we are given
A small company’s net income for the first six months of the year was $76,500
Let's assume net income for first six month as X
so,

and we have
A small company’s net income for the last six months of the year was $100,000
Let's assume net income for last six month as Y
so, we get

now, we have to find the ratio of the first six months of the year to the last six months of the year in simplest form
so, we need to find

we can plug values of X and Y

We can cancel last two zeros

we can factor top term


now, we can cancel 5

It can not be simplified further
so,
.............Answer