Math is never wrong. So… why does the same operation produce different results, depending on who you ask?
Various social media circulate mathematical operations They are variants of the same problem. It’s very easy to answer, but generates heated debates about the final result.
Take a look at this simple operation: 60 / 5(7-5), or what is the same, 60 / 5 * (7-5). What’s the score? For some it is 24, and for others, 6.
And there are math graduates on both sides. What’s going on? To solve this operation, You must apply the order of operationsthat is this:
As we can see, first what is inside the parentheses is solved, then the powers and roots, then the multiplication and division, and finally the additions and subtractions. And, this is important, always from left to right.
To remember this, in Anglo-Saxon countries they use a mnemonic rule, a word easy to remember formed by the initial of each rule:
Learning Mathematics (YouTube)
Learning Mathematics
as we see PEMDAS It is formed with P for parentheses, E for Exponent, M for Multiplication, etc. BODMAS and its variant BEDMAS are the same as PEMDASonly they use other synonymous words to define the same rules.
Applying PEMDAS, BODMAS, or the Spanish order, which is the samethe operation gives us the result of 24. First we solve the parentheses, and then we go from left to right:
60 / 5 * (7-5) 60 / 5 * (2) 12 * (2) 24
It is the result that almost all electronic calculators and calculation apps also obtain.
So, Why are there experts who say that the result is 6? As mathematician Presh Talwalkar explains in this video, there is an old rule from 1917 that still applies in some countries. This rule says that, First of all, you have to remove the parenthesis from the operation.
According to this, the fracture occurs when reaching this step:
60 / 5 * (7-5) 60 / 5 * (2)
According to PEMDAS, BODMAS, and the order that is used in Spain, the parenthesis is solved (although not eliminated), so since we are going from left to right, we first solve the division, and then the multiplication with the parentheses. That gives us 24.
But if we apply the old rule, First you have to remove the parentheses.so the operation 5 * (2) takes precedence
Therefore:
60 / 5 * (7-5) 60 / 5 * (2) 60 / 10 6
and the result is 6.
Who has the reason? UC Berkeley explains that both results are fine. The problem is that the operation is poorly formulated, it is ambiguous. When there is ambiguity, more parentheses must be added.
If you want the result to be 24you have to write: (60 / 5) * (7-5). And if you want sea 6so 60 / (5 * (7-5)). This way you always get the same result, whatever rule you use.
A mathematical operation can have different results, depending on the country where it is resolved. That’s because it’s ambiguous. The solution is to add parentheses to fix the order of operations, because the parenthesis always takes precedence for everyone.
