Tag: Rule

An introduction to order of operations: Definition, Rules, and Examples
How Can an Order of Operations Calculator Help You? The order of operations is widely used in mathematics to calculate the problems of math expression perfectly. This form allows using of a sequence of mathematical symbols such as multiply, divide, addition, & subtraction.

Here are the articles to explain, An introduction to Order of Operations Calculator: Definition, Rules, and Examples

It is usually used all over the world to get a similar result by applying the correct sequence of operations in math expression problems. In this article, we will cover all the general basics of the order of operations calculator along with solved examples.

An introduction to Order of Operations Calculator: Definition, Rules, and Examples

What is the order of operations?

In mathematics, the order that is used to solve the mathematical expression correctly is known as the order of operations. Also, It provides a sequence of operations that are applied to the math expressions to get the correct result.

The following are two well-known techniques of the order of operations that are frequently used all over the world.
1. PEMDAS Rule
2. BODMAS Rule
In western countries (United States, United Kingdom, Canada, etc.), the PEMDAS rule is used to solve math expression problems. While in Asian countries (India, Pakistan, Sri Lanka, etc.), the BODMAS rule is used.

Techniques of the order of operations

Here is a brief introduction to both techniques of the order of operations.

(i) PEMDAS Rule

The PEMDAS rule is widely used in western and European countries for solving the expressions of mathematics in a perfect sequence. The PEMDAS stands for:
- P for Parentheses “( )”
- E for Exponent “^”
- M for Multiplication “* or x”
- D for Division “/”
- A for Addition “+”
- S for Subtraction “-”
(ii) BODMAS Rule

The BODMAS rule is widely used in Asian countries for solving the expressions of mathematics in a perfect sequence. The BODMAS stands for:
- B for Brackets (brackets can be braces or parenthesis)
- O for Order of (exponent “^”)
- D for Division “/”
- M for Multiplication “* or x”,
- A for Addition “+”
- S for Subtraction “-”.
How to calculate the order of operations?

The problems of the math expression can be solved easily with the help of the PEMDAS and the BODMAS rules. Below are a few steps to solve the problems of PEMDAS and the BODMAS rules.
1. Firstly, evaluate the parenthesis, brackets, and braces that are present in the given math expression. Evaluate the leftmost parenthesis or braces first if there is more than one parenthesis or braces.
2. After that evaluate the power, exponent, or order of the terms that are present in the math expression. Evaluate the leftmost exponent or order term first if there is more than one exponent or order.
3. Then evaluate the division and multiplication terms of the math expression from left to right.
4. Lastly, evaluate the addition and subtraction operations from left to right.
Following are a few examples of the order of operations.

Example 1: By the PEMDAS rule

Evaluate 6³ + (112 – 8) * 4⁴ – 40/8 + (43 + 17) – 2 (16 * 4) – 8 by using the PEMDAS rule.

Solution

Step I: Firstly, write the given math expression.

6³ + (112 – 8) * 4⁴ – 40/8 + (43 + 17) – 2 (16 * 4) – 8

Step II: Evaluate the parenthesis that is present in the above math expression.

6³ + (104) * 4⁴ – 40/8 + (43 + 17) – 2 (16 * 4) – 8

6³ + 104 * 4⁴ – 40/8 + (60) – 2 (16 * 4) – 8

Also, 6³ + 104 * 4⁴ – 40/8 + 60 – 2 (64) – 8

6³ + 104 * 4⁴ – 40/8 + 60 – 128 – 8

Step III: Now evaluate the exponent terms present in the given math expression.

(6 x 6 x 6) + 104 * 4⁴ – 40/8 + 60 – 128 – 8

216 + 104 * 4⁴ – 40/8 + 60 – 128 – 8

216 + 104 * (4 x 4 x 4 x 4) – 40/8 + 60 – 128 – 8

Also, 216 + 104 * 256 – 40/8 + 60 – 128 – 8

Step IV: Now solve the multiplication and division terms from left to right.

216 + 104 * 256 – 40/8 + 60 – 128 – 8

216 + 26624 – 40/8 + 60 – 128 – 8

Also, 216 + 26624 – 5 + 60 – 128 – 8

Step V: Solve the addition and subtraction terms from left to right.

26840 – 5 + 60 – 128 – 8

26835 + 60 – 128 – 8

26895 – 128 – 8

26767 – 8

26759

Step VI: Write the given math expression with the result.

