# Maths on the Back of an Envelope

By Rob Eastaway (2019)

## My Notes

```
A * 5 = A / 2 * 10
E.g., 240 * 5 = 120 * 10
A% of B = A * B / 100
E.g., 30% of 50 = 30 * 50 / 100 = 15
A% of B = B% of A
E.g., 30% of 50 = 50% of 30 = 15
```

If 10% doesn’t get you quickly to your answer, try using 1% instead, and multiply up from there.

Whatever the growth rate (be that 1.2%, 4%, 10% or even 30%), the time it will take for the quantity in question to double can be found by dividing it into 72. With an interest rate of 4%, your money in the bank will double in 72 ÷ 4 = 13 years.

The coincidence is that the Golden Ratio is very close to 1.609, which is the ratio of miles to kilometres. So if you want to convert 13 miles to kilometres, then, just by glancing at the Fibonacci sequence, you can estimate that the answer is going to be about 21 km, and you’ll be correct to within 1%.