Calculating an ownership share

Imagine that you have a garden shared with the whole block of flats. The garden is 600 m² in total and your share of the garden is 17/150. How many square metres do you actually own? How would we work that out?

Actually, the unitary method is all we need. The number 17/150 tells us that if we divided the garden into 150 equal parts, we would own 17 of those parts. So first we work out how big one such part would be. Our garden is 600 m², and if we divide it into 150 equal parts, we just divide 600 m² by one hundred and fifty and each part will have an area of

$$\frac{600{\text{m}}^2}{150}=4{\text{m}}^2$$

If our share is 17/150, we own 17 of these four-square-metre parts, so we own

$$17\cdot 4{\text{m}}^2=68{\text{m}}^2$$

So out of the whole garden we own an undivided share of 68 m².

Work out your ownership share

The other way round: how to work out a share from square metres?

Let’s imagine that the whole building is, say, 800 m² and we own a flat in it that is 60 m². How big a share of the building do we own? The simplest thing is to write that our ownership share is 60/800, because if we divide the whole building into 800 parts, each with an area of one square metre, we would own exactly 60 of those parts.

Usually, though, we don’t write an ownership share like this, and instead we try to simplify the ratio. We do that by writing the share as a fraction:

$$\frac{60}{800}$$

and reducing the fraction to its simplest form. We do that by finding a number that divides both the numerator and the denominator of the fraction without a remainder. For example, 10 divides both 60 and 800 without a remainder. We divide both the numerator and the denominator by this number, and we get the fraction:

$$\frac{6}{80}$$

Another number that divides both the numerator and the denominator without a remainder is two. So we divide both the numerator and the denominator by two:

$$\frac{3}{40}$$

No other number divides 3 and 40 without a remainder. That means we have got a fraction in its simplest form. So our share of the building is 3/40. We can check it by dividing the whole building of 800 m² back into 40 parts – each part will have an area of 20 m². We should own three of these parts, which matches, because 3 · 20 m² is 60 m², which is the size of our flat.