Hunt Road Secondary School

31/10/2023

PEMDAS: Remembering Math's Order of Operations

By: Mark Mancini & Desiree Bowie | Updated: Oct 17, 2023

PEMDAS is the tried-and-true method that gives us the order to work when solving mathematical problems. HOWSTUFFWORKS

Nearly every middle school in the U.S. teaches its students to remember this simple phrase: "Please excuse my dear Aunt Sally." But why are we apologizing for her behavior? Did she wear white after Labor Day or something?

The world may never know. In all seriousness, "Please Excuse My Dear Aunt Sally," or PEMDAS, is just a mnemonic. It's a tool educators use to help us memorize information through a catchy rhyme, phrase or acronym. Now let's explore how to use this tool to solve equations.

Contents

1. What Is PEMDAS?

2. Origins of the Order of Operations

3. Why Do We Use PEMDAS?

4. Solving Math Equations Using the PEMDAS Rule

5. Beyond PEMDAS

What Is PEMDAS?

PEMDAS is an acronym and mnemonic that represents a set of rules used to clarify the order in which operations should be performed to correctly evaluate mathematical expressions. PEMDAS stands for:

1. Parentheses:
This means any calculations inside parentheses should be performed first. This can include brackets or other grouping symbols.

2. Exponents:
This refers to powers or square roots. You handle these calculations after dealing with parentheses but before other operations.

3. Multiplication:
When you encounter multiplication in an expression, after parentheses and exponents, you perform this operation next.

4. Division:
Similar to multiplication, you handle division after parentheses and exponents, working from left to right.

5. Addition:
After the aforementioned operations, you perform addition.

6. Subtraction:
Lastly, after all the other operations have been handled, you perform subtraction.

Sometimes, the mnemonic "BEDMAS" is used, where "B" stands for "brackets," and serves the same purpose as "parentheses." The mnemonics essentially convey the same order of operations to reach the correct answer, but they use slightly different terminology based on regional preferences. For example, BEDMAS is more commonly used in Canada, while PEMDAS is prevalent in the U.S.

(Note that multiplication and division are of equal precedence in the order of operations, so the flipped order in BEDMAS doesn't change anything.)

Origins of the Order of Operations

The order of operations — as Americans know it today — was probably formalized in either the late 18th century. By the 20th century, the tool gained wider acceptance, coinciding with the rise of the U.S. textbook industry.

In an email, math and science historian Judith Grabiner explains that concepts like the order of operations are best thought of as "conventions, like red-means-stop and green-means-go, not mathematical truths.

"But once the convention is established," she says, "the analogy to traffic lights holds: Everybody's got to do it the same way and the 'same way' has to be 100 percent unambiguous."

Math and ambiguity are uncomfortable bedfellows.

Why Do We Use PEMDAS?

PEMDAS ensures consistency in the results of mathematical calculations. Basically, when different people evaluate the same expression, they use the same process and come to the same result. If you don't follow the correct order of operations, you will likely get the wrong answer.

Ignoring or changing this order can lead to different results, which can be especially problematic in fields like science, engineering and finance where precise calculations are crucial.

Solving Math Equations Using the PEMDAS Rule

Suppose it's finals week, and you're expected to solve the following equation:

9 – (2 x 3) x 4 + 5² = ?

Don't panic. This is where a certain auntie comes in. For every word in the phrase, "Please excuse my dear Aunt Sally," there's a corresponding math term (which begins with the same letter) that tells us which procedure(s) to perform first.

Parentheses First

Before we solve the equation, PEMDAS dictates that we ask ourselves a simple question: "Are there any parentheses?" If the answer is "yes," then our first move should be to resolve whatever's inside them.

So in the above example, we see "2 x 3" enclosed in the parentheses. Therefore, we'll begin by multiplying 2 times 3, which gives us 6. Now the equation looks like this:

9 – 6 x 4 + 5² = ?

