Percentages are all around us. In the news, at the job, in the store, at the bank. Not everyone thinks it is easy. I know many well-educated people that don’t get it. Most of them know what 10% of 100. But when you ask them what the result is, if you add 10% to 90 apples, some people think the answer is 100 apples. The correct answer is, of course, 99 apples. In the example, you thought you would get 100 apples, but it was only 99. Not as serious, you think. If, instead, it was a deal where you expected $1,000 or $1,000,000 more than you got, the consequences could be more serious. To avoid similar mistakes, I have put together this guide in percentages.
- The shirt is discounted at 30% off the sales price.
- 50% of the exam questions are multiple-choice.
- The home loan interest rate is currently 7.99% p.a.
- The stadium was 80% booked.
- 60% of the population are car owners.
- 40% of the country owns mobile phones.
- Profit was down 8% from the previous quarter.
We come across statements such as these every day of our lives. Statements with statistics. But what do they mean? They sound so overly complicated and confusing. Perhaps we don’t even want to find out. After all, what significance could they have for us? Plenty. The statements above utilize what is known as a percentage. We see statements like this everywhere. They form a part of our lives and ought to be something we understand. A basic operation that you should be able to calculate at any given time, whatever the context or situation. Especially with regards to money, percentages are an often-used term and concept in finance. Best then, we learn about percentages and how to use them to calculate them and their values.
Basic arithmetic operations such as percentages form the basis of ongoing work in mathematics. Still, they go way beyond the world of maths. Percentages are also a part of everyday life, as the statements provided above show. If you did not understand what percentages were or how to calculate them, how would you interpret the above statements, and what would they mean to you? You would be in a world of confusion and misunderstanding, not realizing the importance and significance of the percentage. So let us begin then, in helping you understand percentages and how to calculate them. Percentages are very meaningful in our lives and should be treated seriously.
Percentages are logical and easy to understand the mathematical concept. Once you have learned the idea behind percentages well, you will not forget it. Percentages are one of those mathematical arithmetic operations that make perfect sense once you have understood what and how percentages work. Most of all, one of the best things about percentages is that you will come across this concept in your daily life, beyond the world of the classroom where mathematics is taught. Percentages are one of those concepts that have far-reaching and everyday applicability, making it very practical for you to know and to know right. So it is worth investing the time to obtain the necessary knowledge and know-how.
Getting percentages correct can mean a lot more than you think when considering how much they form part of our world. Look at the world of economics, finance, politics, banking, and money, and percentages will be present. How could you work your way through all of the information provided, if you did not know how to calculate percentages? You would definitely risk losing money.
Percentages have an application that is practical to the everyday world. Some elements of mathematics are so theoretical that they appear to lose their significance for us in an applicable way to our lives. They involve concepts that go way over our heads and seem meaningless to and for us. This does not describe the concept of percentages. You will come across percentages as statistics in newspapers, exam marks, cooking instructions, discounts in stores, health, banking, and many other real-world applications. This makes percentages and calculating percentages a handy thing to know. You will always find a good use for percentages. They will keep you in the know and up to date.
A percentage is a fraction with a denominator of 100. When people speak of percentages, they are saying ‘per 100.’ So 2% would be 2 per 100. Or 2/100 or 2 out of 100. If I were to say that illness struck 2% of the population worldwide, I could also say that 2 out of every 100 people would contract the illness. Such terms are often used in health settings when discussing the prevalence of illnesses and recovery rates. Again, repeating the point that knowing percentages also shows another great reason to get percentages right.
Percentages are a form of basic arithmetic. Percentages, fractions, and decimals are interchangeable, and each one can be transformed into the other. But more on that a little later. First, some history on percentages. Percentages have their origin and basis in Ancient Rome and Greece. The percentage is derived from the Latin word ‘per centum’, Centum means 100. Thus percentages are fractions to the denominator of 100. The current % sign was once a horizontal line with two circles. This symbol came from Ancient Rome.
