Come and study math with us here at tutorela.

We promise you that it is going to be easy and fun😄

The Commutative Property of Addition

Sometimes we come across problems that, at first glance, seem overly complicated and difficult. When this happens, our first step should be to take a deep breath and simplify. One of these useful simplifying tools that make our lives easier is called the commutative property of addition. It allows us to reorder an expression in a way that will be easier to work with. Let's take a look!

The commutative property

Algebraic exercises at any level present us with calculation challenges that can be simplified if we know how to correctly use certain simple algebraic rules. In spite of the mania we have for resorting directly to the calculator, the use of these algebraic rules allows us to carry out calculations that a priori may seem complicated, but that can become relatively easy without using a calculator. In this exercise we will focus on the commutative property, but we will briefly recall other properties, such as the associative and distributive properties.

Perimeter of a triangle

During your math studies you will encounter all kinds of triangles: isosceles, equilateral, right-angled or scalene. One problem that will always come up (and may become your favorite) is calculating the perimeter of a triangle. For many students this is like a gift because all you have to do to calculate the perimeter of a triangle is to do a simple addition.

So how do you calculate the perimeter of a triangle and what is the real challenge in solving such a problem?

Isosceles triangle

The isosceles triangle forms a category of triangles in the classification according to the length of its sides.

Equilateral triangle

Recall that triangles can be classified according to the measure of their angles or their sides. When the classification is made through the measures of the sides, we can classify them as: equilateral, isosceles and scalene.

An equilateral triangle is one whose three sides have the same length.

Types of Triangles

The triangle is one of the essential geometric figures, and many of the test questions in high school deal with this shape. In this article we will learn what a triangle is, what its properties are and what types of triangles exist.

What is the unknown of a mathematical equation?

The unknowns of a system of equations are usually expressed with the letters x, y, z; or with Greek letters such as alpha, beta and gamma. Most of the time we will have to solve the equation by finding the value of the unknown.

Solution of an equation

In this article we will get to know the equations and learn simple ways to solve them.

Time units

Time units play a very important role in our daily life and therefore it is necessary that we understand them well.

Weight units

Weight units are very important and we use them often in our daily lives.

Length units

Units of length are among the most useful units available.

Units of measurement for 11 and 12 year olds

Units of measurement allow us to quantify length, weight, time, money, space, volume and more. Depending on the category there are different units of measurement, it is important to know the conversion rules to move from one unit to another. For example, the units of measure for length are millimeter, centimeter, meter, kilometer, etc. Money units of measure are dollar, cent, peso, cent and more.

Real line or Numerical line

We first encounter the real line (also called the "number line") when we learn about positive and negative numbers, but what is the real line? In this article we explain it to you.

Positive and negative numbers and zero

Positive and negative numbers and zero are a fundamental topic in algebra.

The perimeter of the rectangle

Rectangles have two pairs of opposite, parallel and equal sides.

Coordinate System

When studying mathematics and geometry in middle schools, we often come across questions that deal with various coordinate systems. This is a topic where many and varied questions can be asked. Despite the rich variety, most of the solutions are based on basic rules, some of which we will get to know in this chapter.

The area of a parallelogram: what is it and how is it calculated?

One of the most popular and recurring shapes in geometry problems is the parallelogram. Its name reveals the most salient features of this geometric figure and, in several geometry assignments, students are even asked to calculate its surface area.

The sides or edges of a triangle

The sides or edges of a triangle are a very general topic in geometry that has many uses.

The sides of a triangle, sometimes called the edges, are the straight lines that bound the sides of the plane figure.

The Sum of the Interior Angles of a Triangle

The sum of the angles of a triangle is one of the most common topics in geometry. The theorem of the sum of the interior angles of a triangle is used to solve many geometry problems.

First-degree equations with one unknown

First degree equations with one unknown are a fundamental part of algebra. They will appear in different ways in a wide variety of topics. Therefore, it is more than important to understand from the very beginning the rules that apply to solve these types of equations.

Sides, Vertices, and Angles

Sides, vertices, and angles are basic geometric concepts on which more complex concepts will be based.

Opposite numbers

In the previous articles we have studied the number axis, integers, as well as positive and negative numbers. In this article we will explain what opposite numbers are, and how to identify them.

Integers

In the previous article we studied what the number line is, and of course, positive and negative numbers. In this article, we will study what integers are.

Improper Fractions

In this article, we will learn everything we need to know about improper fractions! We will learn what an improper fraction is, how to identify an improper fraction, how to convert an improper fraction to a mixed number and vice versa, how to convert a whole number to an improper fraction and vice versa, and how to determine which improper fraction is greater than the other. Shall we begin?

Tiling with regular polygons

In this article, we will learn everything you need to know about tiling with regular polygons! First of all, it is worth learning what tiling is and what a regular polygon is.

Families of Parabolas

In this article, we will get to know the family of parabolas and learn everything we need to know about them! Shall we begin?

Variable

In this article, we will learn what a variable is, what its meaning is, its different forms, and where we will encounter it in various mathematical topics.

Numerical Value

In this article, we will learn what a value is, understand its meaning, and see where we encounter it in various mathematical topics. Shall we begin?

Methods for solving a quadratic function

In this article, we will learn the three most common ways to solve a quadratic function easily and quickly.

Finding the Zeros of a Parabola

One of the things we might encounter when working with quadratic functions is finding the zeros of the function. How do we do that? All the answers in the article!

Plotting the Quadratic Function Using Parameters a, b and c

In this article, we will learn together the steps required to plot a function, that is, to transfer a function from a formula of numbers and variables to a graph.

Slope in the Function y=mx

The concept of the slope in the function y=mx is extremely important. The slope in the function y=mx actually expresses the angle between the line and the positive direction of the X-axis.

Function

In this article, we will learn everything you need to know about functions! We will understand what a function is, what its significance is, how it can look, and even practice some exercises on the topic! Shall we begin?

Exponents - Special Cases

In this article, we will focus on the special cases in exponents – exponents of negative numbers, exponents with an exponent of 0, and exponents with a whole and negative exponent. Shall we begin?

Exponents and roots

In this article, we will learn what an exponent is and what it consists of, what a root is, and how to solve exercises with exponents and roots. Shall we begin?

Ways to represent a quadratic function

In this article, you will learn the different ways to represent a quadratic function easily and efficiently. Ready for it?

Algebraic Fractions

An algebraic fraction is a fraction that contains at least one algebraic expression (with a variable). The expression can be in the numerator, the denominator, or both. Come and read everything you need to know about algebraic fractions.

Dividing Whole Numbers by Fractions and Mixed Numbers

Division exercises with fractions and mixed numbers are easy and not intimidating if you just follow the steps.

Reducing and Expanding Decimal Numbers

The topic of reducing and expanding decimal numbers is extremely easy.

Converting a decimal fraction to a mixed number

The transition from a decimal to a mixed number is simple and easy if you just know the right way. To do it correctly without making mistakes, we recommend that you make sure you know how to read decimal fractions properly. If you know how to read decimal fractions correctly, the path to success in transitioning from a decimal to a simple fraction is completely paved for you.

Comparing Fractions

To compare fractions, all we need to do is find a common denominator – that is, bring both fractions to a state where the denominators are the same.

Types of Fractions

In this article, you will learn what a fraction is and how it can be represented in several different ways. Shall we begin?

Ellipse

In this article, you will learn everything you need to know about the special shape ellipse and also how to calculate its area.

Regular Polygon

In this article, we will learn everything necessary about the regular polygon, focusing on topics such as the area of the regular hexagon, tessellation with regular polygons, and measurements of angles in regular polygons.

Height of a Prism

The height of the prism is another important subtopic when we study right triangular prisms. The height of the prism also plays a role in all relevant calculations for the right triangular prism.

Lateral Edges of a Prism

The lateral edges of a prism are another important subtopic when we study right triangular prisms, which will allow us to perform many calculations.

Three-Dimensional Figures

In this article, we will learn everything necessary about three-dimensional figures, focusing mainly on the cuboid, the cylinder, and the prism.

