I know some places use BIDMAS as well. Overall though, to someone who knows little about mathematics, why is this the correct order? What’s the exact logic behind it
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PEMDAS and BIDMAS (and BODMAS and PEDMAS) are all the same – just using different letters/words to describe the same order of operations.
It’s not the only system, but it is one that allows for a fairly efficient way to convey the order of operations to get the correct answer that’s also fairly intuitive for many people.
Without having an order of operations, you would need to have parentheses everywhere, because all the basic arithmetic operations are only defined on two things at a time. Further, two different orders of doing the operations usually yields different results, so it does matter.
But why the particular order that we picked? The glib answer is “because people agreed.” A more insightful answer is that the more complicated operations happen sooner. Multiplication is repeated addition, so more complicated than addition, and happens sooner. Exponentiation is repeated multiplication, so more complicated than multiplication, and happens sooner. This makes the order of operations consistent, and does a good job of eliminating the need for many uses of parentheses.
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There doesn’t need to be any logic behind it, and there’s nothing that makes it the “correct” order.
The only thing that matters is that *we all use the same order*. The order could be absolutely anything; it doesn’t matter. As long as everyone is using the same order, then everyone will come to the same answer for the same question.
PEMDAS and BIDMAS (and BODMAS and PEDMAS) are all the same – just using different letters/words to describe the same order of operations.
It’s not the only system, but it is one that allows for a fairly efficient way to convey the order of operations to get the correct answer that’s also fairly intuitive for many people.
It is not the correct order, it is the agreed upon order.
If we did not have an agreed upon order, math problems would all have to have some sort of key with them, kind of like a map. In other words you take a test, and on the test you have the order of operations to use for all your problems.
It’s kind of like the qwerty keyboard we type on. If you had a different layout on every keyboard you used, it would be really difficult to write. Similar for PEMDAS just on a smaller scale.
There doesn’t need to be any logic behind it, and there’s nothing that makes it the “correct” order.
The only thing that matters is that *we all use the same order*. The order could be absolutely anything; it doesn’t matter. As long as everyone is using the same order, then everyone will come to the same answer for the same question.
It is a convention that, if followed, mathematical expressions can be written in a certain way without ambiguity. There could well be other conventions but this would require the expressions to be written differently. It just happens that for most mathematics, the agreed upon convention is PEMDAS or BODMAS (just different names for the same thing).
We follow conventions all the time especially in languages. They’re mostly the product of some logic and some tradition and, as long as they’re agreed upon, they make life simpler.
One could try to speak like Yoda, “the egg, red is” and more or less be comprehensible but, for most, the conventional “the egg is red” sounds more natural and more easily comprehended.
Mathematics is somewhat more precise and unforgiving because expressions can get fairly long. So without a convention, they add to errors and ambiguities.
So if someone writes 3 * x + 5, the convention is that multiply x by three then add 5. If we reversed the priority 3 * x + 5 becomes add five to x then multiply the sum by 3. Both conventions are workable if used consistently but if the order is interchangeable arbitrarily, math would be more confusing.
Without having an order of operations, you would need to have parentheses everywhere, because all the basic arithmetic operations are only defined on two things at a time. Further, two different orders of doing the operations usually yields different results, so it does matter.
But why the particular order that we picked? The glib answer is “because people agreed.” A more insightful answer is that the more complicated operations happen sooner. Multiplication is repeated addition, so more complicated than addition, and happens sooner. Exponentiation is repeated multiplication, so more complicated than multiplication, and happens sooner. This makes the order of operations consistent, and does a good job of eliminating the need for many uses of parentheses.
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