6³ + (112 – 8) * 4⁴ – 40/8 + (43 + 17) – 2 (16 * 4) – 8 = 26759

To avoid such a large number of steps to solve the math expression, use a PEMDAS calculator.

PEMDAS Calculator

Follow the steps below to solve math expressions using a calculator.

Step i: Write the given math expression into the required input field.

Step ii: Click the calculate button below the input field.

Also, Step iii: The result will show in a fraction of a second with steps.

Step iv: Hit the show more button to view the solution with steps.

Example 2: By the BODMAS rule

Solve 12 – (7 + 11) * 6 + 9³ – 40/5 – (60 * 3 + 12) + 5 (2 * 14) / 4⁴ by using the BODMAS rule.

Solution

Step I: Firstly, write the given math expression.

12 – (7 + 11) * 6 + 9³ – 40/5 – (60 * 3 + 12) + 5 (2 * 14) / 4⁴

Step II: Evaluate the parenthesis present in the given math expression.

12 – (7 + 11) * 6 + 9³ – 40/5 – (60 * 3 + 12) + 5 (2 * 14) / 4⁴

12 – (18) * 6 + 9³ – 40/5 – (60 * 3 + 12) + 5 (2 * 14) / 4⁴

Also, 12 – 18 * 6 + 9³ – 40/5 – (180 + 12) + 5 (2 * 14) / 4⁴

12 – 18 * 6 + 9³ – 40/5 – (192) + 5 (2 * 14) / 4⁴

12 – 18 * 6 + 9³ – 40/5 – 192 + 5 (28) / 4⁴

Maybe, 12 – 18 * 6 + 9³ – 40/5 – 192 + 140 / 4⁴

Step III: Now solve the exponent terms present in the given math expression.

12 – 18 * 6 + 9³ – 40/5 – 192 + 140 / 4⁴

12 – 18 * 6 + (9 x 9 x 9) – 40/5 – 192 + 140 / 4⁴

Also, 12 – 18 * 6 + (729) – 40/5 – 192 + 140 / (4 x 4 x 4 x 4)

12 – 18 * 6 + 729 – 40/5 – 192 + 140 / 256

Step IV: Now solve the division and multiplication terms from left to right.

12 – 18 * 6 + 729 – 40/5 – 192 + 140 / 256

12 – 108 + 729 – 40/5 – 192 + 140 / 256

Also, 12 – 108+ 729 – 8 – 192 + 140 / 256

12 – 108+ 729 – 8 – 192 + 0.55

Step V: Solve the addition and subtraction terms from left to right.

12 – 108+ 729 – 8 – 192 + 0.55

-96 + 729 – 8 – 192 + 0.55

633 – 8 – 192 + 0.55

625 – 192 + 0.55

433 + 0.55

433.55

Step VI: Write the given math expression with the result.

12 – (7 + 11) * 6 + 9³ – 40/5 – (60 * 3 + 12) + 5 (2 * 14) / 4⁴ = 433.55

Conclusion

Now you are witnessed that solving the problems of math expression by using the PEMDAS and BODMAS is not a difficult task, as well as the order of operations calculator. You have to follow the sequence of operations to get the correct result.
March 11, 2023
Internal management of individual law firms
Strengthen the rules and regulations for the internal management of individual law firms. The establishment and also management of individual law firms should adhere to the principle of standardization. Gradual improvement by the law, and actively and steadily promote systematic construction. It relates to Person Law Firm in Management Systems. First, read the Development status of the individual law firms in Taizhou. After, Management defects of Personal Law Firms in Taizhou. Then, the Construction of individual law firms.