The commutative properties of addition and multiplication, and the distributive property

In this article, we will summarize all the basic math rules that will accompany you in every exercise - the commutative property of addition, the commutative property of multiplication, the distributive property, and more!

Advanced Arithmetic Operations

In this article, we will learn important arithmetic rules that will help you in many exercises.

Intersection between two parabolas

When we want to find the intersection points between two parabolas, we compare their equations – according to the method of comparing quadratic equations.

Properties of the roots of quadratic equations - Vieta's formulas

You are probably asking yourselves what Vieta's formulas are and what this strange name means... Please, don't be alarmed by the name – Vieta's formulas are very simple and easy formulas that connect the roots of a quadratic equation (its solutions) to the coefficients of the different terms. They are named Vieta after the mathematician who invented them.

Whole Numbers

In this article, you will learn everything you need to know about whole numbers and practice some exercises with whole numbers.

Dependent Random Events

Random dependent events in probability are a topic that might confuse many students, but by reading the content carefully and meticulously and by clearly understanding the material, you will realize that it is not complicated at all.

Types of trapezoids

In this article, we will learn everything you need to know about trapezoids and understand the differences between the various types of trapezoids. Shall we begin?

Ways to represent a function

In this article, you will learn how to represent a function in several different ways – algebraically, graphically, using a table, or even verbally. Additionally, you will also know how to denote a function. Shall we begin?

Inputing Values into a Function

Generally, a numerical value is input into equations with variables or in mathematical expressions that include variables. This involves replacing the variables in a mathematical expression or equation with specific numerical values. By assigning the numerical value, the general form becomes a particular case.

Increasing Intervals of a function

The increasing interval of a function are an important part of understanding the function. An increasing interval of a function expresses the same values of X (the interval), in which the values of the function (Y) grow parallel to the growth of the values of X to the right. Increasing intervals of one function or another can be clearly seen on its graph.

Decreasing Interval of a function

The decreasing intervals of a function are part of the phases of its analysis. A decreasing interval of a function expresses the same values of X (the interval), in which the values of the function (Y) decrease as the values of X increase to the right. The decreasing intervals of a function can be clearly seen in its graph.

Acute Angles

An acute angle is one of the types of angles that we will encounter during engineering studies.

Prime Factorization with Exponents

From time to time, in order to solve a certain exercise in a simple and correct way, we will have to factorize numbers that are presented to us in order to simplify the expression. We can find out all about it in the article.

Negative Exponents

We are likely to run into numbers rasied to negative powers, but there is nothing to worry about.

Zero Exponent Rule

The zero exponent is an special case in the world of powers. When we see a number that is not 0 raised to zero, the result will be 1.

Congruence of Right Triangles (using the Pythagorean Theorem)

The congruence of right triangles is an important subtopic on the more general topic of triangle congruence.

Similar Triangles

Similar triangles is one of the central topics in plane geometry.

Similarity ratio

The similarity ratio is a central concept when we talk about similarity in triangles and polygons.

Similarity of Triangles and Polygons

In this article we will learn what is the similarity of triangles and polygons. Intuitively, similarities between triangles are porportional increases and decreases of size. In this article we will explain the mathematics behind this intuition. We will know the similarity ratio and learn how to calculate it. After this, we will make an initial understanding of the three similarity theorems. Finally, we will see what similarities there are between polygons.

Fractions

Fractions refer to the number of parts that equal the whole. Suppose we have a cake divided into equal portions, the fraction comes to represent each of the portions into which we have cut the cake.

The Multiplication Tables

When dealing with multiplication tables, we must first understand what lies behind the concept of multiplication.

The lateral faces of the prism

The lateral faces of the prism are an integral part of the study of right triangular prisms or prisms with a triangular base. We use this data to perform several important calculations related to the prism.

Bases of the Right Triangular Prism

The bases are an important part of the prism that we will explore. The data that we are given about the bases of a prism will be of fundamental utility at the moment of making different calculations on the prism.

Right Triangular Prism

The right triangular prism is one of the most important subjects studied in space engineering. It is a three-dimensional shape, which often reminds us of the shape of a Toblerone chocolate bar. This article will focus on the structure of the right triangular prism, its properties, and the ways in which we can calculate its area and volume.

Algebraic Representation of a Function

An algebraic representation of a function is a description of the relationship between the dependent variable (Y) and the independent variable (X) by means of an equation.

Graphical Representation of a Function

As we learned in an article on functions, the standard "correspondence rule" is the connection between a dependent variable (Y) and an independent variable (X). A graphical representation of a function is a description of the relationship between the dependent variable (Y) and the independent variable (X) by means of a graph or drawing, which gives a visual aspect to the concept of the function. From the graph it is possible to understand whether it is a linear function (straight line), a quadratic function (parabola) and more.

Representing a Function Verbally and with Tables

Function describes a relationship between a dependent variable (Y) and an independent variable (X). The legitimacy of this relationship between the variables is called the "correspondence rule". In this article we will learn about the verbal representation and the tabular representation of a function.

The Circumference of a Circle

The circumference is another important part of the circle we will explore. This is a concept that appears in most exercises dealing with circles, and therefore it is necessary to understand it well.

Diameter

The diameter is another important part of the circle we will learn about. The diameter is also involved in quite a few exercises related to the circumference.

Radius

The radius is another important part of the circle we will explore, as it helps us to perform many calculations.

Circle

The circle is an integral part of geometry. We encounter the the circle in many exercises in the various engineering subjects.

Perimeter of a trapezoid

If there is one question you should be happy to get on a quiz in class or on a math final exam, it is how do you calculate the perimeter of a trapezoid? The reason is its very simple calculation, which is based on the sum of all the sides of the trapezoid. As we know, the challenge in this type of questions is not to calculate data with the formula, but to extract the missing data from the question itself.

Plane angle

A plane angle is one of the types of angles that we will encounter during engineering studies.

The formula for the sum of squares

This is one of the abbreviated formulas and it describes the square sum of two numbers.

Multiplication of the sum of two elements by the difference between them

As can be observed, this formula can be used when there is a multiplication between the sum of two particular elements and the difference between the two elements.

The formula for the difference of squares

This is one of the abbreviated multiplication formulas and it describes the square difference of two numbers.

The volume of the prism

The volume of the prism is a very important subtopic when studying right triangular prisms. The volume of the prism reminds us above all that it is a three-dimensional geometric body, which means it has three dimensions (instead of two).

Indefinite integral

An integral can be defined for all values (that is, for all X). However, there are integrals that are not defined for all values (all X), since if we place a certain X or a certain range of values of X, we will receive an expression considered "invalid" in mathematics. The values of X for which the integration is undefined cause the discontinuity of a function. In this article, we will learn about some of them.

Density

The density of decimal numbers is a topic that is immediately related to the comparison of decimal numbers. In reality, there is nothing new in this topic, so, if you know how to compare decimal numbers without difficulty, you will understand it perfectly.

Rate of change represented with steps in the graph of the function

Another creative way that can very efficiently show the rate of change of a function is to draw stair-step lines on the graph. Also, this system allows us to understand the rate of change in a visual way.

Area of a square

Calculating the area of a square is one of the simplest there is. Let's learn it here!

Surface area of triangular prisms

The surface area of triangular prisms is a subtopic of great importance when we study right triangular prisms. Generally, every math student should know how to calculate the surface area of a prism, so you must understand this topic perfectly.

Multiplication of Algebraic Expressions

In algebraic expressions that contain variables or parentheses, it is not necessary to write the multiplication sign. In this article, we will explain everything you need to know about this.

Rate of change of a function represented graphically

One of the most accepted and well-known ways to represent the rate of change of a function is through a graph. Graphical representation greatly facilitates understanding since, as is well known, "a picture is worth a thousand words."

Solution of a system of equations - one of them is linear and the other quadratic

When we encounter a system of equations where one of them is linear and the other quadratic, we can easily solve it using the substitution method.

Identification of an Isosceles Triangle

How can we prove that the triangle we have is isosceles? All the answers are right here.

