If you’re a regular on social media, you would have seen them, sitting there on the page tempting you, images and statements beckoning to you to show your genius of mathematical expertise. They are hard to resist and many fall into the trap of posting and then sharing. Unfortunately the majority of people get them wrong, some even gloat about their mathematical prowess, in relation to others efforts. I’ve even seen people commenting and making statements like ‘My 9 year old just worked it out, no problem.’ Then they all go and post the incorrect answer to the equation!

Why do so many fail? Simple answer, they don’t follow the rules!

There are two main types of mathematical posts (memes), the 'Basic Equation' and the more devious 'Observation Equation', where graphics are used in algebraic form (that’s where an image equals a number).

The ‘Observation Equation’ once the graphic images are converted into numbers, then becomes a ‘Basic Equation’ so we will break down the ‘Observation Equation’ type first with a common example found on social media

Observation Equation

In this meme you have three equations with answers, so you can work out the value of each item shown, which you can then use to solve the final equation and post the answer.

The mistake many make is to dive right in and work out the values and apply to the last equation. DON’T, play spot the difference first, ignore all numbers and just compare the images.

Almost immediately you will see that the fries are in doubles in the third equation but are shown as a single portion of fries in the final equation you have to solve. That is the secret of the graphic type equations, they will often switch a pair, in the examples, to a single in the final equation. This one is fries, but it could be a pair of horseshoes or a pair of boots etc, that suddenly become one Horseshoe or a single boot in the final equation.

So, you know the pair to single item switch is there, now you can work out the values to give you the final equation:

So first line tells you that a Drink is worth 10 (divide 30 by 3)

Second line shows that 10 + Burger + Burger = 20 so a Burger is worth 5 (10 + 5 + 5 = 20)

Third line shows that 5 + Double Fries + Double Fries = 9 so Double Fries is worth 2 (5 + 2 + 2 = 9)

In the fourth and final line you already spotted that the middle image is Single Fries, so you now know to divide Double Fries by 2, so Single Fries are therefore worth 1

Now convert line four into a ‘Basic Equation:

Burger + Single Fries x Drink = ? Now reads as 5 + 1 x 10 = ?

Basic Equation

Right, observations have been done, correctly I hope, and you now have a ‘ Basic Equation’ in front of you to solve, as the final part of the process.

Unfortunately this is also the main part that approximately 90% of the equation solvers get totally wrong. Which then leads to multiple posts, shares and arguments. That’s why these memes are created, because the originator of the meme knows that most of you don’t understand basic elementary school mathematics, which will then lead to the meme possibly becoming ‘Viral’ as a result. Which is what they want if their page has advertising on it.

The error is usually the failure to apply a rule known as the ‘Order of Operations’

Order of Operations

The order of operations is used throughout mathematics, technology, science and many computer programming languages and the order is:

1st - Parentheses - (Parentheses are brackets)

2nd - Exponents - (Exponents are (*b*^{3 }) etc)

3rd - Multiplication / Division

4th - Addition / Subtraction

So whatever the equation just do left to right passes as the ‘Order of Operations above: 1st pass do all the Parentheses (Brackets) calculations; 2nd pass do all the Exponents; 3rd pass, in the order you come to them, do Multiplication / Division; 4th pass, in the order you come to them, do all the Addition / Subtraction to finally solve the equation.

Let’s Solve the Equations

We’ve already broken this one down, remembering the Double Fries sneakily becoming a single Fries in the final equation. So we know the numeric equasion is:

5 + 1 x 10 = ?

No Parentheses, on 1st pass; no exponents on the 2nd pass; on 3rd pass there is only one multiplication so:

1 x 10 = 10

So now the equation becomes:

5 + 10 = 15

Not really rocket science to get to the correct answer which as you can see is:

15

Now for Einstein’s - Are you a Genius?

The equation is:

3 - 3 x 6 + 2 =?

No Parentheses, on 1st pass; no exponents on the 2nd pass; on 3rd pass there is only one multiplication so:

3 x 6 = 18

So now the equation becomes:

3 - 18 + 2 = ?

So on the 4th pass:

3 - 18 = -15

Then:

-15 + 2 = -13

So the correct answer is:

-13

That’s how it is done!

Apply the ‘Order of Operations’ to all these online mathematical memes and equations, be observant concerning any graphics, and you wont go far wrong.

If you know for sure you have the answer correct and people want to argue then just post a link to this page and educate them!

Extra Information - Mnemonics (Acronyms)

You will also see many people throwing things like PEDMAS, BODMAS etc into the posting mix. These are ok as a prompt to remember the ‘Order of Operations’ but they are not correct in a literal sense.

Multiplication and division are equal to each other so when working from left to right you do whichever you come to first, you DO NOT do all the division first, then do all the multiplication on the next pass, or visa versa.