The history of percentages
The Ancient Romans are responsible for the symbol %, which was derived from the symbol that pertained to per centum. Still, it is from Ancient Greece that the idea to count things in one-hundredth first originated from. They just never used the word percentage back then. How things have changed. Who would have thought back in those days that percentages would come to be and signify what they do today? Percentages are everywhere. It is possibly challenging to go through a single day without coming across a percentage somewhere in some way.
It is interesting to note that a percentage is considered to be a number that is ‘dimensionless’ or pure in nature. Money has had a large hand to play in the creation and propagation of percentages. “Why is this,” I hear you say? As the denominations in money grew, so did the concept of percentage or per 100 or a hundredth. As money values grew in number and entered the hundredths, so did our need to count in one hundredth. Thus percentages grew in use and frequency as time went on worldwide. Most in particular, from the 18th century years and onwards, the percentage grew worldwide beyond the ancient world.
Fractions and percentages
Now take a short sidestep from percentages, just for a little while, to explain a related concept you need to know. This concept is about decimals and fractions. You can also turn a percentage into a decimal, a fraction into a decimal, or a fraction into a percentage. A decimal is a fraction with a denominator of 10. Following this idea, here are some examples of decimals and fractions:
0.3 = 3/10= 3 out of 10= 3 divided by 10
0.03 = 3/100= 3 out of 100= 3 divided by 100
0.003 = 3/1000= 3 out of 1000 = 3 divided by 1000
Now back to percentages. A percentage can be written as a fraction or decimal and is to a denominator of 100. Fractions and decimals are interchangeable indices that can help you understand how to calculate percentages better. They are one and the same thing. All three decimals, percentages, and fractions can signify the same amount, given the same value. The expression, however, appears different. So do not get confused by appearance. If the same value is present, they mean the same thing, but they are expressed differently. So they look different. And that is where the difference lies if the value is the same.
To re-iterate, a percentage can be written or expressed as a decimal or as a fraction. For example, the following all mean the same thing:
30% = 0.3 = 30/100
In a statement, this could be, 30% of the oranges were ripe. Or 30 out of 100 oranges were ripe and ready to be eaten.
This is how you perform the calculations to derive a fraction, decimal, or percentage:
30/100= 30 divided by 100 = 0.3
or
30% = 30 divided by 100 multiplied by 100 = 0.3 multiplied by 100
or
0.3 multiplied by 100 = 30% (read as 30 percent)
It is important to understand how all three concepts of decimals, fractions, and percentages work and how they are related. Some examples of percentages, decimals, and fractions now follow so that you can become familiar with the concepts furthermore:
25% is also 25/100 or 25 out of 100. Or, as a decimal, this is expressed as 0.25. To derive the decimal, you move the decimal point two numbers to the left. For example, from 25.00, you move the decimal point two times to the left, and you derive 0.25.
36%, this is also 36/100, or thirty-six out of one hundred, or 36 out of 100. The decimal format would be 0.36.
In the next example, we look at 55%:
55% = 55/100 = 55 out of 100= 55 divided by 100 = 0.55
But let’s go back to the beginning and start again, shall we? Sort of. Now for a deeper explanation. However, this time we will incorporate these ideas of decimals, fractions, and percentages into statements. Let us start with fractions. Here are some statements that incorporate fractions:
Jessica ate 2/3 of the pizza.
The backyard formed 1/3 of the land.
Joan owns 1/2 of the hairdressing salon.
Jack has read 1/4 of the book.
The number above the line of the fraction is known as the numerator, and the number below the line is called the denominator.
To convert a fraction into a decimal, divide the numerator by the denominator. So, applying this rule to the statements with the fractions listed above.
2/3 = 2 divided by 3 = 0.67
1/3 = 1 divided by 3 = 0.33
1/2 = 1 divided by 2 = 0.5
1/4 = 1 divided by 4 = 0.25
To convert a fraction to a percentage, multiply the fraction by 100. So let us apply this to the three statements above:
2/3 multiplied by 100 = 67% =0.67 x 100 =67%
Jessica ate 2/3 of the pizza = Jessica ate 67% of the pizza.
1/3 multiplied by 100 = 33% = 0.33 x 100= 33%
The backyard formed 1/3 of the land = The backyard formed 33% of the land.