Cylinder Area

The cylinder has two types of areas: surface area and lateral area. You can easily calculate both according to this article!

Solving Equations Using the Distributive Property

Solving equations using the distributive property is a method that we generally find in first-degree equations with one unknown. It is enough for a first-degree equation with one unknown to contain parentheses for us to have to resort to this method to solve it.

Constant Rate of Change

Constant rate of change is a basic concept within the topic of functions. It is one of the primary characteristics of a function, therefore, it is very important to understand its meaning well.

Rate of Change of a Function Represented by a Table of Values

Another of the most accepted ways to represent the rate of change of a function is through a table of values. This is a very useful method that allows for an exact calculation of the rate of change.

Variable Rate of Change

In the topic of functions, the variable rate of change is a supplementary concept and, indeed, a "twin concept" to the constant rate of change. In this case as well, it is one of the primary characteristics of a function, therefore, it is very important to understand its meaning well.

From the Quadrilateral to the Parallelogram

We have long been familiar with the beloved and familiar quadrilateral, but today we will reveal how to determine that the quadrilateral in front of us is actually a parallelogram!

Ordered pair

As we have already learned, a coordinate system has two axes, and therefore, any value defined using this system of axes must include two values. These two values are called "ordered pairs". In this article, we will learn what an ordered pair is: how it is displayed and how it relates to the topic of functions.

Formulas for Cubic Expressions

In this article, we will show you 2 formulas that have expressions raised to 3. Enter the article and you will see that it is simpler than it seems.

Multiplication and Division of Real Numbers

The method to solve a multiplication and division exercise of real numbers is very similar to the one we use when we have to add or subtract real numbers, with the difference that, in this case, we must make use of the multiplication and division table that we learned in elementary school.

From a Quadrilateral to a Rectangle

How do we recognize that the quadrilateral in front of us is actually a rectangle? In two quite simple ways!

Similarity of Geometric Figures

The similarity between geometric figures is an interesting topic in the field of plane geometry.

Midsegment of a trapezoid

In this article, we will address the topic of the mid-segment in a trapezoid. We will learn how it crosses through the middle of the two sides from which it extends. If you are interested in learning about the mid-segment in a trapezoid, look at this article, let's begin:

Extracting the common factor in parentheses

Factor extraction is the first operation we try to carry out when we want to break down an expression into factors.

Quadratic Inequality

The quadratic inequality shows us in which interval the function is positive and in which it is negative - according to the inequality symbol. To solve quadratic inequalities correctly, we need to know two fundamental things.

Arcs in a Circle

An arc in a circle is the part located between 2 points on the top part of the circle.

Midsegment of a triangle

If we know its properties, the midsegment can be very useful for us when solving exercises with triangles.

Rotational Symmetry in Parallelograms

What is a shape with rotational symmetry? And what does that have to do with the parallelogram? After reading the article, you will be experts on the topic!

Chords of a Circle

The circle has a variety of parts and concepts that are important to know, including the chords.

Division of Decimal Numbers

The division of decimal numbers is a bit more complicated than the division of whole numbers, but, if you follow these steps in order, we are sure that you will manage!

Distance from a chord to the center of a circle

Have you thought about the distance between the center of the circle and the chord? That's exactly why we're here!

Perpendicular to a chord from the center of a circle

The perpendicular to the chord comes out from the center of the circle, intersecting the chord, the central angle in front of the chord, and the arc in front of the chord. In this article, we will detail and explain more about the topic.

Large Numbers

Sometimes, in certain subjects like biology or physics, some numbers that are very large or very small are mentioned. Instead of writing them down with a lot of digits, powers are used and a unique way of writing is employed.

Probability of Independent Random Events

Independent random events are those that occur independently of each other. Exercises that include this type of random events might seem, at first glance, somewhat unsettling, but whoever knows how to solve them skillfully will be pleased to discover that they are very simple and even enjoyable.

From a Parallelogram to a Rectangle

Do you want to know how to prove that the parallelogram in front of you is actually a rectangle?

Quadratic Equations System - Algebraic and Graphical Solution

When we encounter a system of quadratic equations, we generally want to find out where their points of intersection are. We can do this in two main ways...

Calendar and Time Calculation

In this article, you'll learn to understand the calendar and calculate time correctly! You can calculate time in days, weeks, months, and even years! Isn't that amazing?

Decimal Measurements

In this article, we will learn all about decimal measurements and introduce you to practical methods that will help you convert one measurement to another and even compare them with ease.

Repeating Decimal

In this article, we will introduce you to the repeating decimal and even teach you how to get to it without the need to use a calculator. Are we ready?

Proving Parallel Lines

Parallel lines are important and significant elements in the study of mathematics. In some cases, the information that two lines are parallel will not be given, so we must prove it on our own. How is it done? Everything is written in this guide.

Units of Volume

We use volume units in matters that deal with the geometry of space.

Constant Function

We will say that a function is constant when, as the value of the independent variable X increases, the dependent variable Y remains the same.

Division of Fractions

In this article, you will learn how to operate to divide fractions and discover how easy it is to do so with this method.

Discrete graph

We regularly encounter discrete graphs in everyday life, whether in newspapers, books, articles, therefore it is very important to understand what information lies behind these graphs. In this article, we will learn what a discrete graph is. We will explain it by showing an example of such a graph.

Part of a quantity

The topic of part of a quantity in fractions is pleasant and easy if you understand the principle and logic. Therefore, focus and you will see how you learn to solve questions of part of a quantity without any problem.

Variation of a Function

The variation of a function means the rate at which a certain function changes. The rate of change of a function is also called the slope. According to the mathematical definition, the slope represents the change in the function (Y) by increasing the value of X by 1. There are functions, like the linear function (function with the variable to the first power), in which the slope, or in other words, the rate of change of the function is constant. Other functions may have an increasing or decreasing rate of change, which is calculated separately for each X value.

Hundredths and Thousandths

In this article, we will learn about hundredths and thousandths and learn everything we need to know about them.

Sum of Fractions

In this article, you will learn the easiest ways to add fractions, which will allow you to add all kinds of fractions without any inconvenience.

A fraction as a divisor

What exactly is a fraction? Why is it useful and what do we do with it? All the answers to the questions - in this article!

Exponential Equations

Exponential equations are equations in which the unknown appears as a power. When we encounter an exponential equation, we will try to solve it using one of its two methods.

Subtraction of Fractions

In this article, we will learn how to subtract fractions in a simple and quick way.

Multiplication of Decimal Numbers

To easily solve exercises involving the multiplication of decimal numbers, you must know how to solve multiplications of whole numbers using the vertical form.

Conditional Probability

Conditional probability refers to the case where we have some data that could modify the probability that a certain event had occurred.

Currency Units

We use currency units daily when we perform conversion operations, both in our country and abroad.

Multiplication of Fractions

Multiplying fractions is an impressively easy topic! In this article, you'll learn in a flash how to solve any fraction multiplication exercise.

Measuring Time

In this article, you will learn to measure time! You will be able to know, without asking anyone, when a minute has passed or when two have passed, plus, you will be able to easily solve word problems that include times. Shall we start?

Equivalent Equations

Equivalent equations are an integral part of equations and can be very useful when solving them.

Mixed Numbers and Fractions Greater Than 1

In this article, we will learn what to do when there is a number and a fraction together. All this and much more in this article!

Common denominator

A common denominator is a topic that will accompany you for a long time from now until the end of your math studies, so you should know how to find it easily.

Decreasing function

We will say that a function is decreasing when, as the value of the independent variable X increases, the value of the function Y decreases.

Simplification and Expansion of Simple Fractions

Simplifying and expanding fractions is an easy and enjoyable topic that will accompany you in almost all exercises with fractions. Simplifying and expanding a fraction is actually a multiplication or division operation that is performed on the fraction so that the real value of the fraction does not change and simply looks different.

Addition and Subtraction of Decimal Numbers

In this article, we will learn how to add and subtract decimal numbers in a simple, easy, and quick way. In fact, adding and subtracting decimal numbers is very similar to operations with whole and common numbers that we already know and that we can even solve directly in our heads, without the need to write them down.

