Operations Can Be Described as the Set

¶ … operations can be described as the set of rules that mathematicians have established and agreed to adhere to in order to avoid mass confusion when simplifying mathematical equations or expressions. Actually, without this simple and significant order of operations, learning mathematics would not only be difficult but almost impossible. Therefore, order of operations is important in solving equations or expressions with several operations or in simplifying the equations or expressions.

The main reason attributed to the ability of order of operations to contribute to simplifying expressions and equations is a standard that describes the order for the process through operations like addition, multiplication, subtraction, and division ("Order of Operations Lessons," n.d.). During the process of developing the order of operations, mathematicians were very careful in order to promote the simplification of mathematical equations and expressions.

If the order of operations is ignored, the most possible outcomes include the fact that solving an equation would be very difficult and the possibility of obtaining wrong answers to the equations. The other possible consequence of ignoring order of operations is that a problem can be interpreted in many different ways because of the lack of a standard. If I invented a new notation whose order of operations was made unclear, I would take some necessary measures to make it clear.

The measures to be taken are the three important steps in solving mathematical equations and expressions when using order of operations. These steps are parenthesis, exponents, multiplication and division, and addition and subtraction. This rule helps in making the order of operations for new notation clear and avoiding incorrect answers to equations. Difference among Integers, Real Numbers, Rational Numbers, and Irrational Numbers: Integers are described as a set of real numbers that comprise of the natural numbers, their additive inverses, and zero.

In addition to the fact that the set of integers is in some cases written J. Or Z. In short, the product, sum, or difference of any two integers is also an integer. In this case, the natural numbers that make up integers are whole numbers, which are sometimes written N. In short. On the contrary, rational numbers are those expressed as a ratio between two integers, which implies that every integer is included in the rational numbers because any integer can be written as a ratio.

The sum, product, difference, and quotient that are given to any two rational numbers are the four basic operations in which the set of rational numbers is closed under. Irrational numbers are numbers that cannot be written as a fraction or ration, which means that the number never repeats or ends in decimal form. Since it was discovered that not all numbers are rational, there are expressions or equations that cannot be solved through the ratios of integers.

In contrast, real numbers are the set of numbers that consist of all rational and irrational numbers i.e. all the numbers on the number line ("Number Systems," n.d.). As evident in the above descriptions, there are some major differences among integers, real numbers, rational numbers, and irrational numbers. For an individual who does not understand the difference, there is one major way for explaining this difference.

In this case, integers are numbers without a decimal or portion and can be defined as positive and negative whole numbers while rational numbers are those written as fractions of two integers. While irrational numbers cannot be written as a fraction of two integers, real numbers are rational and irrational numbers. Since numbers play an important role in daily lives, integers, real numbers, rational numbers, and irrational numbers are used in everyday life. They are used to count, measure, label, and order various activities in daily life.

Four Steps for Solving an Equation: The process of solving equations requires the use of various mathematical properties like addition, multiplication, subtraction, and division. The four steps for solving an equation basically involve combining like terms and isolating variables and terms through the use of these properties. The four steps for solving an equation include combining like terms, isolating terms consisting the variable to solve for, isolating the variable to solve for, and substituting the answer into the original equation ("Steps for Solving Equations," n.d.).

As the first step, solving an equation requires combining like terms for the two expressions within the equation. In this case, like terms are those containing the same variable or group of variables that are raised to the same exponent despite of their numerical co-efficient. The second step is to isolate terms that contain the variable, which means getting terms containing that variable on one side of the equation while the other variables and constants are moved on the opposite side of the equation.

This is followed by isolating the variable to solve for that can result in obtaining a numerical coefficient. When a numerical coefficient of one is obtained following isolating the terms containing the variable to solve for, the variable was automatically isolated. The fourth step for solving an equation is substituting the answer into the original question in order to ensure that the answer is correct. In this case, substitution is a process of swapping variables with expressions or numbers as part of checking the answer to ensure it is correct.

When solving an equation and explaining how to solve an equation, the most important factor to consider are the variables in the equation. This is primary because the variables in the equation play an important role in determining the accuracy of the process. The variables should also be critically considered because they help to determine whether the right or incorrect answer will be obtained. Four Steps for Solving a Problem: In most cases, mathematical problems usually require established procedures as well as knowing the procedures and when to apply them.

Moreover, the process of learning to solve a mathematical problem is generally knowing what to search for. In order to identify the necessary procedures for solving an equation, an individual needs to be familiar with the problem situation, gather the appropriate information, and identify and use the strategy appropriately. While there are various steps for solving a problem in mathematics, effective problem solving requires more practice (Russell, n.d.).

The first step for solving a problem is looking at the clues through reading the problem carefully and underlining the clue words or phrases. When looking for clues, it may be important.