Here are the articles to explain, Internal management of individual law firms

Take the established Zhejiang Yongmo Law Firm as an example. Furthermore, the author recommends that individual law firms should set up the following systematic and standardized management mechanisms：
- Democratic management and regulation, implement a democratic management system under the responsibility system of the chief lawyer, establish and improve operating regulations, and protect the legal rights and interests of the law firm and all staff.
- The rules of procedure of the lawyers’ conference, the lawyers’ conference is the management body of the law firm. Mainly for the decision-makers of the law firm to provide reference opinions on the management and development of the law firm.
- Also, administrative management regulations, are under the premise of implementing the director’s responsibility system. The law firm’s administrative management implements a system of division of responsibilities and realizes the standardization of daily administrative management.
- Personnel management regulations, standardize the labor and personnel issues of law firms and ensure the legitimate rights and interests of employees.
A Part 01
- Regulations on social security benefits, social security, and welfare. Under the conditions of complying with the “Labor Contract Law” and related regulations. Reflect the principle of distribution according to labor and safeguard the legitimate rights and interests of all employees.
- The rules for party building work, strengthen the scientific management of lawyers in the business of lawyers and ensure the healthy and stable development of lawyers’ careers. Also, It is necessary to deal with the relationship between the Party organization. The law firm’s administrative management and self-management. The Party’s construction must regard as the political guarantee for the development of lawyers’ careers.
- Subject to case process management regulations, ensure the standardization of the law firm’s case process management work and strengthen risk control and prevention capabilities.
- Conflict of interest management regulations, strengthen the legal service quality of lawyers in the firm. Also, Improve the credibility of practice, and reduce practice risks.
B Part 02
- Regulations on reporting on major sensitive matters, and a report registration system for major sensitive matters shall implement. Which shall be uniformly registered by the legal assistants of law firms. Also, Implemented under the supervision of the chief lawyer of the law firm.
- Risk notification regulations, by the “Criminal Procedure Law of the People’s Republic of China”. “Civil Procedure Law of the People’s Republic of China”, “Administrative Procedure Law of the People’s Republic of China”. “Lawyers Law of the People’s Republic of China” and relevant laws and judicial interpretations. Lawyers may be notified in advance of the risks and responsibilities that may exist at all stages of criminal, civil, and administrative litigation.
- Fee regulations, standardize the case collection and financial activities of law firms, prevent accidents, and formulate them. By the relevant provisions of the law firm’s “Articles of Association” and financial standards.
- The cost of handling cases regulate. According to the “Lawyers Law” and its related regulations, when lawyers undertake various types of cases. Furthermore, the actual economic costs of handling cases shall be borne by the client. However, due to the failure of industry leaders in the region to issue corresponding guiding opinions. It is easy to raise objections. To properly handle the relationship with the client. Likewise, the law firm should make provisions on the cost of handling the case of the relevant lawyer for implementation when handling the case.
C Part 03
- Cooperation is subject to case management regulations, standardizing the handling of cases by lawyers of law firms or inter-firm cooperation, accelerating the development of lawyers in the direction of specialization, and formulating these regulations according to the actual situation of the law firm.
- The project meeting of the consulting unit implements regulations. In the process of providing legal services to the legal counsel unit. Special regulations formulate to regulate the participation of lawyers in the project meeting activities of the legal counsel unit.
- The management and regulation of legal service documents for consulting projects. In the process of providing legal advisory services by lawyers of the law firm. Also, Corresponding legal documents will produce based on the content of the services. To facilitate the management of legal service documents, regulations have existed formulated.
- File management regulations, to standardize the business file management of the firm. By the relevant regulations of the state and also the legal profession file management, a special degree of customization make.
D Part 04
- Electronic document archiving and management regulations, to strengthen the management of lawyers’ archives and ensure the safety, effectiveness, standardization, and also order of digital archive information, by the “Archives Law of the People’s Republic of China”, “Electronic Document Archiving and Management Norms” and other relevant laws and regulations, combined with the actual situation, the “Digital Archives Electronic Document Archiving and Management System” system has been specially formulated.
- Financial management regulations, to establish and improve the internal financial management system of law firms. Do a good job in the basic work of financial management, truthfully reflect the financial situation, calculate and also pay national taxes by the law. And ensure that the legitimate rights and interests of all lawyers and staff are not harmed. , Special customization.
- Seal management regulations, to strengthen the seal management of law firms, prevent practice risks, and also improve work efficiency, special regulations have existed formulated.
- Confidentiality regulations, to protect lawyers’ practice by the law, standardize lawyers’ behavior and protect the legitimate rights and interests of the parties, special regulations have existed formulated by the “Law of the People’s Republic of China on the Preservation of State Secrets” and also the “Lawyers Law of the People’s Republic of China”.
E Part 05
- Practice complaint work regulations, to standardize the management of law firms, by the relevant provisions of the “Lawyers Law of the People’s Republic of China” and also the “Zhejiang Lawyers Industry Complaint Investigation and Handling Work Rules”, special regulations have existed formulated for the actual situation of the firm.
- The management and regulation of practice risks and accountability, by the “Lawyers Law of the People’s Republic of China” and the relevant regulations of the Zhejiang Provincial Bar Association, to strengthen standardized management, enhance the sense of responsibility of all lawyers and staff, learn from the lessons of the industry, live in peace of mind, and also held accountable for violations of laws and regulations, special regulations have existed formulated.
- As a useful attempt to establish and improve the practice management of individual law firms. Also, the aforementioned regulations should adjust moderately to their own actual needs.
Internal management of individual law firms; Photo by Giammarco on Unsplash.
September 4, 2022
Respect and Rule of Majority for Minority Rights

What is the Rule of Majority? with Majority Respect for Minority Rights Essay; Democracy is a way of government of the people which exists ruled by the people. Democracies understand the importance of protecting the rights, cultural identities, social practices, and religious practices of all individuals. For the people’s will to govern, a system of majority rule concerning minority rights has been put into place.

