Is there an easy way to calculate this example in your head?

Question

Mathematics

Example:
k = 1 / (1.06 - 1 / x), where x is any decimal number from 1.01 to 15.00, find k.
It is necessary to perform these calculations in the mind and very quickly, is there a way other than remembering all the results?

Answer 1

It can be simplified even more. This is essentially 1/x, shifted by 1 to the right and up:
The task is reduced to a quick determination of the reciprocal of the number. To two decimal places, divide 100 by x to whole integers, and move the decimal point to the left by two decimal places:
For example, forx = 1.14

I would think so

x - 1 = 0.14
1 / 0.14 = 100 / 14 = 50 / 7
с точностью до 2 знаков считаем целые в 5000 / 7
50 / 7 ≈ 7
... 700               (сотни)
... + 10 / 7 = 710  (десятки)
... + 30 / 7 = 714  (единицы)
итого 7.14
+1 = 8.14
Ответ: 8.14