Basic Workplace Numeracy – Part 1
Working With Fractions, Decimals and Percentages
Does your heart sink every time you see a financial spreadsheet? Or, do you dread those tricky questions about percentages when you give a presentation?
Many people struggle with numbers. This can feel frustrating and shaming. It can slow down your projects, hold you back in your career, and damage your self-esteem. But it doesn't have to be that way. Most of us can learn basic math, or build on the skills that we learned in school.
This article explains some key workplace math around fractions, decimals and percentages. Taking a little time to understand it can make your work life a whole lot easier in the long run.
Why You Need Basic Numeracy
In a 2015 report from the Organisation for Economic Co-operation and Development (OECD), both the U.S. and the U.K. ranked below average for math learning among developed nations.
But the ability to handle numerical data, and to draw logical conclusions from it, is vital in many workplaces. Understanding the principles of basic math can pay dividends, even when calculators and computers can work out the sums for us.
Say, for example, that you're in a meeting with a client, and he or she asks you what the discount you're offering on a product represents as a cash saving. Or, you're asked what percentage of your budget is given over to marketing. A better understanding of math can give you the self-confidence to answer questions like these, and likely boost other people's confidence in you, too.
Working With Parts of Numbers
Most people can cope with whole numbers. You can probably add and subtract, and you likely know your multiplication tables. And when the numbers get bigger, you can use a calculator.
But with numbers that are parts of wholes, you may need to carry out several different calculations, in the right order, to get the correct answer. The good news is that if you break down these calculations into the right steps, they aren't difficult.
We're all familiar with whole numbers (1, 2, 3, and so on). Fractions are numbers, too, but they describe parts of whole numbers.
Fractions are written as one number divided by another, usually with one above the other. For example, a half is written as 1⁄2, and a quarter as 1⁄4.
The number on the top is the numerator, and the number on the bottom is the denominator. The line between the two numbers shows that the top number has been divided by the bottom number.
Generally, the fractions that we use are smaller than the number 1, and have numerators smaller than their denominators 1⁄2, 2⁄5, 3⁄8, and so on).
You can write numbers larger than 1 as fractions (3⁄2, 9⁄5, 8⁄3), but these are usually written as a mixture of whole numbers and fractions (11⁄2, 14⁄5, 22⁄3, and so on).
How to Add Fractions Together
To add one fraction to another, or to subtract one from another, you first need to make the denominators the same.
The quickest way to do this is to multiply the denominators together. This gives you a common denominator – a number that is a multiple of both denominators. For example, in…
1⁄4 + 1⁄3
…you multiply 4 by 3 to get the common denominator, 12.
You then multiply the numerator in each fraction by the same number that you multiplied its denominator by. So:
1⁄4 + 1⁄3 is the same as 3⁄12 + 4⁄12
Then, you add together the numerators. So:
3⁄12 + 4⁄12 = 7⁄12
However, you can sometimes find a smaller common denominator than the one that you get when you multiply the denominators.
For example, if you follow the method above for the sum 2⁄3 + 1⁄6, your calculations look like this:
2⁄3 + 1⁄6 is the same as 12⁄18 + 3⁄18, which equals 15⁄18
You can then simplify 15⁄18. Both 15 and 18 are divisible by 3, so dividing the numerator and denominator by 3 gives us 5⁄6. The fractions are equivalent, but 5⁄6 is the simplest form.
But, in 2⁄3 + 1⁄6, 6 is a lower multiple of both denominators. So, you could keep the common denominator at 6 by multiplying the top and bottom of the fraction 2⁄3 by 2. This keeps the sum as simple as possible.
So instead of this:
2⁄3 + 1⁄6 is the same as 12⁄18 + 3⁄18, which equals 15⁄18, which simplifies as 5⁄6
You calculate like this:
2⁄3 + 1⁄6 is the same as 4⁄6 + 1⁄6, which equals 5⁄6
Just take the shortest route you can to arrive at the answer.
Always represent a fraction in its simplest form. For example, 4⁄6 is really 2⁄3, because both the numerator and the denominator can be divided by 2.
How to Subtract Fractions
To subtract fractions, find the common denominator and then subtract one numerator from the other, like this:
1⁄3 − 1⁄4 is the same as 4⁄12 − 3⁄12, which equals 1⁄12
How to Multiply Fractions
To multiply fractions, multiply the two numerators to get the numerator of the answer. For example, in…
3⁄4 × 2⁄3
…you multiply 3 by 2 to get the numerator, 6.
Then, multiply the two denominators to get the denominator for the answer. Here, you multiply 4 by 3 to get the denominator, 12, like this:
3⁄4 × 2⁄3 = 6⁄12
But you can represent your answer, 6⁄12, in a simpler form, by dividing both the numerator and the denominator by the same number to make smaller numbers.
In our example, you can divide both the numerator and denominator of 6⁄12 by 3 to get an equivalent, but simpler answer of 2⁄4.