Addition and subtraction are also equal, in status, to each other. So once again, from left to right you do whichever you get to first and you DO NOT do all the addition first then do all the subtraction, or visa versa.

Acronyms do NOT make this clear, and doing an equation by following an acronym reminder to the letter will possibly end up with yet another incorrect answer.

So just to clarify you follow:

1st - Parentheses - (Parentheses are brackets)

2nd - Exponents - (Exponents are (*b*3 ) etc)

3rd - Multiplication / Division

4th - Addition / Subtraction

Article Additions - (Excuse the Pun)

I decided that, as this is a bit of an ongoing issue with social media, each time I spot a different one of these mathematical memes, dwelling on peoples lack of knowledge concerning the ‘Order of Operations’, I will add them to this page and solve them:

This popped up on Facebook timeline on 17 December 2016.

The equation is:

11 + 5 + 3 x 2 + 8 x 1 = ?

No Parentheses, on 1st pass; no exponents on the 2nd pass; on 3rd pass there is two multiplications so:

3 x 2 = 6 and 8 x 1 = 8

So now the equation becomes:

11 + 5 + 6 + 8 = ?

So on the 4th pass:

11 + 5 + 6 + 8 = 30

So the correct answer is:

30

With this particular mathematical meme I have noticed by running through some of the posts that it seems a higher percentage than usual are getting the correct answer. Whether that is because it’s a straightforward equation, without the clutter of images to distract, or whether people are actually getting the hang of doing mathematical equations correctly is a possible point for further investigation.

Here comes another one! - *(Or is it?)*

Saw this one, yellow image left, on 18 December 2016, but looks like it’s been circulating for a while, at the time of writing it has over 9.5k likes, 107k comments and over 3.2k shares . The yellow image and the almost identical white image originally appeared on two different puzzle websites in January 2015.

The white one on the right, is NOT an equation and is NOT solved by real mathematics. The puzzle site that published it shows the answer as 30, which is based on the 1’s at the end of the first two lines being part of the 1’s at the beginning of the next line to make them an 11, so they’ve only gone and split an integer over two lines, at what point in time did that become an option? Then not forgetting the ‘Order of Operations’ 1 x 0 = 0 they then add the whole lot together! That is NOT mathematics as you CANNOT split a number from one line to another in that way. But the image does not state it is an equation, it’s just a cheap tacky puzzle that makes little sense in intelligence terms.

Then some numpty has shown the same puzzle, and produced the yellow image on the left, at the same time they’ve added their own little piece of junk - ‘Solve the following equation’!

Now they are giving the impression that there is an equation to solve and it’s no longer just a tacky puzzle. So what is the equation?

Well there is only one real equation on the yellow image and that is just the bottom line. There is no link between the three lines, in mathematical terms, so the first two lines are just a series of 1’s and + symbols and don’t mean anything.

So line three does read 1 + 1 x 0 + 1 = ? which using the usual ‘Order of Operations’ rule equals 2. The solution to the equation is therefore 2, although the numpty that put up this version of the puzzle and added the equation reference still shows the answer as 30 on their own website!

Basically both versions are complete rubbish and should be ignored as they don’t resemble equations or relate to mathematics! They’re really just two versions of the same thing that have been created and circulated by individuals who spent too much time staring out of the window, when at school, instead of paying attention in lesson time. They certainly do NOT understand mathematics.

New Seasonal Graphic for the Same Old Visual Trick

Here it comes again, this one appeared on one of my social media home pages on 7 January 2017, Same old equation with a different graphic.

Exactly the same as the ‘Fast Food’ version just with a seasonal spin, snowflakes, candy and glasses of wine. Last time it was double fries to single, this time it’s double glasses of wine to single… don’t get caught. The answer of course is 15.

How Citrus, a Fruit Salad Version Appears

Same old image trick with this one, that I also spotted on 7 January 2017, just with fruit this time. Image scan first, bingo, ‘Double Cherry’ becomes ‘Single Cherry’.

So first line tells you that a Banana is worth 15 (divide 30 by 2)

Second line shows that Double Cherry is worth 10 (divide 20 by 2)

Third line shows that Apple is worth 4 (divide 8 by 2)

In the fourth and final line you already spotted that the middle image is Single Cherry, so you now know to divide Double Cherry by 2, so Single Cherry is therefore worth 5

Now convert line four into a ‘Basic Equation:

Banana + Single Cherry x Apple = ? Now reads as 15 + 5 x 4 = ?

15 + 5 x 4 = ?

No Parentheses, on 1st pass; no exponents on the 2nd pass; on 3rd pass there is only one multiplication so:

5 x 4 = 20

So now the equation becomes:

15 + 20 = 35

So just to add the cream to the fruity equation the correct answer is:

35