Factoring Trinomials

In this article, we will learn 2 ways to factor trinomials.

Addition and Subtraction of Mixed Numbers

In this article, we will learn how to add and subtract mixed numbers easily, quickly, and effortlessly.

Central Angle in a Circle

A central angle in a circle is an angle whose vertex is at the center of the circle and its sides are the radii of the circle.

Inequalities with Absolute Value

Inequality is a sign that might seem confusing at first glance, replacing the familiar and beloved equal sign, but in reality, it's a simple and clear matter, about which there's no need to stress!

Increasing functions

We will say that a function is increasing when, as the value of the independent variable X increases, the value of the function Y increases.

Multiplication of Integers by a Fraction and a Mixed Number

In this article, we will learn how to multiply a whole number with a fraction and a mixed number without any problem!

Multiplication and Division of Decimal Numbers by 10, 100, etc.

Multiplying and dividing decimal numbers by 10, 100, 1000, and even 10,000 is such a simple matter that, if you practice it a bit, you'll know how to solve these types of exercises even in your sleep! Shall we start?

Inscribed angle in a circle

We are here to define for you what an inscribed angle in a circle is. Also, to give you tips to remember its definition and characteristics in the most logical way.

Exponent of a Multiplication

The third property within the laws of exponents is used when finding a power of a multiplication. Normally, we will find a multiplication inside parentheses and an exponent outside the parentheses.

Area of a right triangle

The area of a right triangle is an important subtopic that is repeated over and over again in exercises that include any right triangle.

Area of a circle

The circular area is a very important subtopic when we talk about a circumference. Some exercises that deal with circumferences include, among other things, calculations of the area of a circle. Therefore, it is important to know this concept in depth.

Continuous Graph

In this article, we will learn what a continuous graph is. We will explain it through a graph of this type and answer all questions.

The Center of a Circle

The center of the circumference belongs to subtopics that make up the topic of the circumference and the circle. We use the concept of the center of the circumference to define the circumference itself, as well as to calculate the radius and diameter of each given circumference.

Multiplying Exponents with the Same Base

Multiplication of powers with the same base is the first property of exponentiation or property of exponents that we must know. When we are presented with exercises or expressions where multiplication of powers with the same base appears, we can add the exponents.

Tangent to a circle

You've arrived at the article where you'll learn everything you need to know about a tangent to a circle in the easiest and most logical way!

Power of a Power

Power of a power is the fifth property of powers or laws of exponents. When we have an expression raised to a power which, in turn, is raised (in parentheses) to another power, we can multiply the exponents and raise the base number to the result of this multiplication.

Power of a Quotient

The power of a quotient is the fourth property of powers or laws of exponents. When we encounter an expression with a quotient (or division) within parentheses and the entire expression is raised to a certain exponent, we can take the exponent and apply it to each of the terms in the expression.

Absolute Value Inequalities

The absolute value might seem a bit intimidating to some of you, as this pair of words is not a common expression in our everyday language and does not remind us of anything we know. Even inequalities might seem at first not so understandable because until now we have only dealt with equations. The absolute value and inequality usually go hand in hand and we are here to explain to you about each one individually and about their combination.

Sum of Angles in a Polygon

The sum of the angles of a polygon is an important topic that appears many times in geometry exercises.

Reading Graphs

One of the most important skills in mathematics is knowing how to read and interpret a graph, particularly when studying the topic of functions. Often, functions are represented by a diagram or some graph, hence the importance of interpreting the data in front of you in order to analyze it and draw conclusions. Indeed, reading information from a graph or table is not "rocket science". This is an acquired skill, which requires understanding a set of basic rules and practices. In this article, you will find a series of tools that will allow you to "dive into" the subject on the right foot.

Perimeter of a Parallelogram

The calculation of the perimeter is a subtopic that must be addressed when talking about parallelograms.

Rate of Change of a Function

One of the most important characteristics of functions is the rate of change. It is crucial that we know it to be able to analyze and understand a function correctly. In this article, we will delve into this topic and see the differences in the rates of change among different functions.

Division of Exponents with the Same Base

Division of exponents with the same base is the second property we will learn. When we encounter exercises or expressions with terms that have the same base and between them the division sign or fraction bar, we can subtract the exponents.

Increasing and Decreasing Intervals (Functions)

It is quite simple to describe the intervals where the function is increasing and where it is decreasing. One must observe the graph and see, on the X-axis, where the extreme points of the function begin and end.

Angle Bisector

The topic of bisectors is one of the most useful topics in geometry.

Right angle

A right angle is one of the types of angles that we will encounter during engineering studies.

Properties of Exponents

It is important that we know and learn all the properties of exponents or laws of exponents so that we can tackle complex exercises of an advanced level.

Angle Notation

Tutorela is here to introduce you to the four ways that are used to denote angles, so, whenever you are presented with an angle, in whatever way, you will be able to identify which angle they are referring to, as well as name them with the correct notation.

Probability for 9th Graders

It's time to delve deeper into a topic we studied some time ago and develop it in other aspects: probability.

Positive and Negative intervals of a Quadratic Function

What do the sets of positivity and negativity mean with respect to the quadratic equation and how are they found? All the answers are in this article!

Increasing and Decreasing Intervals of a Parabola

Like every equation, the parabola also has intervals of increase and decrease. How are they found? Read it here!

Angles In Parallel Lines

In this article, you will learn about all the angles that exist in parallel lines and you will know how to identify them at all times, even while you're sleeping!

Triangle

In this article, we will briefly learn everything necessary about triangles and also practice with some exercises! Let's get started!

Multiplication and Division of Mixed Numbers

In this article, you will see how easy it is to multiply and divide mixed numbers. You will understand the method, practice, and become a specialist in the topic!

Denominator

In this article, you will learn everything you need to know about the denominator and its function in fractions.

Numerator

In this article, you will learn everything you need to know about the numerator and its function in fractions.

Real Numbers

In this article, you will learn everything you need to know about real numbers and practice exercises on the topic.

Irrational Numbers

In this article, you will learn everything you need to know about irrational numbers and how to identify them in various numerical sets.

Rational Numbers

In this article, you will learn everything you need to know about rational numbers and you will practice it in various exercises.

Natural numbers

In this article, you will learn everything you need to know about natural numbers and you will put it into practice in various exercises.

Exponents of Negative Numbers

In this article, you will learn everything you need to know about the exponentiation of negative numbers and understand the difference between a power that is inside parentheses and another that appears outside of them.

Small Numbers

In subjects like biology or physics, sometimes, extremely large or small numbers are used. Instead of writing them down with a lot of digits, powers are used with a unique way of writing.

Equations

In this article, you will learn for the first time what equations are, you will know the different types, and maybe you can even solve some! Shall we start?

Simplifying Square Roots with Variables

In this article, you will learn all the properties of roots with variables and how to find the conditions of those letters (or variables) that are in the radicand. Does it sound complicated? Don't worry! A simple lesson, some exercises, and you'll shine.

Square Root of a Negative Number

Everything you need to know about the root of negative numbers is that... it simply does not exist! Negative numbers do not have a root, if you come across an exercise involving the root of a negative number on a test, your answer should be that it has no solution. Do you want to understand the logic? Keep reading.

Perimeter

In this article, we will learn what perimeter is and how to calculate it for each shape, all of that in the most entertaining and practical way there is!

Mixed Numbers

In this article, we will teach you the basics of everything you need to know about mixed numbers. If you wish to delve deeper into a specific topic, you can access the corresponding extensive article.

Decimal Fractions

In this article, we will teach you, in summary, part of what you need to know about decimal numbers. If you wish to delve deeper into any specific topic, you can always access the corresponding extensive article.

Mode in Statistics

In this article, we will learn about the mode, what it is, and how to find it within a frequency distribution table. We know it might seem complicated, but we assure you that it is a very simple and easy topic.

Median

In this article, we will learn what the median is, how to find it within an even or odd set of numbers, and how it differs from the mean.

