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For this week’s Friday Funny we are going to see how people interpret the Order of Operations rules that they should have been taught at school. Most people know a mnemonic to help remember the basic rules, the actual mnemonic depends on whether you say Brackets or Parentheses, whether you say Indices, Exponents or Orders, and whether you put Multiplication or Division next.
Regardless of which terminology and mnemonic you use, they do not cover all situations as the following example demonstrates:
So here is the equation for you to solve:
Below is a poll for you to record your answer (please answer the poll before reading on):
Disclaimer: The following points are written in my own words, but seem to be ignored by many who learnt the mnemonic without understanding the underlying principles.
Now, that you have answered, here are some points to consider with the Order of Operations (Precedence) rules:
But here some other points that are less well known:
If you correctly follow these guidelines, there is only ever one answer to the equation above.
That said, the equation above has been written to be deliberately ambiguous and confusing on purpose, which is why people disagree on the answer.
Here is the original question:
We can use / instead of ÷ as this is easier on a computer keyboard:
This also helps separate the numerator from the denominator when expressed as a fraction:
The operand 2 (5 – 2) can be expanded during the calculations (if desired), the result is the same:
Adding an explicit multiplication operator changes the order of operations for this equation:
Adding extra brackets/parentheses can change the order of operations for this equation:
Both Google, Bing and WolframAlpha added extra brackets/parentheses which split the implicit multiplication and changed the answer to 18. They calculated:
To force Google, Bing and WolframAlpha to not split the operand we would need to add brackets/parentheses to keep the components of the implicit multiplication together.
So according to the search engines I am wrong, but I firmly believe that the “bond” for implicit multiplication is stronger than explicit multiplication and division and that if adding the brackets/parentheses to “educate” the search engines is required, then so be it.
This might also come down to your age and when you learnt your maths. It seems people who learnt more recently do not differentiate between an implied multiplication and an explicit multiplication.
The best solution to this problem is not to write ambiguous equations and to add brackets/parentheses where required to avoid any possible confusion.
While we are discussing the topic of Order of Operations, which mnemonic did you learn at school? This probably depends on which country you lived in when you went to school. I know, for example, that my British background means I say Brackets, not Parentheses and Maths not Math.
Thanks for your involvement in this ad-hoc research into basic mathematics skills.
This article was originally posted on http://www.winthropdc.com/blog.
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