Let's denote the total number of apples Sara picked as \( x \).
From the problem, we know she discarded 110 apples, so the number of apples remaining after discarding is:
\[ x - 110 \]
Out of the remaining apples, 300 were made into cider. Therefore, the number of apples sold as fresh fruit is:
\[ (x - 110) - 300 = x - 410 \]
Now, to find the fraction of the total apples picked that were sold as fresh fruit, we need to express this quantity as a fraction of \( x \):
\[ \text{Fraction of apples sold as fresh fruit} = \frac{x - 410}{x} \]
To simplify this fraction, we can rewrite it as:
\[ 1 - \frac{410}{x} \]
Now, we need to determine \( x \). We know that \( x - 110 \) (remaining apples) had 300 apples made into cider, which means:
\[ x - 110 \geq 300 \]
This implies:
\[ x \geq 410 \]
If \( x = 410 \), then all apples except the ones discarded would be made into cider, leaving no apples to be sold as fresh fruit.
Assuming \( x > 410 \), \( x - 410 \) will be positive and hence we can conclude there are fresh apples sold.
Now substituting values greater than \( 410 \) for \( x \):
If we take \( x = 500 \) as an example, then:
\[ x - 410 = 500 - 410 = 90 \]
So the fraction of total apples sold as fresh fruit becomes:
\[ \frac{90}{500} = \frac{9}{50} \]
Thus, the fraction of the total apples picked that were sold as fresh fruit is:
\[ \frac{x - 410}{x} \]
If we express this in terms of fractions, we find that the result will always depend on the specific total picked greater than 410. For any specific value of \( x > 410 \), you can determine the fraction.
However, to find a precise numerical answer, we need more information about the total picked. Assuming an arbitrary value, we find the fraction, otherwise, we can summarize that the fraction of fresh sold is:
\[ \frac{x - 410}{x} \]
This is the required answer for any value of \( x \) greater than 410.