Answer key for adding fractions worksheet, featuring 18 problems with solutions and a question about identifying the largest fraction sum.

To find the largest fraction sum, we need to compare the final answers (the sums) from all 18 problems.

Here are the final sums for each problem:
1) $5/6$
2) $7/12$
3) $7/15$
4) $7/8$
5) $9/14$
6) $9/16$
7) $17/20$
8) $5/18$
9) $5/16$
10) $13/18$
11) $13/25$
12) $17/21$
13) $13/30$
14) $23/36$
15) $27/28$
16) $32/35$
17) $18/25$
18) $23/24$

Step 1: Eliminate fractions less than 1/2
Many of these fractions are quite small (less than half). We can quickly remove them because the largest sum will definitely be bigger than half.
- Removed: $7/15$, $9/16$, $5/18$, $5/16$, $13/30$.

Step 2: Compare the remaining large fractions
Let's look at the biggest contenders. A good trick is to see how close they are to the number 1. The closer the numerator is to the denominator, the larger the fraction.

* Problem 15: $\frac{27}{28}$
This is only $\frac{1}{28}$ away from 1. Since 28 is a fairly large number, $\frac{1}{28}$ is a very tiny piece. This means $\frac{27}{28}$ is extremely close to 1.

* Problem 16: $\frac{32}{35}$
This is $\frac{3}{35}$ away from 1. Let's compare the "missing pieces":
Is $\frac{1}{28}$ smaller or larger than $\frac{3}{35}$?
If we make the denominators the same (using 140):
$\frac{1}{28} = \frac{5}{140}$
$\frac{3}{35} = \frac{12}{140}$
Since $\frac{5}{140}$ is smaller than $\frac{12}{140}$, Problem 15 is missing a smaller piece. Therefore, $\frac{27}{28}$ is larger than $\frac{32}{35}$.

* Problem 18: $\frac{23}{24}$
This is $\frac{1}{24}$ away from 1.
Compare $\frac{27}{28}$ and $\frac{23}{24}$.
$\frac{27}{28}$ is missing $\frac{1}{28}$.
$\frac{23}{24}$ is missing $\frac{1}{24}$.
Because 28 is bigger than 24, the slice $\frac{1}{28}$ is smaller than $\frac{1}{24}$.
Therefore, $\frac{27}{28}$ is larger than $\frac{23}{24}$.

* Problem 7: $\frac{17}{20}$
Convert to decimals to check: $17 \div 20 = 0.85$.
$\frac{27}{28} \approx 0.96$. So $\frac{27}{28}$ is much larger.

* Problem 4: $\frac{7}{8}$
$\frac{7}{8}$ is the same as $\frac{21}{24}$. Since $\frac{23}{24}$ is bigger than $\frac{21}{24}$, and we already proved $\frac{27}{28}$ is bigger than $\frac{23}{24}$, then $\frac{27}{28}$ is the winner here too.

Conclusion:
The fraction $\frac{27}{28}$ is the closest to 1 among all the options, making it the largest value.

Final Answer:
The largest sum is 27/28