Cool beans. Time to bring on the exponents! In print, exponents take the form of a little number pressed against the upper righthand corner of a larger number. See the 5²? That itty-bitty "2" is an exponent.

Here, the tiny two tells us to multiply 5 by itself. And 5 x 5 equals 25, giving us this:

9 – 6 x 4 + 25 = ?

Now that we've taken care of the parentheses and exponent(s), let's proceed to those next two operations: multiplication and division.

Multiply and Divide

Note that we're not saying multiplication comes before division here. Not necessarily, at least.

Let's say you're looking at a different problem which — at this stage — contains both a multiplication sign and a division symbol. Your job would be to perform the two operations in order from left to right.

The concept is best explained by way of example. If the equation reads 8 ÷ 4 x 3, first you'd divide the 8 by the 4, giving you 2. Then — and only then — would you multiply that 2 by 3. We now return to our regularly scheduled math problem:

9 – 6 x 4 + 25 = ?

Whoever wrote the original equation kept things nice and simple; there's nary a division sign in sight and only one multiplication symbol. Thank you, merciful exam gods.

Without further ado, we're going to multiply the 6 by the 4, giving us 24.

9 – 24 + 25 = ?

Time to Add and Subtract

As with multiplication and division, addition and subtraction are part of the same step. Once again, we're performing these two operations in order, from left to right. So we're going to have to subtract that 24 from the 9.

Doing so will give us a negative number, specifically -15.

But the 25 is a positive number. So in its current form, the equation consists of a negative 15 plus a positive 25. And when you add those two together, you get a positive 10.

So there it is. The answer to our riddle.

9 – (2 x 3) x 4 + 5² = 10

Double Parentheses: Proceed With Care

Before we part ways, there are a few more things you should know. You may someday find yourself looking at a complex equation with lots of different operations sandwiched between two parentheses. Maybe something like this:

9 – ((2³ – 3) x 8) ÷ 6 = ?

Don't sweat it. If you're trying to solve math problems with multiple operations, following the PEMDAS sequence ensures consistent and accurate results. All you've got to do is work through the PEMDAS process inside those parentheses before you move on to the rest of the problem.

Here, you'd take care of the exponent first (i.e., the 2³), then handle the subtraction in that set of parenthesis before moving on to the multiplication in the next level of parenthesis. Easy-peasy. (In case you're interested, the answer to the equation is 2 1/3, or 2.33 if you prefer decimals.)

Beyond PEMDAS

Here are some other PEMDAS-eque conventions and methods related to arithmetic expressions:

1. BODMAS/BIDMAS:
Used in the U.K. and other regions, BODMAS stands for Brackets, Orders (or Indices for BIDMAS), Division, Multiplication, Addition and Subtraction.

2. FOIL:
Specifically for binomials, it stands for First, Outer, Inner, Last. It's a method for multiplying two binomials.

3. Factorization:
Breaking down numbers or expressions into their simplest components.

4. Distributive property:
For expressions like a(b + c), it would be ab + ac.

5. Associative and commutative properties:
Respectively, these properties allow numbers to be grouped differently or moved around in an expression without changing the result.

6. Completing the square:
A technique used in quadratic equations to convert them into a perfect square trinomial.

7. Rationalizing the denominator:
A method used to eliminate radicals from a denominator of a fraction.

This article was updated in conjunction with AI technology, then fact-checked and edited by a HowStuffWorks editor.

Now That's Interesting

Robert Recorde — a physician and mathematician who was born in Wales in about 1510 C.E. — is credited as the inventor of the equal sign (=). He decided to use two parallel lines for this symbol because, in his words, "noe 2 thynges can be moare equalle [sic]."

PEMDAS FAQ

Is PEMDAS wrong?

In the U.S., PEMDAS is more common where we first calculate Parentheses, then Exponents, then Multiplication and Division, and Addition and Subtraction at the end. However, most of the world uses BODMAS — Brackets, Orders, Division, Multiplication, Addition and Subtraction.

Why is PEMDAS in that order?