Average

In this article, you will learn everything you need to know about the mean or average for 14-year-olds. We assure you that you will master the topic with great ease and you will even be happy to find it on your exam.

Vertical Multiplication

Vertical multiplication is a basic math topic that every student must know and be able to solve. To solve vertical multiplication exercises, in a simple and practical way, you must master the multiplication tables and follow the rules meticulously.

Operations with Fractions

In this article, we will learn how to perform mathematical calculations with fractions.

Vertex of a parabola

In this article, we will study the vertex of the parabola and discover easy ways to find it without too much effort.

Parts of a Rectangular Prism

The rectangular prism! What a magnificent figure! In this article, we will get to know the rectangular prism and its parts.

Lateral surface area of a rectangular prism

In this article, we will learn how to find the lateral area of a rectangular prism, quickly and easily.

Prime Factorization

In this article, you will learn to break down any number into prime factors with the help of two magnificent tricks that you will surely love!

Word Problems

Word problems often scare many students, however, the logic of this topic is the same as that of any other exercise, we just need to correctly identify the data.

From Parallelogram to Square

We know that a square is a type of parallelogram. How can we prove that the given parallelogram is, in fact, a square?

Rhombus, kite, or diamond?

So, what is that mysterious geometric figure that looks like a precious diamond? Maybe it reminds us of that card game? It's a very interesting geometric figure called a rhombus, also known as a kite or diamond (you can choose). Whatever you call it, you should know the properties of this figure and its uniqueness to solve certain geometric problems. So, let's begin...

Isosceles Trapezoid

Today we're going to talk about a very symmetrical shape that knows how to awaken our curiosity, and in certain cases, even reminds us of the roof of a house. And this, ladies and gentlemen, is none other than the isosceles trapezoid. This figure appears in many chapters of mathematics, so, to tackle problems with isosceles trapezoids, we must know well their properties and unique characteristics. So, let's dive into the depths of trapezoids!

Squared Trinomial

More than once we have heard the teacher ask in class: "Who knows how to solve a quadratic equation without the formula?" Or, in other words - Trinomial. But, but... What on earth is a trinomial? What is it about? How does understanding about the trinomial benefit our mathematical knowledge? Does it expand the possibility of having greater mathematical efficiency? Or, in fact, might it be superfluous to include it in the ninth-grade curriculum? In this article, we will answer these questions and learn about the properties of the trinomial that will help us quickly solve quadratic equations, simplify fractions, multiply and divide, deal with fractions, even with the common denominator in fractions with variables in the numerator and in the denominator.

Average for Fifth Grade

The average (arithmetic mean or simply mean) is a simple and fun topic. In this article, we will learn what the average is, how to calculate it, and other peculiarities that are worth knowing about it.

Roman Numerals

In this article, you will learn to identify Roman numerals, to write them from 1 to 12, and the particularities of the Roman numeral system. Shall we begin?

Divisibility Rules for 2, 4, and 10

In this article, we will teach you the best tricks to identify if a number is divisible by 2, by 4, and by 10.

Divisibility Rules for 3, 6, and 9

In this article, we will teach you how to identify, in a matter of seconds! if a number is divisible by 3, by 6, and by 9. Shall we start?

Prime Numbers and Composite Numbers

In this article, we will describe what exactly prime numbers and composite numbers are; we will learn to identify them and get to know special numbers.

Quadratice Equations and Systems of Quadraric Equations

So far, we have learned to solve quadratic equations in various ways such as factoring, completing the square, and the quadratic formula. For equations that are not quadratic, we have learned to solve them using the method of equalization or substitution. Today we will learn about solving systems of quadratic equations and combined systems of equations (quadratic equations and linear equations) and will thoroughly understand the meaning of the system's solution.

How to calculate the area of an ellipse?

While there are subjects that are gradually integrated into the school curriculum over the years, there are subjects that are learned from the first day. One of those subjects? Mathematics. More precisely, first, there are calculation studies, which connect you, the students, with activities in addition and a bit of subtraction. As the years go by, you face more complex topics, and also shapes of which you must know the unique characteristics. One of those shapes, which you are likely also learning about these days, is an ellipse.

Various Forms of the Quadratic Function

At certain times, we will come across functions that look a bit different because they are missing the independent term B or C. In fact, this difference is positive since it makes solving the function easier! How? Let's find out!

Completing the square in a quadratic equation

The procedure for completing the square is another method with which quadratic equations can be solved.

Factored form of the quadratic function

This form is called factored because it uses the factors of a multiplication. With this form, we can easily identify the points of intersection of the function with the X-axis.

Vertex form of the quadratic equation

In this article, we will learn to identify the vertex of the parabola. You really want to understand the topic well, right? Enter to learn.

Standard Form of the Quadratic Function

The quadratic function is one of the topics that will accompany us almost always on our journey through the world of mathematics,

Family of Parabolas y=(x-p)²+k (combination of horizontal and vertical shifts)

In this article, we will study the combination of two families of parabolas, horizontal and vertical, anyone who wants more information is invited to enter.

Family of Parabolas y=(x-p)²

What are the properties of the family of parabolas y=(x-p)²? What can be done with it and how is it solved? All the necessary information appears in this article.

Family of Parabolas y=x²+c: Vertical Shift

Are you not entirely sure what vertical displacement means and need to know how to do it? You've come to the right place!

The functions y=x²

These are the most basic quadratic functions, therefore, it is crucial to understand them thoroughly in order to move forward and delve deeper into the study of the subject.

Square

The square is a very special figure. We already know that, but how is it defined? And how can we recognize it? The square's identity document awaits us right here!

From Parallelogram to Rhombus

How will you realize that the parallelogram in front of you is a rhombus? That's exactly why we're here! We'll teach you 3 criteria that will help you discover it.

Lines of Symmetry in a Rhombus

Is the rhombus a symmetrical figure? What types of symmetry are there? All the answers appear in the following article!

Proof by Contradiction

So far, we have demonstrated propositions directly, following this pattern: because this and that happen... this and that happen... and in this way, the proposition is proven. The time has come to learn another method of proof: The proof by contradiction.

Relations Between The Sides of a Triangle

There is a relation between the lengths of the sides of a triangle. It is very simple to remember and can be easily understood.

Relationships Between Angles and Sides of the Triangle

A triangle is a polygon with 3 sides, magnificent and special, whose sides and angles fulfill certain reciprocal relationships that we can easily remember.

Sum of the Exterior Angles of a Polygon

What should we know about the sum of the exterior angles of a polygon? The answer is simpler than you thought!

Exterior angles of a triangle

Until today, we have dealt with internal angles, perhaps also adjacent ones, but we have not talked about external angles. Don't worry, the topic of the external angle of a triangle is very easy to understand, and its properties can be very useful for solving exercises more quickly.

Measurement of an angle of a regular polygon

When you want to discover the size of an angle of a regular polygon with ease and speed, all you will need to do is use a formula.

Angles in Regular Hexagons and Octagons

What the heck is a regular polygon? And what should we know about it? All the answers await you here!

Sum of the Interior Angles of a Polygon

Sometimes we'll want to calculate the internal angles of polygons, even of unknown and exceptional shapes. How is it done? Here is everything.

Addition and Subtraction of Algebraic Fractions

Here we will learn how to add or subtract algebraic fractions.

Factoring Algebraic Fractions

Factorization is a basic operation that we must do to simplify the exercise; in fractions, we must factorize according to the order of mathematical operations. Are you interested? Read the article.

Writing Formal Proofs in Geometry

Writing formal proofs in geometry is a very important skill.

Notation of a Function

The notation of a function actually refers to determining the "name" of the function. It is customary to symbolize a function using letters from the Latin alphabet when the two most common notations are: Y and F(X). What is the X in parentheses and what do these letters symbolize? Let's learn in the article!

How to calculate the weighted average?

Along with classic average calculations, you will often be asked to calculate the weighted mean. The way to calculate it is different and requires you to understand the importance of such a value that is given to you as data.

