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A math teacher says,
"Ann has four apples and John has three apples. How many apples do they have together? Who can solve this sum/problem/task?"
Can you please tell me which word the teacher would use here?


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Problem or sum.
In the beginning there was nothing, which exploded.


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Problem and task work for me. But, you can also just say: "Who can solve this?"


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Thank you very much. And what about the following? Can a teacher also call it a problem, a sum and a task?
A swimming pool has 2 inlet pipes. One fills the pool in 4 hours, the other in 6 hours. The outlet pipe empties the pool in 5 hours. Once the outlet pipe was left open when the pool was being filled. In how many hours was the pool full?


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I would call that a problem, it has more that needs to be solved to get the answer than a sum.
I lack the imagination for a witty signature.


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Thanks a lot, Sarriesfan.
I'm sure that '2+2=' is a sum. Do you call '42=' a sum, too? If so, it sounds strange, doesn't it?
And what do you call '5*5=' and '25:5='?


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Those are a subtraction, a multiplication and a division Helenej.


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Yes, but 'sums' is another word for arithmentic for younger agegroups  all four processes are 'sums'.  adding up, taking away, multiplying and dividing. You don't learn 'sum' as addition until much later in much more advanced maths, where you differentiate between the technical terms a sum (addition) and a product (multiplication). So, the language is set by its use in early childhood. "42" is a sum. As is 245/12. Or three squared. In ordinary language, 'summing up' and summarising are more to do with simplifying, bringing out the main points. Although it is 'bringing things together' there is no clash with the mathematical meaning, where a sum is any use of arithmetic. A problem is when you have to work out which sums you need to do, in order to solve it. And a task is something you have to do. " Solving the problem" is a task. Like "cleaning the floor" is a task. Doing a sum is a very simple task, hardly worth the label. But the problem is not the task.


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Thar 
I remain in awe of your ability to explain so clearly and succinctly. That would probably have had me drivelling on for most of the page!


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It must be another British/American thing, because when I was in school, a sum was always addition. I'm not sure how they teach it today. I'll have to ask the grandchildren...
And "doing sums" would have made one sound uneducated in my experience. We did addition/subtraction/multiplication/division problems, or exercises in the early grades.
A great many people will think they are thinking when they are merely rearranging their prejudices. ~ William James ~


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That's interesting  whereas if we're asked to provide 'the sum of' the square of the other two sides, we know those two sums must first deal with finding the square of each side, and then doing a sum to find the sum of those two individual sums; which process is summed up in Pythagorus's Theory. Simple, really.


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Romany wrote:That's interesting  whereas if we're asked to provide 'the sum of' the square of the other two sides, we know those two sums must first deal with finding the square of each side, and then doing a sum to find the sum of those two individual sums; which process is summed up in Pythagorus's Theory. Simple, really. ..Welll, I waren't never too gud at cipherin'...
A great many people will think they are thinking when they are merely rearranging their prejudices. ~ William James ~


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Well, I were purty good at 'rithmetic back in my skool daze, but I doesn't remember ever hearin' 'bout no "sums" 'cept when we was doin' addition.


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Romany wrote:Thar I remain in awe of your ability to explain so clearly and succinctly. That would probably have had me drivelling on for most of the page! I agree  that was a great explanation of how I understand it. In early school (say from four years old to seven) the subject is "sums", not "ciphering" or "mathematics". It really includes only the four simple actions, simple fractions  that's about it. Usually, tests consist only of 'sums' (" 73 x 54 =?"; " 27 + 984  63 = ?") Then one starts on maths  decimals, powers, roots  and algebra. Tests at this level may be pure theory ( If a+b=27 and ab=14, what are 'a' and 'b'?) or they may be problems (like your 'swimming pool' one). At about eleven, we started on logarithms, followed shortly by the calculus. A 'problem' includes working out which sums you need to do, then doing them. Noone ever called any of them 'tasks'. Wyrd bið ful aræd  bull!


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Romany wrote: me drivelling on for most of the page!
Yes. Drivelling & kibitzing


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