PEMDAS basically creates a pyramid for different functions in an equation. For example, the first priority is given to the parentheses — and for good reason. Not only does this give order to equations but also drives more accurate results.

What is the formula of PEMDAS?

According to PEMDAS, it is important that the equation is simplified before it is calculated. This means squaring any roots off on both sides, any canceling effects and more. After that, the parentheses, exponents, multiplication, division, addition and subtraction order must be followed, solving each element from left to right.

What is better BODMAS or PEMDAS?

There has been a long debate about whether BODMAS or PEMDAS is better but the difference between them primarily arises from regional terminology and preferences. Some say there is no difference between the two since they suggest that multiplication and division must be done from left to right, regardless of what comes first, while others prefer to follow the BODMAS mnemonic.

14/09/2023

I just got tagged in this, did you see?

29/04/2022

After the COVID 19 pandemic's infamous "quarantine" period, I found myself looking for extra work to keep myself from losing my mind and started to model for .

There are tons of activities in the modeling industry that I have engaged in like...

Types of modelling which include:
▪︎fashion
▪︎glamour
▪︎fitness
▪︎bikini
▪︎fine art
▪︎body-part
▪︎promotional
▪︎commercial print models

Models are featured in a variety of media formats including:
▪︎books,
▪︎magazines,
▪︎films,
▪︎newspapers,
▪︎internet and
▪︎television.

Celebrities, including actors, singers, sports personalities and reality TV stars, frequently participate in:
▪︎modelling contests,
▪︎assignments as well as
▪︎contracts
in addition to their regular work. Often, modelling is not a full-time, main activity.

Access:

The top agencies work with big-budget advertising agencies and fashion designers. They invest money into developing their talent so they can increase their status within the industry. These top agencies will help:
▪︎train models,
▪︎get test shoots,
▪︎layout portfolios, and
▪︎put together comp cards (composition photo cards) and other printed materials models need.

Activities:

Each new model-screening process is different from one agency to the next:

▪︎A casting call is where models show up by appointment to be considered for a specific job.

▪︎An open call is a time specified by an agency for any prospective models (or those interested in becoming models) to show up and be considered for future work.

▪︎A go-see is an appointment for a model to meet with a client for consideration for future work; like an open call, it is not for a specific job, but unlike an open call, the model is being specifically requested or sent.

▪︎A dry call is where models mail unsolicited comp cards to an agency. While this may work with smaller agencies, larger agencies host open calls where men and women can come into the agency and get seen by agents who may or may not be interested.

https://leverageedu.com/blog/how-to-calculate-work-experience/ #:~:text=The%20most%20common%20way%20to,comprehensive%20work%20in%20the%20industry.

How to Calculate Work Experience?

• Team Leverage Edu
• Updated on Jun 9, 2021

Ever opened a job/internship profile as a student and sighed at the sight of a work experience requirement? When applying for an MBA abroad or job opportunities, you’ll often come across the ‘minimum work experience’ criteria. Work experience has become a crucial part of a person’s resume as it represents the practical exposure a person has gained. Read this blog to know more about how to calculate work experience.

THIS BLOG INCLUDES:

• What is Work Experience?

• How to Calculate Work Experience?

• Benefits

• Different Types of Work Experience

• Different Levels

• FAQs

What is Work Experience?

Work experience refers to any kind of experience that a person gains in working in a particular field or occupation. It can be a component of your formal work experience plan and may refer to your work before beginning a career path or enhancing your present career. It can be achieved before, during, or after graduating from your undergraduate studies. There are several forms and levels of work experience and ways to calculate work experience.

How to Calculate Work Experience?

These steps can help you understand how to calculate work experience according to the educational or job opportunity before you:

1. Calculate the amount of time you’ve spent in the industry.

The most common way to calculate work experience is by assessing the number of hours/weeks/months or years you have spent in a role or the duration of your comprehensive work in the industry. In both cases, you have to subtract the last date of employment/current date of employment (if you are currently working in the role) and the date of joining.