Area of a Regular Hexagon

If you want to know how to calculate the area of a regular hexagon, here in this article you can find the answer. As we already know, what generally makes solving exercises of this type difficult is having partial knowledge of geometry, since the formula is usually quite easy to apply, and does not require complex arithmetic operations. So, how is the area of a regular hexagon calculated?

Perpendicular Lines

Perpendicular lines are those that create a right angle between them, that is, 90 degrees.

Absolute Value

The "absolute value" may seem complicated to us, but it is simply the distance between a given number and the figure 0. Read this article to understand it perfectly.

Order or Hierarchy of Operations with Fractions

The order of operations with fractions is no different from the order of operations without fractions. This means that if you know how to solve a certain exercise based on the order of mathematical operations, you will also know how to solve an exercise with fractions in the same way.

Estimation for Fifth Grade

Estimation exercises are simple and pleasant when you approach them with logic. In this article, we will teach you what estimation is and how you should tackle addition or subtraction exercises.

Comparison of Decimal Numbers

The comparison of decimal numbers is a very simple matter if we know how to approach it.

Addition and Subtraction of Real Numbers

After studying real numbers, it's time to learn how to use them in an equation. Initially, our goal with equations is to simplify them to make it more comfortable to solve the exercises; we do this by grouping operations and adding and subtracting real numbers.

Congruent Rectangles

Congruent rectangles are those that have the same area and the same perimeter.

The exponent of a power

The exponent of a power is an important subtopic within exponentiation.

Division of Whole Numbers Within Parentheses Involving Division

The division of whole numbers within parentheses where there is a division refers to the situation in which we must carry out the mathematical operation of dividing a whole number by the result of dividing two elements, that is, by their quotient.

The Distributive Property in the Case of Multiplication

The distributive property of multiplication allows us to break down the largest term in the exercise into a smaller number.

Scalene triangle

The scalene triangle is one of the types of triangles found when classifying them according to the difference in the length of their sides.

Obtuse Triangle

An obtuse triangle is another type of triangle in the classification of triangles according to angles.

Acute triangle

The acute triangle is one of the types of triangles that exist when classifying them according to their angles.

Solving Equations by Simplifying Like Terms

Simplifying like terms in an equation is something that almost always occurs when we are going to solve it. It's enough for a first-degree equation to contain more than two or three terms for us to have to resort to this method to find the final result.

Solving Equations by Multiplying or Dividing Both Sides by the Same Number

Solving equations by multiplying or dividing both sides by the same number is another useful and common method when it comes to finding the value of any type of equation.

Solving Equations by Adding or Subtracting the Same Number from Both Sides

Solving equations by adding or subtracting a number to both sides of the equation is one of the most common and useful methods for doing so. This method is very simple and easy to apply.

Elimination of Parentheses in Real Numbers

In previous articles, we have studied real numbers and the grouping of terms, as well as the function of parentheses in the order of mathematical operations. In this article, we move forward and combine the topics in order to understand when and how we can eliminate parentheses in real numbers.

Order of Operations with Parentheses

In previous articles, we have seen the order of operations for addition, subtraction, multiplication, and division, as well as the sequence we should follow when there are exponents. When the exercise we need to solve includes parentheses, we always (always!) start with the operation contained within them.

Order of Operations: (Exponents)

As part of the hierarchy of basic operations, we learned that parentheses always come first.

Multiplicative Inverse

Two numbers are multiplicative inverses when their multiplication results in 1.

Abbreviated Multiplication Formulas

Abbreviated multiplication formulas will be used throughout our math studies, from elementary school to high school. In many cases, we will need to know how to expand or add these equations to arrive at the solution for various math exercises. As with other math topics, even in the case of abbreviated multiplication formulas, there is nothing to fear. Understanding the formulas and lots of practice on the topic will give you complete control. So let's get started :)

How is the radius calculated using its circumference?

There are many questions that can be asked about circles and radii, and one of the most common questions is how to calculate the radius from the circumference of the circle. So, how is a radius calculated using the circumference?

How to Calculate Average Speed?

Apparently, your math teacher also shared with you the most important advice for solving problems: understanding what is being asked of you. Some students master the material taught, but because they have difficulty understanding what is being asked of them, they lose many points on exams. One of the common mistakes students make is not paying attention to the following two terms:

  • Average rate
  • Average speed

Sum and Difference of Angles

Since angles are a quantitative concept, meaning we describe them using numbers, we can add and subtract them.

Types of Angles

In this article, we will learn what an angle is, explore its different types, corresponding angles, and alternate angles between parallel lines. Angles are a quantitative concept, meaning they are measured with numbers. Therefore, we can compare them.

Functions for Seventh Grade

On one hand, functions are a fairly abstract concept, but on the other hand, they are very useful in many areas of mathematics. The topic of functions dominates many fields, including algebra, trigonometry, differential calculus, integral calculus, and more. Therefore, it's important to understand the concept of functions so that it can be applied in any of the fields of mathematics. This article will be dedicated to this.

Graphs

The graph is a concept that we encounter not only in math studies but also in everyday life, therefore it's very important to learn how to produce and understand the information that this tool represents. In this article, we'll understand what a graph is and what types of graphs there are.

Obtuse Angle

An obtuse angle is one of the types of angles that we will encounter during our engineering studies.

Domain of a Function

The domain of a function is all those values of X (independent variable) that, if we substitute them into the function, the function will still be valid and defined. The domain of a function is an integral part of function analysis. Moreover, a definition set is needed to create a graphical representation of the function.

Value Table

A value table is the "preparatory work" that we are often asked to do before creating a graphical representation. Therefore, it is an inseparable part of the subject of graphs in general and the topic of functions in particular. In this article, we will understand what a value table is and how to complete it.

Long Division

Long division might seem tricky or complex, but believe me, if you take it slowly, step by step, you'll reach the correct answer quite easily.

Placing Fractions on the Number Line

In this article, we'll learn how to place fractions on the number line easily, quickly, and without any trouble.

Midsegment

We're here to teach you everything you need to know about the midsegment, from its proof to its wonderful properties that will help us solve exercises.

Algebraic Method

In this article, we will cover several topics related to the algebraic method: powers, distributive property, factorization, and repeated distributive property. You can find more comprehensive and detailed articles for each of these topics.

Congruence Criterion: Side, Angle, Side

There are four criteria to determine if a triangle is congruent. In this article, we'll study the first criterion of congruence: Side, Angle, Side. We'll learn how to use it and look at examples.

How do you simplify fractions?

In this article, we will learn how to reduce fractions. Reducing fractions is a basic operation that can be used to change the structure of a fraction while maintaining its value. Reducing fractions makes it easier to continue working with this type of arithmetic expression.

Triangle Height

Calculating the height of a triangle is a fundamental aspect when studying everything related to this geometric shape.

Surface Area Units or Area Measurements

We typically use units of area for certain geometry problems. In this article, we'll explore different surface measurements like cm², m², and km², and learn how to convert between them.

Calculating the Area of a Rectangle

The rectangle is one of the most common geometric figures you will come across and calculating the area of one is a typical exam question.

Rectangle

The rectangle is one of the basic figures of plane geometry and features frequently in related exercises. In order to properly tackle such exercises, it is important to understand the various properties rectangles.

The Pythagorean Theorem

The Pythagorean Theorem is one of the most well-known theorems in the field of geometry and engineering, as well as one of the most feared topics among mathematics students in general.

Subtracting Whole Numbers with Addition in Parentheses

Subtraction of whole numbers with addition in parentheses refers to a situation where we perform the subtraction operation on a sum of terms that are in parentheses.

The Distributive Property of Division

The distributive property of division allows us to break down the first term (the number being divided) of a division operation into a smaller, more manageable number.

The Associative Property of Multiplication

Are complicated multiplication problems getting you down? They don't have to anymore! Today we're going to learn how to simplify those migraine-inducing, multi-factor multiplication expressions by using the associative property of multiplication.

The Associative Property of Addition

Have you ever come across a messy addition problem? Wish you could just rearrange the operations to make it easier? Well, you can! The associative property of addition lets you do just that.

