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The answer: 5-5×5+5

Math equations seem all the rage on social media (they were never that interesting at school) and almost all of the clickbait equations are only difficult if you aren’t conversant in the order of operations.

The order of operations is the mathematical convention used to determine how to calculate mathematical equations. There are various acronyms commonly used to help students understand the convention and they vary from country to country, but include PEDMAS, BEDMAS, BODMAS and BIDMAS. You can read more about it here.

Because of the order of operations, we are required to calculate an equation in the following order:

  1. Brackets (or parenthesis)
  2. Exponents (as in 2 squared ie 22)
  3. .Multiplication and division (from left to right)
  4. Addition and subtraction (from left to right)

The result? Let’s drill down this equation:

5 – 5 x 5 +5 (we calculate the multiplication before addition or subtraction)

= 5 – 25 + 5 (then from left right)

= -20 +5

= -15

That’s the right answer. Now go back to Facebook and show off how smart you are.

And by the way…reality check…around 30% get this right, not just 1%. Still, you can still show off about being in top 1/3 can’t you?

Why the Answer isn’t -25

Although the acronyms for BEDMAS etc can be helpful for students it is also often misleading with people mistakenly applying (multiplication and division) or (addition and subtraction) in an erroneous order of operation rather than applying them simultaneously.

The explanation is better described here by one Facebook commenter whose brains exceed the sum of all the people who write for bluemoonwalk.com (and we think we’re pretty smart BTW).

The order of operations is universal, not country-specific.

The error (applying addition before subtraction) is a common and understandable one and stems from a subtle misconception about notation.

Think of the operation of subtraction as the addition of a negative number, like so:

10 – 3 = 10 + -3 = 7 or 5 – 10 = 5 + -10 = -5

Now because addition is commutative, you can swap terms around and still get the same answer (ie. a+b = b+a).

We can try that on the above expression and we should get the same answer:

5 – 10 = 5 + -10 = -5 & 5 – 10 = -10 + 5 = -5

In the original question in the post, there is no 25+5 in the expression. It’s a negative 25.

What you should be calculating is -25 + 5.

This resolves the ambiguity.

To wit:

Left to right: 5 – 25 + 5 = -20 + 5 = -15 & Addition first, but taking into account the above (brackets included for clarity only): 5 – 25 + 5 = 5 + [ -25 + 5 ] = 5 + [-20] = -15

Or, applying commutativity:

5 – 25 + 5 = -25 + 5 + 5 = 5 + 5 – 25 = – 15