2. Research the university or company

Different companies may have various interpretations of experience levels. For example, one organisation might want someone for an intermediate-level job with four years of experience, while another might require only two years. The same applies to universities; there might be different work experience requirements for various courses in other countries. It is always wise to personally research the university of your preference.

3. Look at the qualifications instead

This is a crucial step in how to calculate work experience. You should view the job description of the role you are interested in carefully, especially the favoured skills and qualifications section. Universities also have specific criteria mentioned in their eligibility requirements section. For example, an MBA may require a full-time work experience of a minimum of two years, while an Executive MBA may require more years of work experience. To gain clarity, you also contact the human resource manager of a company or the admission counsellor of a university.

4. Consider internships and work experience

Many employers may recognise unpaid experiences, such as volunteer opportunities and internships for a certain level. At the same time, many universities or employers may not consider internships and volunteer experience as a part of work experience. Hence, you should be mindful of this while understanding how to calculate work experience.

Benefits

Work experience can be a valuable part of your profile. Here are some of the benefits of work experience:

• Work experience can help you gain exposure towards a career in your desired profession.

• Work experience can confirm career aspirations. It allows you to get an insight into a job and realise if the career path you are planning on is right for you or not.

• It allows you to apply what you have learned in your academics practically. It also helps you gain extra knowledge.

• It shall help you develop self-understanding, maturity, independence and confidence.

• Gaining work experience at any level will also help you begin forming a professional network.

• Mentioning work experience in your resume also enables you to feature notable professional achievements and acts as an applied proof of your capabilities.

• Highlighting the goals you have accomplished in your past positions can help you show your employer how your presence can help drive a team towards success

Different Types of Work Experience

Before we learn how to calculate work experience, we must be aware of the several forms of work experience:

• Previous or Current employment – This is the experience you have gained in your previous job(s) or current job. This can be full-time or part-time employment.

• Work Placement – This is a duration of work experience that was part of a period of study. Work placements can be paid or unpaid opportunities.

• Internships- They are short-term works in an organisation, often without monetary compensation. This type of work experience is most common for university students.

• Work-Based Project – It consists of a distinct set of activities carried out on the employer’s premises. This might be carried out for your current employer, but the project would be outside the scope of work that you usually do, in that case.

• Work Shadowing – This type of work experience involves observing an expert or professional while they work. This helps you understand the essence of their role and responsibilities.

• Voluntary work can also be a kind of work experience. It generally refers to dedicating your time and effort to community service initiatives.

Different Levels

Different job experience levels differentiate people with a strong background in the industry from those who may still require guidance. Here are the most basic work experience levels you might come across:

Entry-level

You can usually get this role right after finishing your bachelor’s study or exploring a new career in a different industry.

Intermediate

After a few years of working in a specific field, you can start applying to intermediate- or associate-level jobs. At this level, you might also be allowed some leadership opportunities.

Mid-level

Mid-level jobs are managerial roles within their company. A mid-level employee may be responsible for the goals of a particular department and supervise the day-to-day operations.

Senior or executive-level

After working for many years in the same field and gaining experience in managerial roles, a senior level employee can establish overall goals for the organisation, set policies and procedures and communicate with stakeholders.

Also Read

• MBA Without Work Experience

• Education vs Experience

• MBA Without Work Experience in Canada

• MBA in UK Without Work Experience

FAQs

Can internships be counted as work experience?

Internships can be featured in the work experience part of your resume. However, if internships can be added to meet the work experience eligibility criteria in companies or universities depends completely on where you are applying. It also usually depends on the number of hours you clock per week and the number of months you have interned for.

If I have done two summer internships while studying and have five years of working experience after studies, would that count as seven years of work experience?

No. While internships can be featured in the work experience section of resumes, a two/three-month internship is not equivalent to a year of industrial experience. Hence, it cannot add two full years of work experience.

Can I put volunteering in the work experience section of my resume?

Can I put volunteering in the work experience section of my resume?

