In the Idol contest, $\frac{7}{9}$ of the school's population decided to vote. There were 3 contestants and the votes for these contestants were divided in the ratio of $\frac{1}{3}:\frac{5}{6}:0.5$. Given that the school's population has 1440 students, calculate the number of students who voted for the contestant with the most votes. Answer ... students

1. Calculate the number of students who voted.

Number of voters
$=\frac{7}{9}\times 1440=1120$

2. Find the largest share of the votes using the ratio.

The ratio is
$\frac13:\frac56:0.5=\frac13:\frac56:\frac12$
Multiplying all parts by $6$,
$2:5:3$
The contestant with the most votes has $5$ parts out of $2+5+3=10$ parts.
$\frac{5}{10}\times 1120=560$