The Associative Property

To make things easier when solving algebraic problems, we have a few properties that we can use to simplify expressions. Think of them as tools you can use to reshape an expression. The main properties we are focusing on at this level are: the associative, the commutative and the distributive properties. In this article, we get to know the associative property and its uses.

As we move forward, let's take a moment to briefly review our other properties: the distributive and the commutative properties.

The Commutative Property of Multiplication

Does the commutative property addition seem fairly intuitive - great! Now, let's take things a little further by exploring the commutative property of multiplication. This property is another useful tool that allows us to simplify and solve multiplication exercises efficiently and easily.

Exponents for Seventh Graders

Do you feel like you've mastered multiplication? The times tables are easy for you? Well, then it's time to take multiplication further - with exponents! Exponents tell us how many times to multiply a number by itself. They also allow us to write a large number in a simple way. When will I use this? Continue reading to explore exponential numers and their different applications.

Area of a trapezoid

Finding the area of a trapezoid may look complicated at first, but don't worry! In this article we will show you a simple way to calculate the area of a trapezoid using only three values.

Sequences

The study of sequences is a major part of mathematics. Therefore, gaining a firm understanding of its concepts is necessary before moving on to more advanced areas of the field.

Recurrence Relations

The topic of recurrence relations is an important one for mathematics students as it appears frequently in post-primary grades and on graduation exams. It is not complicated, although it does require a basic understanding of the concepts behind the theory. In this article, we will try to explain them in a simple and clear way.

The Distributive Property for Seventh Graders

The first step to solving a scary, complex multiplication equation is to simplify it. Often, what seems complicated is actually fairly simple. This is where the distributive property comes to helps us! The distributive property helps us to rewrite our expressions by breaking down large numbers into smaller, more manageable chunks.

The Extended Distributive Property

Does using the distributive property seem easy by now? Great! It's not so hard, it just takes some practice. Let's go a bit deeper - now we'll explore the extended distributive property. Here we'll see expressions with two sets of parentheses. Don't worry! Using the same principles that we've already learned, we'll find that the extended distributive property isn't any different than the basic distributive property.

The Distributive Property

The distributive property is a tool that helps us to simplify complex expressions by breaking down large numbers into smaller, simpler terms.

Parabola

The quadratic function, or the parabola, is a function that we will work with a lot throughout the years of studying mathematics in high school, so it is important to understand what it means and what to expect when solving its questions.

Converting Decimals to Fractions

Converting a decimal number to a simple fraction is easier than you might think. To do it without making mistakes, we recommend reviewing the reading of decimal numbers and making sure you know how to do it well. If you truly know how to correctly read decimal numbers, you are guaranteed success when trying to convert a decimal number to a simple fraction.

What is a Decimal Number?

The decimal number might sound like a somewhat challenging concept to you, but believe me, after reading this article, you will not fear encountering it on the exam, you will even be glad to see it.

Area

What is an area? What does it mean? How is the area of different geometric shapes calculated? All the answers can be found in this article!

Area of Equilateral Triangles

You don't have to worry about calculating the area of the equilateral triangle!

Area of a Scalene Triangle

Even with the scalene triangle, we should not fret about calculating its area!

Area of Isosceles Triangles

Isosceles triangles are no different from other triangles, and neither is finding their area!

Ratio

The ratio describes the "relationship" between two or more things. The ratio links the given terms and describes how many times greater or smaller a certain magnitude is than another.

Scale

Questions about scale deal with the relationship between the actual dimensions of an object and those of the drawing that represents it.

Inverse Proportion

Inverse proportionality indicates a situation in which, when one term is multiplied by a certain number of times, the second term is decreased by the same number of times and vice versa.

Direct Proportion

Direct proportion indicates a situation in which, when one term is multiplied by a certain amount, the second term undergoes exactly the same thing.

Finding a Missing Value in a Proportion

Sometimes we will be given only a whole ratio between two terms and a third piece of data that is part of another ratio. Usually, it will be stated that there is a proportion between the ratios and that we must find the missing data in the ratio.

Proportionality

Many students believe that proportionality is a super complicated topic, but believe me, it's not like that at all, it's entirely based on ratio or relationship and circumstances you have already studied.

Division in a given ratio

In a division according to a certain given ratio, we will have a defined quantity that we must divide according to that ratio.

Equivalent Ratios

Equivalent ratios are, in fact, ratios that seem different, are not expressed in the same way but, by simplifying or amplifying them, you arrive at exactly the same relationship.

Symmetry in a parabola

Not very clear on what symmetry in a parabola is? This article will bring some clarity!

The quadratic function

In past articles, we had seen what a function is and linear functions, now it's time to study a quadratic function, so we will start by asking ourselves: **What is a quadratic function?** A quadratic function is a second-degree polynomial with a single variable whose largest exponent is 2, the general form of a quadratic function is as follows:

Diagonals of a Rhombus

The diagonals of a rhombus have several special properties, in this article we will study these characteristics and see how they could be used when solving exercises with rhombuses.

Area of a Deltoid (Kite)

There are many geometric shapes that can be found during the solving of engineering problems at all different stages of study, such as in high school, in matriculation exams, and even in psychometry. One of the less trivial shapes is the deltoid, and as part of the questions surrounding it, students are often asked to calculate the area of the deltoid.

Factorization

Factorization allows us to convert expressions with elements that are added or subtracted into expressions with elements that are multiplied.

The Application of the Pythagorean Theorem to an Orthohedron or Cuboid

The uses of the Pythagorean theorem in an orthohedron or cuboid is an interesting subtopic within spatial geometry.

Numerical Sets: Natural Numbers, Integers, Rational Numbers, Irrational Numbers, and Real Numbers

The topic of numerical sets is very important within the field of algebra.

Inequalities

Inequalities are the "outliers" of equations and many of the rules that apply to equations also apply to inequalities. In terms of writing, the main difference is that instead of the equal sign "=", we use the greater than ">" or less than "<" signs. Inequalities can be simple or more complex and then contain fractions, parentheses, and more.

Representation of Phenomena Using Linear Functions

Representing phenomena using linear functions actually allows us to simplify many verbal questions using a simple linear graph. From the graph, we can very easily calculate the slope, which is actually the rate of change and even many other parameters.

Positive and Negativity of a Linear Function

The positivity and negativity of a linear function are an important subtopic when we discuss the search for functions.

Finding a Linear Equation

Finding a linear equation is a very important subtopic when we talk about the linear function. Finding the equation of a line is actually plotting the linear function using y=mx+b or y=mx. In this article, we will detail how we can find the linear equation using 5 different methods.

The Linear Function y=mx+b

The linear function y=mx+b is a fundamental topic in the field of functions. The linear function actually represents a graph of a straight line that intersects with the vertical Y-axis at a certain point.

Graphical Representation of a Function that Represents Direct Proportionality

The graphical representation of a function that represents direct proportionality is a very important subtopic in the subject of functions.

Linear Function

The linear function is a fundamental topic in the field of algebra, and therefore it is very important to understand its properties and rules.

Scale Factors, Ratio and Proportional Reasoning

Scale Factors, Ratio and Proportional Reasoning are very important and similar topics that often appear in algebra and geometry exercises.

Statistics

We know that the word statistics can sound a bit threatening and incomprehensible, perhaps because we don't usually use it in our daily conversations. Statistics really is a kind of language of its own, but after you read this article you will see how, in a matter of minutes, you will know all you need to know about this topic to be able to solve exercises without blinking an eye.

Identifying a Parallelogram

Do you want to know how to identify a parallelogram from miles away? After this article, you'll immediately know when it refers to a parallelogram and when to another square.

Symmetry in Trapezoids

What symmetry is there in the trapezoid? The following article refers to this:

Diagonals of an isosceles trapezoid

Come and learn about the properties of the diagonals of an isosceles trapezoid.

Solving Equations by Factoring

To solve equations through factorization, we must follow certain basic rules.

Multiplication and Division of Algebraic Fractions

When we want to multiply or divide algebraic fractions, we will use the same tools that we use for the multiplication or division of common fractions, with some small differences.

