Tips for quick division (rules, simplifications etc.)

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