Basic Workplace Numeracy
Skills – 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
Skills
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.
Fractions
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.
Tip:
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
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:
431.26
+ 522.31
953.57
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:
286.47
− 125.32
161.15
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…
23.25
× 6.25
...as...
2325
× 625
...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!