Could you explain ratios to me?

Imagine there's a cake, and you wanted to share that cake evenly between three people. You would cut the cake into three pieces and each person would get a piece. Now, imagine you had another cake and still three people, but not everyone wanted the same amount of cake: Jake wants 1 piece, Tommy wants 2, and Sam wants 3. Since they want 1, 2 and 3 pieces, you could say that the ratio here is 1:2:3, and that in total there are 6 pieces. What you would do here is cut the cake into 6 pieces. That way you can give Jake 1 piece, Tommy 2 pieces and Sam 3 pieces. But keep in mind that 'ratios' are the same thing as 'proportions', and what you're actually doing is sharing a particular thing amongst groups in different amounts. Another example would be: you have 10 litres of water, which is to be shared between John and Peter in the ratio 1:3, respectively. Doing the same as before, add the proportions for each person together - which will equal 4. So now, for each 4 parts, John would get 1 and Peter would get 3. How many '4 parts' are there in 10 litres? 10 ÷ 4 = 2.5 Another meaning of this is: each 'part' is equal to 2.5 litres. So if John wants 1 part, he would get 2.5 x 1 = 2.5 litres, and since Peter wants 3 parts, he would get 2.5 x 3 = 7.5 litres.