https://file.aiquickdraw.com/mathbot/file/17254946886982gvvrgme.jpg

The given expression in the image is:

\[
3 \frac{3}{7} + 5 \frac{1}{3}
\]

This is a sum of two mixed fractions. To add them, let's first convert the mixed numbers into improper fractions.

### Step 1: Convert Mixed Numbers to Improper Fractions

1. \(3 \frac{3}{7} = \frac{(3 \times 7) + 3}{7} = \frac{21 + 3}{7} = \frac{24}{7}\)
2. \(5 \frac{1}{3} = \frac{(5 \times 3) + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3}\)

### Step 2: Find a Common Denominator

To add \(\frac{24}{7}\) and \(\frac{16}{3}\), we need a common denominator. The least common denominator (LCD) of 7 and 3 is 21.

Now, convert both fractions to have a denominator of 21:

\[
\frac{24}{7} = \frac{24 \times 3}{7 \times 3} = \frac{72}{21}
\]
\[
\frac{16}{3} = \frac{16 \times 7}{3 \times 7} = \frac{112}{21}
\]

### Step 3: Add the Fractions

Now that both fractions have the same denominator, we can add them:

\[
\frac{72}{21} + \frac{112}{21} = \frac{72 + 112}{21} = \frac{184}{21}
\]

### Step 4: Simplify (if necessary)

\(\frac{184}{21}\) is already in its simplest form, but we can convert it back to a mixed number:

\[
184 \div 21 = 8 \text{ remainder } 16
\]

Thus, \(\frac{184}{21} = 8 \frac{16}{21}\).

### Final Answer:

\[
3 \frac{3}{7} + 5 \frac{1}{3} = 8 \frac{16}{21}
\]

Would you like further details or have any questions? Here are five related questions to explore:

1. How do you subtract mixed fractions?
2. What are the steps to convert improper fractions back to mixed numbers?
3. How can you simplify fractions effectively?
4. How do you multiply two mixed fractions?
5. What are some tips for finding the least common denominator quickly?

**Tip:** When adding or subtracting fractions, always look for the least common denominator to simplify the process.

Learn how to add the mixed numbers 3 3/7 and 5 1/3 with a step-by-step solution. This problem covers essential mathematical concepts such as converting mixed numbers to improper fractions, finding a common denominator, and adding fractions with the same denominator. Suitable for students in Grades 5-6.

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