# Business Maths Part II: Learning Percentages

In this section,we shall learn about handling/calculating percentages at workplace.

## Using Percents

Trends, profits, productivity—concepts like these are often expressed as percentages. For that reason, it's very useful to have a basic understanding of what percentages mean and how to work with them. Percentages are basically a comparison tool. They help business people set priorities and describe critical factors that affect day-to-day and long-term decision-making. Percentages are often used to clarify underlying data.

Knowing how to work with percentages will enable you to:-

- handle essential business calculations

- compare and analyze data

- express a part of a whole quantity or amount.

Business calculations may include such things as markups and gross profit percentages. Companies frequently use percentages to compare and analyze data, using profitability ratios, break-even analysis, and the concepts of return on assets and return on investment, for example. Amounts are shown as a proportion of some total amount in observations such as this: "More than 50% of sales are from farm-produced products". Percentages are always expressed in relation to something else, as a percentage "of" some whole number, quantity, or object. Percentages tell a story, which is what makes them such a useful tool—and so widespread in business.

Look around your workplace or flip through any business publication. You'll see that almost any expression of value, productivity, change, or proportion can be expressed in terms of percentages. Today's organization is all about trends and allocation of resources. When you understand the form and use of percentages, you will be able to do a better job of understanding and communicating vital business information.

## Understanding Percentages

Percent simply means parts per hundred. Anything that can have a quantity associated with it can be defined as a percentage. If you divide a whole quantity into 100 equal units, one of those units equals one percent. To determine percentage, the whole amount has to be established. That whole amount equals 100%. For example, if your business had £1,250 in cash, £1,250 would equal 100% of your cash. Whatever number you arrived at as your total would be defined as 100% of the total cash in your business.

Since 100% is a multiple of ten, percentages bear a close relationship to decimal numbers. One hundred percent is one whole quantity, so it would be written as the decimal number one:1.0. Percentages can easily be converted in to decimal numbers simply by moving the decimal point two places to the left. So, for example, 1% = 0.01, 15% = 0.15,90% = 0.90. Whatever your total quantity is, whether 333.3 cabbages or 10,000 paper clips, it gets divided by 100, and each 1/100 represents 1% of the total. To divide a number by 100, just move the decimal point two places to the left.

### Solving for a number

There are three key elements in a typical percent problem:-

1. Base – the whole quantity or value

2. Rate – a percentage, decimal, or fraction

3. Portion – the result when the base is multiplied by the rate.

Generally, in percentage problems, two values are given, and the third must be calculated from those given values. The mathematical process, or formula, to determine Portion is: Portion = Rate x Base

In a business environment, there are three steps to solve for a portion (not a percent and not a whole):

1. Identify key elements

2. Set Up the formula

3. Calculate Portion.

The first step is to identify the key elements. Keep in mind that Rate is usually expressed as a percentage, or as a fraction or decimal; the Base is usually preceded by the word "of" when you have to solve for a portion; and the Portion is a part that is neither a percentage nor the whole quantity or value. If the Rate is less than 100%, the Portion is always less than the Base. The Rate, if expressed as a percentage or a fraction, must be converted to a decimal number before you can perform the multiplication.

The key to solving workplace problems is identifying the three key elements. Then you can plug the numbers in to the formula Portion = Rate x Base, and perform calculations to determine the missing element. Usually, once you formulate the correct math equation, you can calculate the correct answer. In percentage problems, identifying the elements pretty much dictates the formula to be used. If the missing element is Portion, the formula is always Portion = Rate x Base.

### Solving for a percent

Percentages are useful because they make it very easy to compare things. For example, profits might be expressed as a percentage of revenues, marketing costs as a percentage of sales, or statistics in terms of a percentage of change. When you are trying to determine a percentage (Rate), the pie tells you that the formula is Rate = Portion divided by Base. Remember, Rate is the percentage you're solving for. Portion represents a part of the whole, and Base is the whole object or number that you are taking a percentage "of".

Identifying Portion can be somewhat tricky when you are determining Rate of increase or decrease. You need to identify the original and the new amounts of the Portion, and find the difference between them. In solving for Rate, the process is to compare Portion to Base, and express the results using the % symbol.

Businesses frequently use percentages to clearly communicate comparative data in a wide range of areas. If you don't know how percentages work, you may have difficulty understanding important information. For example, here are some excerpts from recent headlines:-

-Companies spend 45% of T&E budget on air travel.

-Small companies will see online sales grow 336%.

-Stock mutual funds rose 30% last year.

Steps used to solve a real life problem:-

1. Identify the key elements.

2. Set Up the formula.

3. Calculate Rate.

Do you see how the percentage (Rate) formula allowed you to compare the amount spent on air travel to the total T&E budget? This kind of information can be very helpful to company decision makers, who might be looking to cut T&E costs, for example. Knowing that a big chunk of the T&E budget is devoted to air travel, executives can look for ways to reduce that expense, because they can see that reductions in that area will have a big impact on the entire budget.

Did you understand how the percentage was calculated? Determining the percentage of profit helps businesses make correlations between sales and costs, so that managers can make better business decisions. People are data-driven these days, and figuring out percentages is a necessary skill for many employees. Percentages are very helpful in the presentation of business data. Just remember that they are considered in the relation to the whole (Base) and are always calculated on the basis of 100.

Always, use the formula Rate = Portion divided by Base.

### Solving for whole base

When the Portion (part of the whole quantity) is known, and you also know the percentage (Rate) of the whole the portion represents, it is possible to determine the Base (the whole quantity). For example, your company might get 15% of a customer's outsourced machine tooling work. You know you got an order of 1,200 parts for finish work. Solving for the whole will tell you how much work the customer outsources. In another example, a competitor might claim that it dominates the market by supplying 29% of a certain product. If you know the competitor sells 6.5 million units per year, you can figure out the total market for this product.

The easiest way to remember what formula to use to solve percent problems is to use the pie chart. Becoming proficient at using decimal numbers and percentages in the workplace is a great achievement. The rewards that come with this level of success are both professional and personal. Performing these calculations and recognizing the significance of these numbers takes time and patience to master, but the results will surprise you—improved understanding and hence, improved job performance.