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# Why is mental division so hard? watch

1. I consider myself to be pretty good at mental arithmetic, addition, subtraction and multiplication. I can do most normal problems double checked in my head in a few seconds (23*146 for example).

However division is completely difficult, I can by all means do it but not for large numbers, with such I have to approximate and do trial and error in my head until I get near the number.
Is this normal for division to be a much slower process? Or are there ways I can speed up?

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2. Bump

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3. It depends on your thought process; it's likely to be more difficult since you use multiplication far more often IRL and the process is completely different to division.
4. (Original post by Luneth)
It depends on your thought process; it's likely to be more difficult since you use multiplication far more often IRL and the process is completely different to division.
Yes, but division is different.
For example 169/13, (unless you know the answer by rote) in your head you have to trial and error with 10, 12, 13 until you get 13.

With division you are finding an unknown variable IN a calculation rather than the end product.

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5. If you're trying to do division problems as difficult as 23*146 then you're doing pretty well for yourself.

Maybe you're setting your standards too high and/or you need more practice.
6. (Original post by SeanFM)
If you're trying to do division problems as difficult as 23*146 then you're doing pretty well for yourself.

Maybe you're setting your standards too high and/or you need more practice.
23*146 is multiplication, I can do that given a minute or so (3358).

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7. (Original post by SeanFM)
If you're trying to do division problems as difficult as 23*146 then you're doing pretty well for yourself.

Maybe you're setting your standards too high and/or you need more practice.
lol
8. (Original post by icantfeelmyface)
23*146 is multiplication, I can do that given a minute or so (3358).

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I'm just using 23*146 as an example of a difficult problem (it may seem easy to you though!). If you're trying division problems of a similar difficulty for division then it'll be pretty tough.

And thinking about it, division is probably the most difficult operation out of addition/subtraction/multiplication anyway. Don't be too hard on yourself
9. (Original post by Shadez)
lol
Poor wording but that is what I meant. See post above.
10. (Original post by icantfeelmyface)
Yes, but division is different.
For example 169/13, (unless you know the answer by rote) in your head you have to trial and error with 10, 12, 13 until you get 13.

With division you are finding an unknown variable IN a calculation rather than the end product.

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The reason is that you need to know your tables. So basic division is easy but do you know your 13 times table.

Your estimate and try is the best solution but you can use maths knowledge to help. For instance 169 end in a 9 and so can never be divided by 10 (would end in 0( or 12(would be and even number). Numbers ending in 9 are often prime numbers ie 19, so which numbers aren't and what are there factors. 9 (factors 1,3,9) and 49 (factors 1,7,49) so which numbers in yours estimated range end in 3 or 7. So 2 numbers to try 13 or 17.
Numbers follow patterns so use them to help you.
11. (Original post by m2igm)
The reason is that you need to know your tables. So basic division is easy but do you know your 13 times table.

Your estimate and try is the best solution but you can use maths knowledge to help. For instance 169 end in a 9 and so can never be divided by 10 (would end in 0( or 12(would be and even number). Numbers ending in 9 are often prime numbers ie 19, so which numbers aren't and what are there factors. 9 (factors 1,3,9) and 49 (factors 1,7,49) so which numbers in yours estimated range end in 3 or 7. So 2 numbers to try 13 or 17.
Numbers follow patterns so use them to help you.
I don't "know" tables. When I was young, I learned them up to 12, but now I don't use tables as such. For example 12*13=156, I just do that in my head in a second, so I don't learn tables like that any more.

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12. (Original post by icantfeelmyface)
Yes, but division is different.
For example 169/13, (unless you know the answer by rote) in your head you have to trial and error with 10, 12, 13 until you get 13.

With division you are finding an unknown variable IN a calculation rather than the end product.

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First times by a power of 10 to see what the largest number you can make that is less than or equal to 169 is, then subtract and divide by the smaller number, which is wayyyy easier than trying to divide by the big original number.

Step 1
In this case it's 10. Now do 10 * 13 = 130.

169 - 130 = 39

Step 2
Then there are clearly three 13's in 39, so the answer is 10+3 = 13.

Hope that made sense!
13. Symbols such as 'divide', 'multiply' etc are made up by mathematicians to describe a variety of ideas.

Sometimes they specify an operation for which there is a good algorithm, such as in the case of x, +. Other times they simply mean the reversal of a well known operation, such as division and multiplication, or integration and differentiation. In general, reversing a process can be much harder than doing it forwards.

In the case of division, there are a variety of good algorithms, of which 'guided trial and error' is one. However, there is no reason for this to be the case with all mathematical processes. For example, there is no algorithm for integration - it's simply a case of recognising whether the expression belongs to a particular 'type'.

In short, the fact that an equation can be easily specified doesn't mean it can be easily solved. Division is well studied, but to be honest I'm not sure what the optimal algorithm is - maybe there's a better one than the one you used.

Edit: Keyhofi just gave an example of a different algorithm

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