EMTeachline interactive arithmetic software - solving arithmetic problems

EMMentor Arithmetic

EMTeachline Mathematics Software - interactive math problem solving, test authoring

Get a private math tutor right on your desk! All students need help at some point, so be sure to get the help you need. With dozens of interactive learning techniques and a unique system of error analysis, EMMentor provides a qualified training of problem solving skills. He will offer you a task, ask you questions, give you hints as you need them, analyse your answers, trace your errors, detect gaps in your theoretical knowledge and problem solving skills and generate optimal exercises to close these gaps. EMMentor is here to help you figure out how to learn math for yourself. Those who stick with EMMentor will come away with a stronger understanding of fundamental math concepts, improved higher-level thinking skills and excellent practical skills in solving math problems! Free fully functional downloadable version of EMMentor is available. Our online demos enable you to try a number of training techniques and observe examples of error analysis.

Parameters of the program

Name of program:	EMMentor_Arithmetic
Number of problems:	36319
Number of similar variants:	15
Languages of interface:	English, German
Price:	178 EUR
Size of archive:	4217 kb

Abstract. EMMentor_Arithmetic is a new generation interactive training program that offers a large number of math problems, a variety of appropriate techniques to solve problems and a unique system of performance analysis with methodical feedback. Students at all levels can practice at their own pace, review their own work, monitor their weaknesses and achievements, and get methodical recommendations for building missing math knowledge and skills.Covered topics are arithmetic and pre-algebra. The program includes 36319 math problems of 11 levels of complexity, from basic to advanced. For each math problem, EMMentor offers a set of methodical tasks to be discharged at each step of problem solution. Your work will be throughly analysed with respect to multiple parameters. You can review the distributions of your errors throughout the solution steps, over formulas and other math concepts, over topics, etc. Based on this joint error distribution, EMMentor provides an optimal set of tasks for error correction. In addition, EMMentor offers a number of test authoring options that automate creation of math tests, quizzes, homeworks and exams of varied complexity and enable automatic generation of a number of variants around each test. The tests with or without the solutions can be printed out or stored in a file and re-used. Dozens of variant tests are ready for students to review and reinforce their math skills. Each definition, rule etc can be instantly translated to German or another available language.

System Requirements:

Pentium 2 or higher

64 MB RAM

Windows 98 or higher

Internet Explorer 5.5 or higher

Plug-in MathPlayer (downloadable from here)

Program's detail

●	Examples
●	Press release
●	Contents of the program
●	Characteristics of similar programs

Examples

An online sample of math problems and problem solutions from this program is provided below:

●	Problems: Arithmetic

EMTEACHLINE MATHEMATICS SOFTWARE - YOUR PERSONAL MATH TEACHER

Press release

ABSTRACT. EMTeachline Software has released a PC-based interactive mathematics software brand EMMentor that tutors in solving math problems. This encyclopedic software contains hundreds thousands of fully explained step by step solutions to math problems from basic to advanced and thousands of related definitions, rules, formulas and theorems. Based on a unique teaching technology, EMMentor controls, analyses and grades your performance, detects gaps in your theoretical knowledge and problem-solving skills, and generates an optimal set of tasks to close the revealed gaps. This software helps kids grasp math concepts and build problem solving skills much more effectively than any classroom teacher. For teachers and parents, EMMentor offers a comprehensive objective analysis of children's performance, with tables and plots, and methodical recommendations for error correction. Easy-to-use authoring options automate development of math tests and homeworks. The software is designed for mathematics self-study. Provides an ideal help for math teachers. Suitable for elementary, middle and high school use.

1. SOFTWARE OVERVIEW

The EMTeachline Interactive Mathematics Software EMMentor provides kids and teens with the chance to build outstanding problem-solving skills in math without any external help. Based on a brand-new teaching technology, this highly interactive software will help you much more effectively than any classroom teacher.

EMMentor includes a set of original interactive training techniques and a unique system of performance analysis with methodical feedbacks. Each technique consists of a set of questions asked at each step of task performance and a system of multiple choice answers with hints. Based on an analysis of your answers, the software detects gaps in your theoretical knowledge and problem-solving skills and summarises your errors. To correct errors and develop missing skills, EMMentor offers an optimal set of exercises.

The error analysis is made for a particular task performance, as well as for a number of tasks performed during the selected period of time. EMMentor shows, in tables and on plots, how many errors were made and how many hints were used at each step of solution within one technique, the distributions of errors and hints throughout the techniques, over formulas and other math categories, the total number of errors per topic, etc. The concluding methodical recommendations are based on an objective analysis of these joint error distributions. Any teacher or tutor will find this function to be extremely useful.

As a multilingual tutoring program, EMMentor offers a way for children to learn math lexicon in a foreign language. Translation of any text to German or another available language is easily obtained by double-clicking on it. Those kids who study not in a native language will find this option invaluable.

