Tips for quick division (rules, simplifications etc.)

Case Calculations Division
New answer on Jul 08, 2020
3 Answers
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Anonymous A asked on Oct 12, 2018

Dear community,

which techniques or recommednations do you have in order to quickly calculate e.g. 16.000/17.500 or 222/233 up to two decimals (=0,XX)?

Thank you very much in advance!

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Anton
Expert
replied on Jul 08, 2020
FREE 1st session in November | From Lawyer to MBB | Top in FIT | 10x your structuring skills | Message to get Free Prep Checklist

Hi,

I would be happy to share few insights on how to better tackle quick maths BUT you should take into account that it should be your last priority in preparation. MBB focuses on accurate calculations and interpretation of graphs vs speed of calculations.

So let's get on to the practice:

  • The "9-trick"

To add 9 to any number, first add 10, and then subtract 1. For example, we change the addition 9 + 4 to 10 + 3, which is much easier to solve. But this "trick" expands. Can you think of an easy way to add 73 + 99? Change it to 72 + 100. How about 485 + 999? How would you add 39 + 27 in your head? Let 39 become 40… which reduces 27 to 26. The addition is now 40 + 26.

  • Doubles + 1

Memorize the doubles from 1 + 1 through 9 + 9. After that, a whole lot of other addition facts are at their fingertips: the ones we can term "doubles plus one more". For example, 5 + 6 is just one more than 5 + 5, or 9 + 8 is just one more than 8 + 8.

  • Use addition facts when adding bigger numbers

Once you know that 7 + 8 = 15, then you will also be able to do all these additions in your head:

70 + 80 is 15 tens, or 150

700 + 800 is 15 hundreds, or 1500

  • Subtract by adding

​This is a very important principle, based on the connection between addition and subtraction. You really don't need to memorize subtraction facts as such, if you can use this principle. For example, to find 9 − 6, think, "6 plus what number makes 9?" In other words, think of the missing number addition 6 + ___ = 9. The answer to that is also the answer to 8 − 6.

This principle comes in especially handy with subtractions such as 13 − 7, 17 − 8, 16 − 9, and other basic subtraction facts where the minuend is between 10 and 20. But you can also use it in multitudes of other situations. For example, 63 − 52 is easier to solve by thinking of addition: 52 + 11 makes 63, so the answer to 63 − 52 is 11.

  • Five times a number

To find 5 times any number, first multiply that number times ten, then take half of that. For example, 5 × 48 can be found by multiplying 10 × 48 = 480, and taking half of the result, which gives us 240.

  • Four and eight times a number

If you can double numbers, you already have this down pat! To find four times a number, double that number twice. For example, what is 4 × 59? First find double 59, which is 118. Then double that, and you get 236.

Similarly, eight times a number just means doubling three times. As an example, to find 8 × 35 means doubling 35 to get 70, doubling 70 to get 140, and (once more) doubling 140 to get 280. However, personally I would transform 8 × 35 into 4 × 70 (you double one factor and halve the other), which is easy to solve to be 280.

  • Multiply in parts

This strategy is very simple, and in fact it is the foundation for the standard multiplication algorithm. You can find 3 × 74 mentally by multiplying 3 × 70 and 3 × 4, and adding the results. We get 210 + 12 = 222. Another example: 6 × 218 is 6 × 200 and 6 × 10 and 6 × 8, which is 1200 + 60 + 48 = 1308.

Hope this helps,

Anton

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Vlad
Expert
Content Creator
replied on Oct 12, 2018
McKinsey / Accenture Alum / Got all BIG3 offers / Harvard Business School

Hi,

In that case, if you need a precise answer, I believe you should just do the division on paper. They only thing you could do is playing with the zeros (e.g. 1600/175) and then move it back.

Best

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Anonymous replied on Jul 08, 2020

Dear Chris,

Remember here about estimating and adjusting.

For example: 96,840/529

Step 1: Estimating

We will have a simplified version of: 96.84/52.9, taking out 3 zeros in the numerator and 1 zero in the denominator which means that we will return 2 zeros in the last step.

Technically we need a step of “rounding” here. But in this case, we can just skip it and make an overall adjustment later.

Now turn division into multiplication and find x:

52.9 x ? = ~96.8

We know 53 x 2 = 106

Thus, ? is a little bit lower than 2.

Step 2: Adjusting

With a downward adjustment for 2, we have 1.8. And with zeros, it is 180.

The correct answer is 183.06

Hope it helps,

Best,

André

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Anton

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