Ratios are a way of splitting something up into portions. For example you could split up a bag of 20 sweets and give your friend 5, your parents 5 each and yourself 5 (the rest).
We can convert ratios to fractions by dividing each ratio “part” by the total number of parts. For example if we had a ratio 5 : 2 we can convert these to fractions:
$$ \dfrac{5}{\color{red}{(5 + 2)}} : \dfrac{2}{\color{red}{(5 + 2)}} $$
We can use this when distributing something amongst the ratio. For example let’s share $416 in the ratio 5:3. :
$$ \dfrac{5}{\color{red}{(5 + 3)}} : \dfrac{3}{\color{red}{(5 + 3)}} $$ $$ \dfrac{5}{8} \times \$ 416 = \$ 260 $$ $$ \dfrac{3}{8} \times \$ 416 = \$ 156 $$ $$ \$ 156 + \$ 260 = \$ 416 $$
A useful thing to do with fractions is to make a certain part 1. This is known as reduction to its simplest form. For example let’s try doing this with the ratio 4:3:7. :
$$ \dfrac{4}{\color{red}{4}} : \dfrac{3}{\color{red}{4}} : \dfrac{7}{\color{red}{4}} = 1 : \dfrac{3}{4} : \dfrac{7}{4} $$
$$ \dfrac{4}{\color{red}{3}} : \dfrac{3}{\color{red}{3}} : \dfrac{7}{\color{red}{3}} = \dfrac{4}{3} : 1 : \dfrac{7}{3} $$
$$ \dfrac{4}{\color{red}{7}} : \dfrac{3}{\color{red}{7}} : \dfrac{7}{\color{red}{7}} = \dfrac{4}{7} : \dfrac{3}{7} : 1 $$