Adding Fractions Worksheets - Free Printable

Problem Overview:

The task involves solving a series of fraction addition problems and identifying the largest sum among them. The worksheet provides step-by-step solutions for each problem, and the final question asks to identify the largest fraction sum.

Solution Explanation:

#### Step 1: Understanding Fraction Addition
To add fractions, we need to ensure they have a common denominator. If the denominators are different, we find the least common denominator (LCD) and convert each fraction to an equivalent fraction with that denominator. Then, we add the numerators while keeping the denominator the same.

#### Step 2: Reviewing Each Problem
Let's go through a few examples to understand the process:

1. Problem 1: $\frac{1}{3} + \frac{3}{6}$
- Convert $\frac{1}{3}$ to $\frac{2}{6}$ (since the LCD of 3 and 6 is 6).
- Add: $\frac{2}{6} + \frac{3}{6} = \frac{5}{6}$.

2. Problem 4: $\frac{1}{2} + \frac{3}{8}$
- Convert $\frac{1}{2}$ to $\frac{4}{8}$ (since the LCD of 2 and 8 is 8).
- Add: $\frac{4}{8} + \frac{3}{8} = \frac{7}{8}$.

3. Problem 15: $\frac{6}{28} + \frac{3}{4}$
- Convert $\frac{3}{4}$ to $\frac{21}{28}$ (since the LCD of 28 and 4 is 28).
- Add: $\frac{6}{28} + \frac{21}{28} = \frac{27}{28}$.

#### Step 3: Identifying the Largest Sum
The worksheet already provides the solutions to all the problems. We need to compare the sums to find the largest one.

- Problem 1: $\frac{5}{6}$
- Problem 2: $\frac{7}{12}$
- Problem 3: $\frac{7}{15}$
- Problem 4: $\frac{7}{8}$
- Problem 5: $\frac{9}{14}$
- Problem 6: $\frac{9}{16}$
- Problem 7: $\frac{17}{20}$
- Problem 8: $\frac{5}{18}$
- Problem 9: $\frac{5}{16}$
- Problem 10: $\frac{13}{18}$
- Problem 11: $\frac{13}{25}$
- Problem 12: $\frac{17}{21}$
- Problem 13: $\frac{13}{30}$
- Problem 14: $\frac{23}{36}$
- Problem 15: $\frac{27}{28}$
- Problem 16: $\frac{32}{35}$
- Problem 17: $\frac{18}{25}$
- Problem 18: $\frac{23}{24}$

Among these, the largest sum is $\frac{27}{28}$.

#### Final Answer:
The largest fraction sum is $\boxed{\frac{27}{28}}$.