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Order Of Operations

‘Order of Operations’ is one of the most important but most neglected parts of Excel.

Beyond simple formulas, it impacts everything you do in Microsoft Excel, whatever level you’re at.

Ignore it at your peril!

If you currently use Excel (or you haven't yet started but are thinking about it) then make sure you read through this entire post and understand it fully before moving on to your next task. It will make a huge difference to your progress.

Prefer to watch instead of read?

In this previous post, I explained how to get started with Excel formulas even if you’re a complete beginner.

My next question is …

The French have produced a LOT of world-renowned mathematicians over the years.

At school you learnt about Descartes and Pascal, but there are many more famous mathematicians including rather a lot of Bernards and Edouardos (search 'French mathematicians' and you'll see what I mean!).

So what does an unknown French mathematician from the 1600s have to do with Excel?

In Excel there is an important rule called the Order of Operations. It’s actually a set of rules that are followed globally, and if you don’t *know* or don’t *follow* the rules there could be disastrous consequences.

*Like a famous London consulting firm that lost millions because of a simple error in a formula that led to incorrect forecasts and costly recommendations. And probably a very awkward conversation for a certain guy or gal!*

Nobody knows for sure who created the Order of Operations, but it seems they evolved in the 1600s. A French mathematician by the name of DuPlus (probably pronounced ‘Doo Ploo’), is widely considered to be the guy who formulated the rules.

When you have a formula with 3 or more components, the order of operations tell you in which order to process them.

For example, consider this

= 2 + 3 * 4

Many people think the answer is 20. After all, if you work left-to-right, 2 + 3 = 5 and 5 * 4 is 20. Stands to reason, right?

However the correct answer is 14.

Why? Because the multiplication is done first, then the addition.

- Excel first calculates the answer to 3 * 4, which is 12.
- Excel then calculates the answer to 2 + 12 which is 14.

Formulas are always calculated in a set order.

This is high-primary school or early-high-school maths. Everybody learnt it. Many people have forgotten it. Don’t worry - you are not alone.

The BEDMAS acronym helps you to learn the order. Excel uses symbols to represent mathematical operators. Below, I’ve explained what BEDMAS stands for and the mathematical symbols that Excel uses.

Anything in brackets is calculated first. You can add brackets to change the natural order.

For example,

= 2 + 3 * 4

gives the answer 14, but

= (2 + 3) * 4

gives the answer 20

In layman's terms exponentiation is talking about powers, for example 4^{2}, or 4 squared can be expressed as 4 to the power of 2.

To write a power / exponential in Excel, use the little Chinaman's hat - ^ - which is displayed when you press Shift 6.

For example,

= 4 ^ 2

gives the answer 16 (4 x 4), and

= 5 ^ 3

gives the answer 125 (5 x 5 x 5)

Unless you're an engineer, exponentials are used much.

For example:

= 100 / 2

= A1 / A2

For example:

= 1000 * 1.1

= A3 * A4

For example:

= 1 + 2 + 3

= A5 + A6

For example:

= 100 - 50

= A7 - A8

It doesn’t actually matter whether you multiply or divide first. Or add or subtract first. But when you have a mixture of addition and multiplication or subtraction and division, then the order is vital.

For example:

= 8 + 6 - 2

is the same as

= 8 - 2 + 6

Don't risk it. Play it safe. Stick to the list.

So that’s the Order of Operations. Learn it. Get to know it inside out and upside down. It’s important.

I have heard and seen lots of different acronyms used. Here’s a selection:

- BEMDAS
- BOMDAS
- BODMAS
- BIMDAS
- BIDMAS
- PEMDAS

As you can see, the last 4 letters in every acronym are the same, even if ‘M’ and ‘D have sometimes been swapped.

- ‘P’ stands for Parentheses (which is a fancy way of saying Brackets).
- ‘I’ stands for Index or Indices which is another way to say ‘Powers’.
- ‘O’ is a horrible letter for this acronym. It can mean:
- ‘Order’ (which doesn’t do anything in this context),
- ‘Of’, as in ‘to the power of’ (i.e. ‘of’ is the 4th word which doesn’t do much to help you remember it), or
- ‘Ordinals’ which is another way to say ‘powers’.

The most creative (and amusing) acronym is the last one - PEMDAS. It stands for Please Excuse My Dear Aunt Sally. For some reason, that always conjures an image of some fat flatulent Aunt - but perhaps that’s just me!

Test yourself on these

Have a go at these in your head or on a piece of paper, then check your answers in the section below.

= 6 - 4 / 2

= 2 * 3 ^ 2

= 2 + 3 * 5

= 2 + (3 * 5)

= (2 + 3) * 5

= 3 ^ 2 * 3

Okay, here’s the answers:

- Answer is 2 –> 4 / 2 equals 2, then 6 - 2 equals 4.
- Answer is 18 –> 3 ^ 2 (or 3 squared) equals 9, then 2 * 9 equals 18.
- Answer is 17 –> 3 * 5 equals 15, then 2 + 15 equals 17.
- Answer is 17 –> (3 * 5) equals 15, then 2 + 15 equals 17 - the brackets don’t change anything - I was just testin’.
- Answer is 25 –> (2 + 3) equals 5, then 5 * 5 equals 25.
- Answer is 27 –> 3 ^ 2 (or 3 squared) equals 9, then 9 * 3 equals 27.

As you develop more spreadsheets, you’ll need to use the ‘Order of Operations’ a lot.

BEDMAS is the acronym that will help you remember the order.

Don’t ignore it.

Become familiar with it. You need to know these rules inside out and backwards.

Make it your homework tonight to memorise the 6 letters depicting the order of operations. There’s plenty of TV ad breaks. Mute the TV and use the time.

I hope you have enjoyed this mini-series on creating simple formulas in Excel.

Did this clear something up for you? If so, please share on your socials and/or post a brief comment below.

Likewise, if something didn't make sense or you have a question, pop it into the comments below. I'll be waiting ...

Cheers. Here's to your learning and success. Enjoy the rest of your day.

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