Simplifying Algebraic Fractions

In this article, we will learn how to simplify algebraic fractions. We will learn when it can and when it cannot be done.

Factoring using contracted multiplication

In this article, we will teach you how to factor according to the formulas for contracted multiplication

Uses of Factorization

Factorization is the main key to solving exercises more complex than those you have studied up to today.

Powers

Powers have a set of rules and norms that are very important to know in depth in order to solve power exercises quickly and without making mistakes. Don't worry, Tutorela provides you with everything you need to know about powers. So, shall we get started?

Cylinder Volume

A cylinder may seem like a scary way to calculate at first glance, but in fact it only takes a little familiarity with its volume formula to show that this is not the case.

Cylinder

The cylinder shape is widely used in our everyday life, for example in a toilet paper roll or a magician's hat. In fact, the cylinder occupies a place of honor in the field of space engineering. Therefore, it is important to know the salient features of this spatial shape in order to know how to tackle quite a few mathematical problems in the field of space engineering.

Verbal Problem Solving With a System of Linear Equations

In this article, we will present the topic of solving verbal problems with a system of linear equations.

Solving with the method of equalization for systems of two linear equations with two unknowns

There are several ways to solve equations, in this article we will work with the equalization method.

Substitution method for two linear equations with two unknowns

There are several ways to solve systems of linear equations, now we will concentrate on the substitution method.

Algebraic solution for linear equations with two unknowns

These questions can be solved in several ways, the algebraic resolution includes two methods:

Solution with graphical method for linear equations with two variables

There are several ways to solve quadratic or quadratic equations, now we will see how to do it with the graphical method.

Linear equation with two variables

There are many types of equations, among the most basic are linear equations that can have a diverse number of variables. In this article, we will see how to solve linear equations with 2 unknowns.

Two linear equations with two unknowns

The word "system" might already sound complex and stressful, and then they combined it with the term "linear," and as if all this were not enough, they also added two unknowns instead of one. We know that this topic might seem terrifying and daunting to you, but hey! don't panic, that's exactly what we're here for. We promise to teach you everything you need to know to master this topic perfectly and quickly solve any exercise that comes your way. Do you doubt it? Stay with us.

Triangle similarity criteria

In this article we will go deeper into the conditions required for two triangles to be considered similar and we will define the three criteria of similarity of triangles.

Probability Properties

The properties of probability are a central theme in this field, and several of the principles of probability are based on them.

Relative Frequency in Probability

Relative frequency is a central topic within the field of probability.

Probability frequency

Frequential probability is a very important topic in the field of probability.

Probability Representation on a Number Line

The representation of probability on the number line is a fundamental topic in the area of probability.

Side, Side, Angle

We're adding a fourth to the three congruence theorems that we've already learned.

Combining Powers and Roots

The root is the operation opposite to exponentiation, and exponents are the operation opposite to roots. It's no wonder we'll encounter a lot of exercises in a perfect combination, and we must know very well how to maneuver between the two. It's exactly for this reason that we're here to teach you rules that will help you combine roots and powers.

Square Roots

Radication is another rule of roots that must be learned.

Square root of a quotient

One of the three properties of roots is the root of the quotient.

Square root of a product

With the square root of a product, we can break down the factors of the products and leave a separate root for each of them.

Square Roots

A square root is the inverse operation of a power

Scientific notation of numbers

In various disciplines such as biology or physics, there are many cases where very large or very small numbers are indicated. Instead of writing a number with dozens of digits, use specific powers and specific writing methods.

Probabilities of outcomes and events

It is quite possible that when you read this title you will not understand exactly what its creator intended. Tutorela is here to reassure them and explain that in a few minutes they will know exactly the intention and the calculation of their possible outcomes and probabilities.

Probability

Probability is among the topics that tend to confuse students the most, but it can actually be understood in a simple way.

Key Metrics in Statistics

In statistics, there are a number of key metrics on which it is based.

Relative frequency

Relative frequency in statistics is an important concept in the field of statistics.

Statistical frequency

Frequency in statistics is a key concept in the field of statistics.

Data Collection and Organization - Statistical Research

Data collection and organization is a very important topic in the field of statistics, and the ability to collect data for various studies is based on it.

Factorization: Common factor extraction

In this article we will learn how to factor by taking out the common factor.

Equations with Fractions

In this article, we will learn how to solve fractional equations.

Special Cases of Equations

In this article, we will learn about cases of special equations. Equations with infinite solutions, equations with no solution.

Trapezoids

What is a trapezoid, what are its properties, and the secret trapezoids you can discover? All these questions will be answered in this article!

Equation with variable in the denominator

In this article we will learn about equations with variables in the denominator and we will learn how to solve them. We will learn it through many examples and we will advance each time with a higher level of difficulty.

Estimation

The topic of estimation is very important within the branch of algebra; it can even help us to make approximate calculations of all sorts in our daily lives.

Congruence Criterion: Side, Side, Side

There are 4 criteria to determine that two triangles are congruent. In this article, we will learn about the third criterion of congruence: Side, Side, Side.

Congruence Criterion: Angle, Side, Angle

There are four criteria to determine when two triangles are congruent. In this article, we will study the second criterion of congruence: Angle, Side, Angle. We will look at some examples to understand how to use this criterion.

The Area of a Triangle

Whether you are preparing for a test or are about to take university entrance exams, it is essential to know how to calculate the area of a triangle—regardless of its type (right angled, isosceles, etc.). So, how do you calculate a triangular area? This guide will clear up all of your doubts concerning one of the most frequently asked questions in geometry exams.

Logarithms

Logarithmic laws are an excellent example of yet another pair of scary words encountered during math studies, but if you delve a little deeper into the topic and understand what's behind these words, the fear can completely dissipate.

Parallelogram

Did you notice the quadrilateral that is formed at the intersection of 2 train tracks? What is it called? What are its characteristics? Let's take a look at the train tracks, why are there 2 parallel tracks? For the train to not derail, there must be 2 tracks that always maintain the same distance from each other. This is the definition of parallel lines that never meet because the distance between them is always the same. At the moment when 2 train tracks intersect, a quadrilateral is formed between them, which has 2 pairs of opposite sides parallel, which is the parallelogram. In this article, we will talk about what a parallelogram is and learn how to prove it.

The Area of a Rhombus

An integral part of the curriculum also includes geometric shapes, which feature, among other things, the rhombus. It's important to note that even if you are a high school student, you will still be asked to solve problems that include these same shapes, rhombuses included. So, how do you calculate the area of a rhombus?

Kite

Often, when we sit on the beach facing the sea, we observe a good number of kites. Have you examined their shape? It's a deltoid shape. The deltoid has a somewhat complicated shape. It is a quadrilateral but not a square, and it has a shape similar to a rhombus and a parallelogram, but their definitions are different. In this article, we will learn what a deltoid is and how to identify it.

How to Calculate Percentage

Percentages are one of the most studied topics in mathematics. And one of the most common exercises that every math student must know how to solve is how to calculate percentages.

Congruent Triangles

More than once, we've heard the principal telling the teacher, "Have you noticed that there is no overlap between the students and the study material? Well, your goal is to create that overlap." So, what is an overlap in everyday language? Overlap is a coincidence between two or more elements. Also, when we talk about triangles, we can find different types of coincidences. There are triangles that are equal only in their angles and are called similar triangles, and there are triangles that are equal in both their angles and sides, being identical to each other. We will call these latter triangles congruent triangles, and we will learn about them in this article.

What is a square root?

What are those mysterious square roots that often confuse students and complicate their lives? The truth is that to understand them, we need to grasp the concept of the inverse operation. What do we mean by this? When we solve an exercise like "How much is 5 squared?" it's clear that 5 multiplied by 5 gives us a result of 25. This is the concept of powers or, to be more precise, squaring a number. To apply it, we multiply the figure or number by itself. But what happens when we encounter an exercise where X squared equals 25? In this case, we must perform an inverse operation, and this is when square roots come into play.

Rules of Exponentiation

In this article, we'll start by recalling the definition of an "exponent," and then we'll focus in an organized manner on the different rules of exponents: