i) Find the number of sheep if he has 180 cows.
ii) Find the ratio of the number of sheep to the total number of cows the farmer has?
iii) Find the ratio of the number of sheep to the total number of animals.

Explanation

According to the question
The ratio of the sheep and cows is 8\;:\;3 or \large\frac{8}{3}
i) If the number of cows is 180
Then the number of sheep is =\large\frac{8}{3}\normalsize\times180
\rightarrow 480.
So that the farmer has 480 sheep.

ii) To find the ratio of the number of sheep to the total number of cows the farmer has:
\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\large\frac{Number\ of\ sheep}{Total\ number\ of\ cows}
\rightarrow\large\frac{480}{180}
\rightarrow\large\frac{8}{3}
\therefore The ratio of the number of sheep to the total number of cows is 8\;:\;3

iii) Total number of animals with the farmer =(Number of sheep + Number of cows).
\rightarrow\left(480+180\right)=660
To find the ratio of the number of sheep to the total number of animals:
\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\large\frac{Number\ of\ sheep}{Total\ number\ of\ animals}
\rightarrow\large\frac{480}{660}
\rightarrow\large\frac{8}{11}
So, the ratio of the number of sheep to the total number of animals with the farmer is 8\;:\;11

Ans: i) The farmer has 480 sheep.
ii) The ratio of the number of sheep to the total number of cows is 8:3
iii) The ratio of the number of sheep to the total number of animals 8\;:\;11