in a school 1620 pupils the ratio of boys to girls is 4:5. what is the nunber of girls in the school??????????

I quite like to do these without algebra - I'll see if I can demonstrate my method.

the black numbers are the ones you have been given.

the ratio of boys to girls is 4:5 so in total there is some multiple of 9 students altogether.

Next you have to say

$$\begin{tabular}{|c|c|c|}\hline boys & girls & Total\\\hline 4&5&\textcolor[rgb]{1,0,0}{4+5=9} \\\hline & &1620\\\hline \end{tabular}$$

$$\\\textcolor[rgb]{1,0,0}{1620\div 9 = 180} \quad $180 is the multiplication factor$\\ so\\ $number of boys is $4\times 180 = 720 \quad $Put that in the box under the 4$\\ and\\ $number of girls is $5\times 180 = 900 \quad $Put that in the box under the 5$\\\\ $Total number of $ \textcolor[rgb]{0,0,1}{ \;purple\;penguins\;} $ is $ 720+900=1620 $ that checks out very nicely. $ \\\\ $The purple penguins is an insider joke - don't worry if you don't get it - you can google it if you want, then you will know what I am talking about.$$ $

If the ratio of boys to girls is 4:5, then the ratio of girls to boys is 1:5, which is 1/5.

1/5 of 1620  =  (1/5) x 1620  =  324 

If the ratio is 4:5, then 4/9 are boys and 5/9 are girls.

Then....5/9 x 1620 = 900 girls

And 4/9 x 1620 = 720 boys