Welcome to Day 8
This topic may be tricky so give close attention to this one.
We again follow the base system - Not exactly, but depending on the base calculation will differ.
Consider base 10
Cube for 13
13 = (13 + 3 x 2)/(9 x 3)/3 x 3 x 3
= 19/27/27 (But since the base is 10 only one number will remain in each left hand side.
Therefore answer is = 19/29/7
= 21/9/7.
Steps involved
- First we double the excess number from the base 10 and add to the original number i.e. 13- 10 = 3. Then 3 x 2(double the excess) + 13 (original number) = 19
- Then we subtract 13 from base, get 3, which we multiply with 9 ( the excess number of the left hand side number minus the base i.e. 19 -10 ). So basically - excess from original number from 10 x excess from the left number which we got in step 1. We get 3 x 9 = 27.
- Then we take the cube of the unit digit of the original number.
- And doing the required calculation for the base 10, we get the answer 2197.
Cube for 15
15 = (15 + 5 x 2)/(15x5)/5 x 5 x 5
= 25/75/125
=25/87/5
=33/7/5
Steps involved
- First we double the excess number from the base 10 and add to the original number i.e. 15- 10 = 5. Then 5 x 2 + 15 (original number) = 25
- Then we subtract 15 from base, get 5, which we multiply with 15 ( the excess number of the left hand side number minus the base i.e. 25 -10.) So basically, 15 x 5 = 75.
- Then we take the cube of the unit digit of the original number.
- And doing the required calculation for the base 10, we get the answer 3375.
97 = (97 – 2 x 3)/(-3 x -9)/-3 x -3 x -3
= 91/27/-27
=91/26/73
Steps involved
- First we double the excess number from the base 100 and subtract to the original number i.e. 100 - 97 = -3. Then -3 x 2 -3 (original number) = -9
- Then we subtract 97 from base, get -3, which we multiply with -9 ( the excess number of the left hand side number minus the base i.e. 100 - 91.). So basically, -3 x -9 = 27.
- Then we take the cube of 100 – 97.
- And doing the required calculation for the base 100, we get the answer 912673.
In similar manner,
52 = (52 + 2 x 2)/(2 x 6)/08
= 56/12/08
= 14/06/08
104 = (100 + 3 x 4)/3 x 4 x 4/4 x 4 x 4 = 112/48/64
This may be a tough lesson and with the limitation it is not easy to explain this method only through text. But I am sure once you go through the above steps a few more time, then you will easily get the hang of this method. So good luck and make sure you practice.
I hope this lesson was fun and you enjoyed it as much as I enjoyed writing it down for you!
See you tomorrow.
Rahul Makhija
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Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
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