You can then divide both the numerator and denominator of 2⁄4 by 2, to make 1⁄2. So:
6⁄12 is the same as 1⁄2
How to Divide Fractions
To divide one fraction by another, look at the fraction that you're dividing by, and turn it upside down. So, in…
1⁄4 ÷ 1⁄2
…you turn the 1⁄2 upside down. So:
1⁄2 becomes 2⁄1
Then, multiply the two fractions together:
1⁄4 × 2⁄1 = 2⁄4
And finally, simplify your answer:
2⁄4 is the same as 1⁄2
Decimals represent the tenth, hundredth, thousandth (and so on) parts of a number. Most numerical data that you see in the workplace involves decimals. Sales figures, data analyses, and worksheet hours, for example, commonly use decimal figures.
How to Add Decimals
You add decimals in exactly the same way as you add whole numbers. Start on the right-hand side of the sum, and move from right to left, adding the decimals first, then units, then tens, and so on.
The key thing to remember is to line up the decimal points in the numbers you're adding, one above the other, like this:
How to Subtract Decimals
The same rules apply for subtraction. Subtract decimals in the same way as you would subtract whole numbers, working from right to left and remembering to line up the decimal places:
How to Multiply Decimals
To multiply and divide decimals, start by multiplying the numbers exactly as if there were no decimal point at all. So calculate…
...which equals 1,453,125.
Now, count how many numbers came after the decimal points in the numbers that you multiplied together, and move the decimal point that many spaces to the left.
In our example, a total of four numbers came after the decimal points in the original sum. So, take the answer 1,453,125 and move the decimal point four places to the left (from the right-hand end of the number). This gives you a final answer of 145.3125.
How to Divide Decimals
The easiest way to divide decimals is to make the two numbers that you're working with into whole numbers. To do this, simply move the decimal point to the right. But, remember that you have to move the decimal point by the same number of places in both numbers. So, for example, in the calculation…
56.48 ÷ 22.6
…you move the decimal point two places to the right in both numbers, like this:
5648 ÷ 2260
The answer, 2.499, is the same in both cases.
The principle here is that it's much easier to divide whole numbers than to divide decimals. However, long division is still tricky for numbers with three digits or more, so this may be a good time to reach for your calculator!
Understanding percentages is an important skill. Discounts, product margins, cost-of-living data… it's almost all expressed in percentages.
A percentage is a part of a whole, expressed in hundredths (“per cent” literally means, “by 100” or “one hundredth part”). So 23% of a quantity is 23 hundredth parts of it, or 23⁄100.
A percentage is usually indicated by the symbol %, but it can also be written out as percent or per cent.
How to Calculate and Add a Percentage of an Amount
Let's say that you need to add a 7% sales tax to the price of an item, so that you know what the total price will be.
The pre-tax price is $70, so start by working out 1% of that starting quantity. Remember that “percentage” means “one hundredth part.” So 1% of 70 is one hundredth part of 70. Another way to say this is 1⁄100 × 70.
If you make that into fractions, it's 1⁄100 × 70⁄1, which equals 70⁄100. That simplifies to 7⁄10.
You can express this as the decimal 0.7. Our example uses money, and in dollars, 0.7 represents 70 cents.
Now that you've worked out 1%, you can find out what 7% is by multiplying the 1% figure by 7:
0.7 × 7 = 4.9
So, the sales tax to add is $4.90. Adding this to the pre-tax price of $70 makes a total cost of $74.90.
How to Subtract a Percentage
Let's say that you want to offer a 20% discount on a product that has a pre-discount price of $300.
First, calculate 1% of 300:
1⁄100 × 3 = 3⁄100
You can write 3⁄100 as the decimal 0.03. In dollar terms, this is $3.
You then multiply 0.03 by 20, to get your 20% figure:
0.03 × 20 = 0.6
This gives 0.6. In dollar terms, that's $60, so the discount that you need to subtract is $60. Therefore, you can calculate the final price like this:
$300 − $60 = $240
How to Give One Number as a Percentage of a Another
Suppose that your organization employs 40 people, and 14 of them work part-time. You want to know the percentage of team members who work part-time.
Start by converting the question into a fraction:
14 out of 40 is the same as 14⁄40, which simplifies as 7⁄20
To make 7⁄20 into a percentage, the fraction needs to have a denominator of 100. So, multiply your denominator (20) by 5, to make 100. Then multiply the numerator by the same number:
20 × 5 = 100 and 7 × 5 = 35, which gives you a fraction of 35⁄100
The answer, 35⁄100, equates to 35% (35 out of 100), which means that 35% of your organization's employees work part-time.
If you can't make the denominator into 100 using simple multiplication, it's best to use a calculator. Calculate one number as a percentage of another by dividing the numbers and multiplying the answer by 100.
Numerical skills are important in the workplace. They allow you to understand and manipulate data, and to feel confident when you're making decisions that are based on numbers or quantities.
Fractions, decimals and percentages all involve parts of whole numbers. Working with them requires a number of separate, but simple, operations.
Some key terms include:
- Numerator: the top part of a fraction. The number of parts of something.
- Denominator: the lower part of a fraction. The total number of parts that make up the whole.
- Decimal point: the point that separates numbers larger than one from numbers smaller than one.
- Percentage: a hundredth part of something.
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