The problem in the image is:

$2 \frac{12}{15} + 3 \frac{1}{3} = 2 \frac{12}{15} + 3 - \square = \, ?$

Let's solve it step-by-step.

Step 1: Convert Mixed Numbers to Improper Fractions

1. Convert $2 \frac{12}{15}$: $2 \frac{12}{15} = \frac{2 \times 15 + 12}{15} = \frac{30 + 12}{15} = \frac{42}{15}$

2. Convert $3 \frac{1}{3}$: $3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}$

Step 2: Find a Common Denominator

The denominators are 15 and 3. The least common multiple of 15 and 3 is 15.

1. Convert $\frac{10}{3}$ to have a denominator of 15: $\frac{10}{3} = \frac{10 \times 5}{3 \times 5} = \frac{50}{15}$

Step 3: Add the Fractions

Now we can add $\frac{42}{15}$ and $\frac{50}{15}$.

$\frac{42}{15} + \frac{50}{15} = \frac{42 + 50}{15} = \frac{92}{15}$

Step 4: Simplify or Convert to Mixed Number

Now, let's convert $\frac{92}{15}$ back to a mixed number.

1. Divide 92 by 15:

   • $92 \div 15 = 6$ with a remainder of 2.

2. Write as a mixed number: $\frac{92}{15} = 6 \frac{2}{15}$

Final Answer:

$2 \frac{12}{15} + 3 \frac{1}{3} = 6 \frac{2}{15}$

Would you like more details on any step or have additional questions?

1. How do you convert mixed numbers to improper fractions?
2. What are common methods to find the least common multiple?
3. How do you convert improper fractions back to mixed numbers?
4. Can fractions with different denominators be directly added or subtracted?
5. How do you handle fraction simplification?

Tip: When adding fractions, always convert them to a common denominator before performing the addition.