. Integers.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Test the validity of equality

• Test the validity of fractional equalities. Integers.Fractional algebraic expressions reduced to a fraction with reciprocal expression in numerator. Method of substitution. Test the validity of equality