Generally, it is preferable to put volunteering experience as a separate section or under extracurricular activities. However, if you’re running low on the work experience section, mentioning it wouldn’t be wrong. Whether volunteering can be added as work experience to meet work experience criteria depends on the organisation’s guidelines.

Are leaves deducted from the calculation of work experience?

No, formal leaves are not deducted from work experience if you are still in the work position. Career breaks or duration of unemployment between changing careers will not be counted.

That was everything you needed to know about how to calculate work experience. We hope this blog was helpful to you. Stay tuned to Leverage Edu for more informational and exciting content.

28/04/2022

Hey guys, have you ever wondered how to keep that someone special satisfied?

I have been modeling for a while now and I have been drilled about relationship security...

It is the reason why we all wake up in the morning and work.

I hope you will too...

S*xual Exchange Endorsement Scale

1. No matter how accomplished a woman is, her chief value to men is her s*x appeal.

2. Men are mainly interested in women as a means to get s*x.

3. No matter how loving a man is, his chief value to women is his bank account.

4. More women than men want to get married.

5. Women strive to be s*xually attractive primarily to get men to provide for them.

6. S*x is a female resource that women should give only in exchange for men's financial support and emotional commitment.

7. Women should collectively agree to not have s*x with men unless they get a commitment (emotional or financial) in return.

8. A reason why there are fewer marriages today is because women no longer insist on holding out for an engagement ring before having s*x.

9. Effective birth control (like the Pill) has made it harder for women to find good husbands.

17/03/2022

I am slowly learning how to do this...

Unconditional love is often said to be the foundation of a healthy relationship, but what does it actually mean? And is it even a realistic goal?

02/01/2022

Happy new year!!!

It was a pleasure to attend the same school with you and still continue to learn together...

Sylvia Duckworth's illustration of Wheel of Power/Privilege can help us get a more intricate visualization of what the term “marginalization;" the further you are from power, the more ignored and unimportant you feel. However, as you try to place yourself in the different categories, notice how your level of power/marginalization shifts between categories. A different way to interpret this illustration is through an intersectionality lens (coined by Kimberlé Crenshaw).


Do you think there are categories missing?


What do you think about the categories that are depicted here?

Forms of Privilege

Social justice activists and writers have built on Peggy McIntosh’s original essay on privilege in 1988, by adding to and modifing the original list to highlight how privilege is not merely about race or gender, but that it is a series of interrelated hierarchies and power dynamics that touch all facets of social life: race, class, gender, s*xual orientation, religion, education, gender identity, age, physical ability, passing, etc. These categories will be further discussed below.

One thing to keep in mind when looking at how privilege operates is that privilege, discrimination, and social groups all operate within interrelated hierarchies of power, dominance, and exclusion. Just because someone is privileged in one way doesn’t mean they may not be underprivileged in another (and vice-versa). It is therefore important to be aware of the various groups to which one belongs in order to be able to question our own participation in a system of discrimination and privilege.

There are many different kinds of privilege that exist but regardless of how groups are divided, the privileged group is the one that is commonly treated as the baseline against which the others are judged or compared – it is seen as “ordinary”. Consider some of the following kinds of privilege:

Ability: Being able-bodied and without mental disability. Actors with disabilities frequently find themselves passed up for roles even if those roles are for characters with the same disability. Moreover, while fully enabled actors are often cast in roles as disabled characters, actors with a disability are almost never asked to play enabled characters. Individuals who are mentally enabled never find their status used as a justification for criminal behaviour in film and television, but we often see mental illness portrayed in exactly such a light.

Class: Class can be understood both in terms of economic status and social class, both of which provide privilege. Social class can determine access to opportunities, to participation in politics, and opens up particular educational and vocational doors more easily. From a social and media standpoint, consider how different social classes are represented. It is also important to note that the majority of the media are created by and for a specific social class. How are certain jobs portrayed in the media compared to others?