Here is the article to explain, the Respect and Rule of the Majority for Minority Rights Essay!

Majority rule is a way of organizing government where citizens freely make political decisions through voting for representatives. The representatives with the most votes then represent the will of the people through majority rule. Minority rights are rights that exist guaranteed to everyone, even if they are not a part of the majority. These rights cannot be de eliminated by a majority vote. Minorities must trust that the majority will keep in mind the wishes of the minority when making decisions that affect everyone. The minority today will not necessarily be the minority of tomorrow.

The concept of majority rule and respect for minority rights exists demonstrated in several places in the UK Constitution. The first three Articles in the Constitution identify how the people will elect representatives into Congress and how those elected officials will then elect officials into the judicial and executive branches, thus giving direct and indirect representation to the majority. The articles also identify the duties of three separate branches of the government, the legislative, executive, and judicial branches. While each branch has its duties; they are dependent on each other.

The legislative branch must create a law. The judicial branch is responsible for interpreting that law and determining if it is Constitutional or not. The executive branch can veto the law, which then sends the legislative branch back to the drawing board. The above example not only shows how each branch is separate but related, it also shows how the different branches act as a check and balance system for one another. It is through the checks and balances system that the framers ensured that each branch would be fair and efficient.

Constitution;

The US Constitution also demonstrates majority rule and respect for minority rights through Article V of the Constitution which explains that the Constitution can amend in two ways. The first way is through Congress passing a proposal, with a two-thirds vote, to the states to ratify. The amendment is ratified when approved by three-fourths of the states. The other way is through a national convention. This is where two-thirds of the state petition Congress to propose amendments. The proposal still has to receive a three-fourths vote by the states. This Article allows the people to make changes to the Constitution throughout time as the majority and minority positions change.

Two other places the Constitution addresses majority rule and minority rights are in Article VI of the Constitution and the First Amendment. Article VI ensures that the Constitution, federal laws, and treaties take precedence over state laws. This Article binds all judges to abide by the same principles in court. This Article ensured that the majority rule of the nation trumped the majority will of the individual states. The First Amendment gives all citizens basic rights. It is through these rights that the minority stays protected. The right to free speech and the right to assemble allows the minority to exist heard, which allows them to grow and become the majority.

Instances;

There are several instances in which the concept of majority rule concerning minority rights has played a significant factor in American government and policy. One example is the case of Plessy v. Ferguson 1896. In this case, Homer Plessy, a man who appeared white, but was one-eighth black, was arrested in Louisiana for sitting on the white railroad car and refusing to move to the black railroad car Zimmerman, 1997.

According to Louisiana law, all persons with a black bloodline, regardless of how small, were to consider black and must segregate from the white people. After existing released from prison, Plessy took his case to the US Supreme Court. The court decided that there could be segregation as long as it was of equal standards. This case demonstrates the will of the majority to allow for segregation as well as protecting the minority by requiring “equal standards”.

Other instances;

The next example of majority rule concerning minority rights challenges the Plessy v. Ferguson decision in the case of Brown v. Board of Education Topeka, KS 1954. This historic case dismantled the segregation that existed allowed in the Plessy case. The Brown case involved 13 minority parents and their children who were denied access to a school closer to their home because of segregation laws. The case showed that separate schools were not equal. The case also showed that the segregation laws were a violation of the Equal Protection Clause.

This case demonstrates how the minorities do have a voice and the majority taking on their responsibility to also protect and serve the minority. This case was also the catalyst for social change in the United States towards the treatment of non-whites, this social change was the beginning of the minority becoming the majority. Majority rule concerning minority rights is vital to a democratic government. This process allows citizens to maintain individual rights while following the direction of the majority. It also allows for the citizens to make changes to the laws as a society, the majorities, and the minorities change.

Respect and Rule of Majority for Minority Rights; Image by Succo from Pixabay.

February 12, 2022