Question

Sam and Brett share £54 in the ratio of 5:4 how much does each person get

Answer 1

In short, we split 54 by (5+4) and give 5 pieces of that quotient to Sam and 4 pieces of it to Brett, 

$\bf \cfrac{Sam}{Brett}\qquad 5:4\qquad \cfrac{5}{4}\qquad \qquad \cfrac{5\cdot \frac{54}{5+4}}{4\cdot \frac{54}{5+4}}\implies \cfrac{5\cdot 6}{4\cdot 6}\implies \cfrac{30}{24}$