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Subtraction of Integers: Properties, Rules with Solved Examples

Subtracting integers is the method of discovering the difference between two numbers. The original value may increase or decrease depending on whether the numbers are positive, negative, or a combination. Subtracting integers involves finding the difference between integers with the same or different signs. In this article, we will learn more about subtracting integers.

#subtracting integer

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Graphing Proportional Relationships

A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same. For example, we consider the relationship between x and y. When x is one, y is three. When x is two, y is six. When x is 9, y is 27. This is a proportional relationship. Why is that? Because the ratio between x and y is always the same value. The ratio between y and x is also constant. 

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How to Write a Quadratic Function in Standard Form

Quadratic Functions are defined as second-degree polynomial equation, which means it has at least one term with a power of two. Quadratic Functions are so named because Quad stands for ‘four’ (squared), and a quadratic function’s greatest degree should be 2.

Quadratic Functions can be represented in 3 forms: 

Standard Form : ax² + bx + c = 0

Vertex Form :  a(x – h)² + k = 0

Intercept Form : a(x – p)(x – q) = 0

#Quadratic Functions

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How to Add Decimals? Definition & Examples

A decimal is a fraction whose denominator is the power of 10, i.e., 10, 100, 1000, and many more. It is denoted by the ‘dot (.)’ between numbers. The dot in a decimal number is called a decimal point, while the digits following the decimal point are smaller than one.

For example, the number 345.808 is a decimal number.

Here, 345 is the part of a whole number, and 808 is a fractional or decimal part below that 1 in value.

If we move from left to right places in a decimal number, the decimal place value determines the tenth, hundredth, thousandth, and so on places. Tenth place means 1/10 or 0.1 in decimal form. At the same time, a hundredth place means 1/100 or 0.01 in decimal form.

#Decimals

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Division With Area Model: Definition with Examples

The area model with division is very helpful in solving division problems. Long division is considered one of the most complex topics to learn. Notably, the area model has great usability here. Students can apply the long division with the area model. Division of large figures is very easy with it. This method is simple to understand and apply.

Division With Area Model focuses on mental math. With this method, we can better understand the numbers. In this, we solve the problem based on division by subtracting multiples. We continue this process until we get a zero. Either we will get a zero or a remainder digit.

#Division With Area Model #multiples

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Solving System of Equations by Elimination

Do you know how to solve systems of equations by elimination? If not, then you are at the right place. There are several ways to solve the system of equations. One way is by using graphs. Graphing works well when the coefficients of the variables in the equation are small, easy to deal with, and the solution has integer values. Another method is substitution. Substitution works well when we can easily solve one equation for one of the variables and when there are not too many fractions in the resulting expression.

#Solving System #equations

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Rhombus and its Properties

A rhombus is a form of quadrilateral in Euclidean geometry. It is a specific case of a parallelogram, in which the diagonals cross at 90 degrees. The basic attribute of the Rhombus is its unique shape. The shape of a rhombus is similar to that of a diamond. As a result, it is also known as a diamond. In a rhombus, look for symmetry lines for its proper identification.

#Rhombus #quadrilateral

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Classification and Properties of Triangles

A triangle is a geometrical figure that has three sides and three angles. Do you remember a polygon with the least number of sides? Well, that is a triangle. A polygon is a simple closed curve. It is made of line segments. Can we make a closed curve with a single line segment? The answer is no. Even if we try to make a curve with two line segments, it won’t be possible. So we need to make three segments and intersect them to form a closed curve, that is, a triangle. So, a triangle is a closed curve made up of three line segments.

#triangle

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Fractions: How to Multiply Fractions by a Whole Number

Multiply fractions by a whole number is a straightforward operation. It is one of the basic concepts taught in the lower grades. It is taught to enhance the arithmetic capacity of the students. Students are often confused while multiplying and dividing the fractions. This article will review the techniques to multiply a fraction by a whole number with some examples.

Before learning how to multiply a fraction by a whole number, let us look at some basic terminologies we shall use in multiplication. Are you well aware of what fractions are? Fractions, in general, are numbers that are presented in the form of p/q. For example, 2/3, 9/2, etc.

#Fractions #whole number

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Numerical Expression: Definition, Simplification With Examples

Definition of a Numerical Expression: The term numerical refers to something that involves numbers. We know that expression is nothing but just a phrase. Thus, numerical expression is a phrase involving numbers. In mathematics, a numerical expression is a set of numbers that have been written together by utilizing arithmetic operators addition, subtraction, multiplication, and division.

#Numerical Expression

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Normal Distributions: Definition, Table and Examples

Normal Distributions are also called the Gaussian Distributions. A normal distribution is the most significant continuous probability distribution. Early mathematicians and statisticians noticed the same shape for various distributions—so they named it the normal distribution, i.e., normally occurring distribution. 

Definition: The Normal Distribution can be defined by the probability density function for a continuous random variable in a system. If f(x) is the probability density function, X is the random variable; then it defines a function that is integrated between the range or interval (x to x + dx).

#Normal Distributions #mathematicians

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Number sequences: Definition and Types

As discussed earlier, sequences are lists. Number sequences are therefore defined as lists of numbers that show certain patterns. When you understand the pattern of any sequence, you can figure out the next number in the sequence.

For example, consider the list below of numbers, 

2, 4, 6, 8, 10

Observe the sequence. You will find that the sequence is a list of even numbers. You will be able to recognize what number comes next now. 

The next number in this sequence would be 12.

#Number sequences

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Subtract Fractions with Unlike Denominators

Fractions are parts of a whole, i.e., they represent a section of a collection. The word fraction comes from ‘fractio,’ a Latin word that means ‘to break.’ The Egyptians used fractions to solve mathematical problems, including dividing food and supplies. Ancient Romans wrote fractions as words and not numbers. Indians first wrote fractions as numbers that appeared as one number above another. The Arabs were the first to add the line between the numbers differentiating them as numerators and denominators.

#numerators #denominators. #Fractions

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Solving Proportions: Definition, Solved Examples

A proportion can be defined in a variety of ways. According to one definition, a proportion is an equation having two equal ratios. In other terms, a percentage is when two fractions are joined in the center by an equal sign. Variables can be found in one or both of the fractions in proportions.

Apart, share, or quantity regarded in comparison to a total is generally referred to as a proportion. When two ratios are equal, they are in proportion, according to the definition of proportion. 

#fractions #proportion.

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Solving System of Equations by Substitution

Solving System of Equations by Substitution method is useful for solving a system of equations. It is most easily applicable to systems of linear equations. In this article, we will review the method of substitution. We will discuss what the substitution method is and how to solve system of equations by substitution. Also, we will solve multiple examples. It will aid in better understanding. So, let us begin the discussion.

#Solving System #linear equations

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Increasing and Decreasing Intervals – Definition, Formulas

Increasing and decreasing intervals of real numbers are the real-valued functions that tend to increase and decrease with the change in the value of the dependent variable of the function. To find intervals of increase and decrease, you need to determine the first derivative of the function. This is done to find the sign of the function, whether negative or positive. The function interval is said to be positive if the value of the function f (x) increases with an increase in the value of x. In contrast, the function interval is said to be negative if the value of the function f (x) decreases with the increase in the value of x. 

#Intervals #functions