Final answer:
The ratio 5 : 1 7/9, when expressed as a fraction, is 80/9. This is found by converting 1 7/9 to an improper fraction 16/9 and then setting up a proportion with the ratio 5 being represented as 5/1.
Step-by-step explanation:
The question asks to convert the mixed number 1 7/9 and the ratio 5 to a single fraction in its simplest form.
To start, we convert the mixed number to an improper fraction.
As 1 7/9 can be rewritten as 1 + 7/9, it is equivalent to (9/9) + (7/9), which gives us 16/9.
Next, we interpret the ratio 5 as a fraction, giving us 5/1.
Now, to express the ratio 5 : 1 7/9 as a fraction, we set up the proportion 5/1 = x/(16/9).
To find the value of x, we cross multiply, giving us x = (5/1) * (16/9), which simplifies to 80/9.
Therefore, 5 : 1 7/9 as a fraction is 80/9 which is already in its simplest form.