1/2 multiplied by 100 = 50% = 0.5 x 100 =50%
Joan owns 1/2 of the hairdressing salon = Joan owns 50% of the hairdressing salon.
1/4 multiplied by 100 = 25% = 0.25 x 100 = 25%
Jack has read 1/4 of the book = Jack has read 25% of the book.
REAL-LIFE PERCENTAGE SCENARIOS
Percentages can be used in a variety of places, so they are very useful to understand. You will not be wasting your time in any way whatsoever to acquire the knowledge around percentages. I will outline some percentage calculations used in real-life scenarios and in different contexts. These real-life scenarios that use percentages demonstrate a form of arithmetic known as consumer arithmetic. Consumer arithmetic is used in daily life in transactions involving a buyer or consumer.
The situations where percentages can be found that follow are often used and are of most use to the consumer. Basically, it is where people come across percentages most often in daily life.
THE RETAIL STORE
How to calculate discount percentages is a very helpful thing to know in the world of retail. How often have you seen in a catalog certain statements about items being marked 25% off or all items in the shop are 50% off? Knowing how to use percentage calculations means that you can work out how much this will cost you in dollar value and what it all means financially for you. The bottom line is the financial dollar. This is the most relevant daily use of a percentage.
Knowing percentage calculations in retail settings and shopping can help you budget and plan your spending wisely. This can mean that you can save money and increase the savings that you have in the bank. Or you could purchase items at a lower price than is normally available. The percentage calculation has very wide use in retail and shopping settings and can help you save your money. You can grab a bargain, organize repayments for a large purchase or secure that outfit you always wanted to buy on sale.
THE BANK
Where would the bank be without percentages? Look at any savings account, cheque account, term deposit, and reference to interest rates. The interest rates are displayed as annual percentages. Understanding what percentages are and calculating them means that you can work out how much interest your savings account will make per day. Or, alternatively knowing the current credit interest rate can help you calculate your credit card repayments per month.
Knowing about percentages will help you calculate your repayment per year on your home loan. You could also calculate the repayment required per month for the money you intend to borrow to go on a holiday or buy a car. What a wonderful thing to know then what percentages are and how to calculate them. You would be able to work out what you could afford as a repayment.
Ultimately, percentage calculations could mean financial savings or loss as you make plans incorporating interest rates in your budgets. To not know about interest rates or to ignore interest rates means an impact on your dollar. Could there be any reason other than to stay in ignorance? When banking consumers take out loans or tie up savings, they do so with variable interest rates. Being able to calculate percentages can come to good use… Knowing percentages means that a consumer could calculate the impact of fluctuating interest rates.
THE MEDIA AND STATISTICS
You will find statistics appearing in newspapers, magazines, publications, and television reports quite often. Headlines such as “62% of U.S. adults get their news from social media, says the report,” (Tech Crunch, 27/05/2016) or “A fifth of adults have forgotten how to do fractions or percentages” (The Guardian, 8/03/2016) are only two examples of a plethora of newspaper articles that quote percentages. The media in all its forms is most prevalent in the use of percentages for statistics.
There are many situations you will encounter outside of the classroom that utilizes percentages. Newspaper articles, journalist reports, politicians’ speeches, and other spheres, such as retail and banking. Knowing about percentages will hold you in good stead. They are an essential basic arithmetic operation used in mathematics and many subject areas, from economics, finance, engineering, and healthcare.
The rest of the article will involve problems and answers that include percentages and/or calculating percentages before a final summary of percentages and their applications in the world. By now, you would have worked out that percentages are a lot more than that concept you learned in the high school classroom and one that functions importantly in everyday life.
EVERYDAY PERCENTAGE CALCULATIONS
It is one thing to understand all of the concepts surrounding decimals, from fractions to percentages, and how to derive one from the other, but how do you do the calculation when presented with percentages daily, in more complex terms? Furthermore, how do you work out the percentages in the calculations or the numbers that they represent? We will now look at some more complicated questions and examine the world of percentage calculations.
