Efficient ways of doing division calculations?

maths maths project skills
Recent activity on Dec 08, 2018
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Anonymous A asked on Dec 06, 2018

There seems to be a number of methods for doing addition / subtraction / multiplication / percentage calculations more efficiently, whether that's mentally or on paper.

Are there any such methods for making division calculations more efficient? I can't seem to find any on YouTube or in PrepLounge.

I'm pretty accurate and speedy with the rest of the math requirements, but would like to brush up my division skills.

Any advice much appreciated.

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Anonymous replied on Dec 08, 2018

Hey there,

A method I use a lot which works for generally more simple calculations: breaking down divisions into simpler parts. The key principle here is that it's easier to divide by small numbers - 2, 3, 5, 10.

The easiest is when the number you are dividing by is a square of two (4, 8, 16 ,32, etc.)

520 / 8 = 520 / (2 x 2 x 2) - so now, you just divide by 2 three times! 520, 260, 130

You can also do the same with dividing by 3.

380 / 6 = 380 / (2*3) = 190/3. Now to figure this out, find the closest multiple of three basically throuhg quick trial and error in your head. In this case, it's 180 = 3*60. if 180/3=60, then 190/3 is 60+(10/3), or 63.33

Finally, a tip to divide by 5: I always think of dividing by 5 as dividing by 10, multiplying by 2 (because 5=10/2). So for example:

740 / 5 = 740/(10)*2 = 74*2 =148.

This last trick with 50s of course also works with 50, 500, etc.

Hope this helps!

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Vlad
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replied on Dec 06, 2018
McKinsey / Accenture Alum / Got all BIG3 offers / Harvard Business School

Hi,

The best thing - learn the division table up to 1/11 (i.e. 5/6 = 83.3%). It will help you calculate any percentage problems.

E.g. if your revenue is 530k and the market is 6.2.M, the market share is close to 5/6 and you can adjust depending on the numerator / denominator / zeros

Best

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Guennael
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replied on Dec 08, 2018
Ex-MBB, Experienced Hire; I will teach you not only the how, but also the why of case interviews

Some good advice already. Ultimately though, the answer is simple: practice, practice, practice. Use a software-based tool, or just do pages of divisions on paper. There is no secret, hard work is the key.

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Alexander updated an answer on Dec 07, 2018

Division is something I'm currently working on myself. In my experience, it is often fastest to guess a seed value, check by multiplying it with the divisor and then correct your results accordingly. The better your seed value, the less you'll have to adjust and the faster you'll get to the result. I've found that knowing multiplication tables can help a ton with getting a good seed value, so I'd recommend learning those to speed up your calculation.

Take, for example, 864/32. You can approximate this as 900/30, which you know from multiplication tables as 30 (well - 3x3=9, but that's the same thing). You then check: 32x30 is 960, so you're over and your result needs to be under 30. Since you're 100 too high (960 vs 864) and your divisor is 32, you can estimate quickly that you need to remove 3 and 27 is, indeed, the answer. I'd recommend doing a check to make sure that this is indeed the answer - typically, multiplying only the last digits is precise enough and quite fast.

Another way to approach this would be to simplify the equation using a partial prime factorization. Let's use 864/32 again - both numbers are divisible by 2, which you can use to simplify to 432/16. Doing this again yields 216/8, and again to 108/4. At this point, you can probably figure it out - subtract 80, which is 20*4, and then calculate the remainder, 28/4 = 7, to come up with 27. This simplification approach works really well in this case and with even numbers in general. If you look up divisibility rules (long Wikipedia article), you'll find some other numbers you can easily divide out to simplify your equation.

That's it - two different approaches. The one with the seed value is helpful in all cases, the other one can be faster if the numbers are convenient. Practice helps a ton when deciding which one to take (as it does with most mental math...). Hope this helps!

(edited)

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