Covered subject areas are arithmetic, pre-algebra, algebra, trigonometry and hyperbolic trigonometry. All math problems are graded in 11 complexity classes from basic to advanced and provided with fully explained step by step solutions. Comprehensive tutoring material is provided for each solution step. The available test authoring options automate development of tests, quizzes, homeworks and exams. All developed materials can be printed out or stored in a file and re-used.

2. SKILLS COVERED

Arithmetic and Pre-Algebra: Operations: multiplication, division, addition, subtraction. Fractions, powers. Numeric expressions: estimation, equivalencies, problem-solving. Solving arithmetic problems using algebraic formulas.

Algebra: Polynomial and fractional rational expressions: transformation, simplification, evaluation. Solution of linear, quadratic, cubic, biquadratic, reciprocal and fractional algebraic equations and inequalities. Proofs of algebraic identities. Solution methods: Substitution, factoring, grouping, Bezout theorem, formulas of short multiplication, method of intervals and more. Related theory: definitions and rules, proof of algebraic formulas and theorems.

Trigonometry and Hyperbolic Trigonometry: trigonometric and hyperbolic functions, arcus functions. Trigonometric and hyperbolic expressions: transformation, simplification, evaluation. Solution of trigonometric and hyperbolic equations. Proofs of trigonometric and hyperbolic identities. Solution methods: universal substitution, sum, product and addition of trigonometric functions, power reduction, multiple argument, shift of argument and more. Related theory: definitions and rules, proof of trigonometric and hyperbolic formulas.

3. USER OPTIONS

For math students: You will get a diagnosis of all vacancies in your math skills. You can train the missing problem solving skills with the help of dozens of interactive training techniques. You can effectively learn definitions, rules and other math concepts, study solution methods, pick up skills of verbal formulation of math transformations, learn proofs of math formulas and theorems, develop reasoning skills etc. And in parallel, you can learn math lexicon in a foreign language!

For math teachers: You can use an extensive bank of math problems; arrange problems by topic, complexity level, solution method and type of task; compile math tests, quizzes, homeworks and exams of varied complexity; create your own didactic materials and problem-solving lesson plans; generate numerous similar variants of math tests; use dozens of ready variant tests. For each student of yours, you can get an objective analysis of his/her work, revealing his/her weak and strong points, together with an optimal set of tasks for error correction.

Contents of the program

Themes

Arithmetic II. Standard calculations. Integers
Arithmetic III. Algebraic methods. Integers

Chapters and sections

Arithmetic II. Standard calculations. Integers
Chapters	Sections
Perform operations	Perform operations. Arithmetic operations on a set of integers I Perform operations. Arithmetic operations on a set of integers II Perform operations. Arithmetic operations on a set of rational numbers Perform operations. Arithmetic operations with fractional numeric expressions Perform operations. Arithmetic operations with fractional numeric expressions. Reduction of fractions Perform operations. Arithmetic operations with fractional numeric expressions. Equal denominators Perform operations. Arithmetic operations with fractional numeric expressions. Different denominators Perform operations. Arithmetic operations and operations of exponentiation. Fractional expressions
Compare values of expressions	Compare values of expressions. Arithmetic operations on a set of integers I Compare values of expressions. Arithmetic operations on a set of integers II Compare values of expressions. Arithmetic operations on a set of rational numbers Compare values of expressions. Arithmetic operations with fractional numeric expressions Compare values of expressions. Arithmetic operations with fractional numeric expressions. Reduction of fractions Compare values of expressions. Arithmetic operations with fractional numeric expressions. Equal denominators Compare values of expressions. Arithmetic operations with fractional numeric expressions. Different denominators Compare values of expressions. Arithmetic operations and operations of exponentiation. Fractional expressions
Test the validity of numerical equality	Test the validity of numerical equality. Arithmetic operations on a set of integers I Test the validity of numerical equality. Arithmetic operations on a set of integers II Test the validity of numerical equality. Arithmetic operations on a set of rational numbers Test the validity of numerical equality. Arithmetic operations with fractional numeric expressions Test the validity of numerical equality. Arithmetic operations with fractional numeric expressions. Reduction of fractions Test the validity of numerical equality. Arithmetic operations with fractional numeric expressions. Equal denominators Test the validity of numerical equality. Arithmetic operations with fractional numeric expressions. Different denominators

Arithmetic III. Algebraic methods. Integers
Chapters	Sections
Simplify and evaluate expressions reduced to linear expressions. Integers	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 quadratic expressions. Integers	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. 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 high-degree expressions. 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. 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	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	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. 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 quadratic expressions. Integers	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. 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 high-degree expressions. Integers	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. 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 fractional expressions. Integers	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.
Test the validity of equalities reduced to linear equalities. Integers	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 quadratic equalities. Integers	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. 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. 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 high-degree equalities. Integers	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. Properties of fractions. Test the validity of equality
Test the validity of fractional equalities. Integers	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 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

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