(a) A cook needs 500 g of butter for a 5 kg cookie batch. What percentage is 500 g of the cookie batch?
500 g of butter divided by 5000 g of cookie batch multiplied by 100 = 10% or
500/5000 x 100 = 10%
So the butter is 10% of the cookie batch.
(b) In an examination, a law student received a mark of 80 out of 120. What percentage is the mark 80 out of 120?
80 divided by 120 multiplied by 100 = 67% or
80/120 x 100 = 67%
So, 80 out of 120 is also 67%
(c) A college received a 25% discount on a textbook order of $1000. How much did the school pay?
25 divided by 100 multiplied by $1000 = $250 or
25/100 x 1000 = $250
$1000-$250 = $750
The college paid $750.
(d) Which is the smaller amount: 50% of $500 or 25% of $1000?
Part One: 50 divided by 100 multiplied by 500 = $250 or
50/100 x 500 =$250
Part Two: 25 divided by 100 multiplied by 1000 = $250 or
25/100 x 1000 = $250
The percentages represent the exact same amounts.
(e) A business owner borrows $1000 at 20%. How much will his simple interest payment be for the year, based on the borrowed amount?
$20 divided by 100 multiplied by 1000 = $200 or
20/100 x 1000 = $200
The repayment interest will be $200 for the year.
(f) The annual profit of the retail store decreased by 30% from the previous year. If the store made $100,000 in the previous year, how much profit did the business make this year?
30 divided by 100 multiplied by $100,000 = $30,000 or
30/100 x 100,000 = $30,000
$100,000 – $30,000 = $70,000
So the store made $70,000 in profit, down $30,000 from the previous year.
(g) Sally’s take-home pay for the fortnight increased by 20%. If Sally’s fortnight earnings prior to the increase were $1500, how much does she earn now?
20 divided by 100 multiplied by $1500 = $200 or
20/100 x 1500 = $200
$1500 plus $200 = $1700
Sally now earns $1700.
(h) The number of women on boards is up by 2% from the previous year. What is the new figure if 1100 women were found on company boards worldwide in the previous year?
2% plus 100% = 102%
102 divided by 100 multiplied by 1100 = 1122 or
102/100 x 1100 =1122
There are now 1122 women on the company boards worldwide.
Not knowing basic percentage calculations can lead to missed opportunities and not having a correct image of certain topics. Potential savings, money loss prevention, tipping correctly at restaurants, calculating sales tax, and more can be calculated using percentages. Thus, percentages study is a worthwhile and wonderful undertaking, and to learn such a skill to keep for life is important.
Working with percentages is also important for the workplace. In any workplace, one needs to know how to do basic operations. But in some sectors such as economics, finance, statistics, and banking, working out the percentage becomes important for one’s livelihood. Economists, statisticians, sales representatives are a few of the professions that work with percentages. There are many others.
The media and its staff are heavy users of percentages. Journalists use percentages to back up their ideas and present knowledge by chemists, politicians, healthcare, statisticians, and businesspeople. Percentages are also used by companies that undertake research on their demographics, their own staff, and also their consumers. Interpretation of all of these figures requires knowledge. Fractions are also used to represent statistics and are another way, like decimals of presenting percentages. It is important to know all three.
Let us talk further about how percentages could be used in the workplace. A sales representative makes a 25% commission on each product that he sells. He would be able to calculate what money is owed to him through the use of percentage calculations. Another application is the use of percentages to describe social-cultural conditions. For example, statistics examining how many women are on the boards worldwide can be expressed as a percentage. Many women’s rights groups lament the low level of women being seen on boards.
One would imagine that all people know what percentages are and how to calculate percentages, but that is simply not true. Statistics in reports indicate that many people have no idea how to calculate percentages. What a loss for those people! There is so much information that has been presented or seen by them, and they simply do not have the ability, skills, or knowledge to comprehend this. Just from seeing from the real-world scenarios, there is a whole world excluded to them, which they are essentially left out of through lack of knowledge.
Percentages are on a spectrum from simple calculations to more complex calculations. Essentially, calculating percentages is a skill you need. If you do not have this skill, make certain that you obtain it.