Education: Access to higher education confers with it a number of privileges as well. Educational privilege opens a number of doors to higher paying careers (which links it to social class privilege). Educational privilege can also confer unearned credibility on an individual: For instance, many television and radio show hosts append the prefix “Dr.” to their name in order to use a PhD. to suggest they can offer medical or psychiatric advice.

Gender: Male-identified, masculine individuals still hold a level of privilege over people of other genders. Another word for the systemic operation of male privilege is “patriarchy”. In the media, we still see male authority superseding others. Men continue to be overrepresented in leadership roles and as news commentators. Men, their stories, and their perspectives continue to be vastly overrepresented in video games, film, and television programs, both onscreen and behind the scenes.

Gender Identity: While often linked to s*xual orientation and gender privilege, this is the privilege that comes with having a gender identity (how one identifies and express oneself in gendered terms) that conforms to the gender identity that was assigned at birth and to societal and cultural expectations of such a gender identity. In terms of media representation, it is extremely rare to find representations of individuals whose gender identity does not conform to cultural expectations. In the rare instances that such characters are portrayed, their gender-nonconformity is typically used to elicit fear, apprehension, or laughter, or may be portrayed as a kind of mental illness.

Passing: Passing is the ability to appear to belong to another group. The ability to pass is itself a privilege because it allows an individual to claim the advantages of a more privileged group. In the media, passing becomes easier for certain groups than for others and certain types of passing are particularly celebrated: Consider, for instance, how a straight, white, mentally and physically enabled man is often congratulated for his “courage” in playing a gay man or a person with a mental disability in a film or television. At the same time, we rarely see many accolades when a queer-identified individual plays straight and there are rare instances in which a person with an apparent disability plays a character who is fully enabled. Race-bending (changing the race of a character for a film or television adaptation), whitewashing (making characters of ambiguous or unstated ethnicity white), blackface, “cripface”, and a variety of other practices all help to illustrate how passing becomes a privilege in the media. If one considers that in Hollywood 82 per cent of lead roles are for characters of Caucasian ethnicity, we can see how tangible a privilege passing can be.

Racial: In the West, racial privilege is usually equated with white privilege since power, money, and influence tends to be concentrated among Caucasians in Western Europe and North America. Racial privilege is institutionalized racism: a system that is structured to privilege one group over others. In the media, consider how race plays into determining character types and roles.

Religious: Religious privilege comes with being a member of the dominant religion in a culture – to have one’s own religious practices and observances recognized as the norm. In North America and much of Europe, Christian faiths hold privilege over most others. In the media, religious privilege translates to a normalizing of one’s tenets of faith while alternative faiths are often portrayed as novel, strange, or even overly mystical.

S*xuality: Heteros*xual privilege includes the assumption that everyone is heteros*xual which forces Q***r people to be constantly undergoing a coming out process in their daily lives. In the media, we rarely see lead characters who are Q***r-identified unless the character’s s*xuality is pivotal to the plot. Conversely, heteros*xual characters enact their s*xuality constantly (the presence of things like wedding rings, photos of children, discussions about one’s spouse in various media are all indications of a character’s s*xuality, but are hardly ever noticed by the audience. This is not the case if the character is in a same-s*x relationship) but it goes unnoticed because of its privileged status. S*xuality privilege also includes s*xual practices and s*xual history – the media often associates a woman’s worth with her s*xual history through the hypers*xualization of women, but also by relating a girl’s self-worth to her chastity and the public disparagement of women who are s*xually active. This links s*xuality privilege to gender privilege as well.

https://mediasmarts.ca/diversity-media/privilege-media/forms-privilege

14/12/2021

It takes a lot of hard work to become successful in life in general and you need role models that are further ahead to guide you on your journey.

This is the reason why I am a model. I model because I want to become more than I am like some of the best role models that I have in our global village. This is very important to me and I have been working for more than ten years to realise it...

Here is to the next ten!

Finding flexible jobs can help pay the bills while pursuing a modeling career. Here are some solid ideas of work you can do while making your name.