To solve the expression \( \frac{10}{3} - \left( -\frac{35}{12} \right) \), we need to follow these steps:

1. Recognize that subtracting a negative is the same as adding the positive value.
2. Find a common denominator to combine the fractions.

Let's work through it:

### Step 1: Change the operation
\[ \frac{10}{3} - \left( -\frac{35}{12} \right) = \frac{10}{3} + \frac{35}{12} \]

### Step 2: Find the common denominator
The least common multiple (LCM) of 3 and 12 is 12. So, we need to convert \(\frac{10}{3}\) to a fraction with a denominator of 12.

\[ \frac{10}{3} = \frac{10 \times 4}{3 \times 4} = \frac{40}{12} \]

### Step 3: Add the fractions
\[ \frac{40}{12} + \frac{35}{12} = \frac{40 + 35}{12} = \frac{75}{12} \]

### Step 4: Simplify the fraction
To simplify \(\frac{75}{12}\), we need to find the greatest common divisor (GCD) of 75 and 12, which is 3.

\[ \frac{75 \div 3}{12 \div 3} = \frac{25}{4} \]

So, the simplified form of \(\frac{75}{12}\) is \(\frac{25}{4}\).

### Final Answer
\[ \frac{10}{3} - \left( -\frac{35}{12} \right) = \frac{25}{4} \]

Would you like more details or have any questions?

Here are 5 numbered questions you might want to ask:
1. How do you find the least common multiple (LCM) of two numbers?
2. What is the process to convert a mixed number to an improper fraction?
3. How do you simplify complex fractions?
4. Can you explain the steps for finding the greatest common divisor (GCD)?
5. How do you add and subtract fractions with different denominators?

**Tip:** When working with fractions, always find the least common multiple (LCM) of the denominators to combine them easily.

Learn how to solve the expression \( \frac{10}{3} - \left( -\frac{35}{12} \right) \) with a detailed step-by-step solution. This problem covers arithmetic operations with fractions, including addition and subtraction. Suitable for students in Grades 6-8.

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