How many parts would you divide each number into on a number line for the following problem: \( \frac{5}{3}-\frac{3}{12} \) ?

To solve the problem \( \frac{5}{3} - \frac{3}{12} \), we first need to find a common denominator for the fractions involved. 1. **Identify the denominators**: The denominators are 3 and 12. 2. **Find the least common denominator (LCD)**: The least common multiple of 3 and 12 is 12. 3. **Convert \( \frac{5}{3} \) to have a denominator of 12**: \[ \frac{5}{3} = \frac{5 \times 4}{3 \times 4} = \frac{20}{12} \] 4. **Now we can rewrite the expression**: \[ \frac{5}{3} - \frac{3}{12} = \frac{20}{12} - \frac{3}{12} \] 5. **Subtract the fractions**: \[ \frac{20}{12} - \frac{3}{12} = \frac{20 - 3}{12} = \frac{17}{12} \] Now, to answer the original question about how many parts to divide each number into on a number line, we can consider the denominators of the fractions involved. - The first fraction \( \frac{5}{3} \) can be divided into 3 parts (since the denominator is 3). - The second fraction \( \frac{3}{12} \) can be divided into 12 parts (since the denominator is 12). Thus, when considering the number line for the operation \( \frac{5}{3} - \frac{3}{12} \), you would divide the number line into 12 parts to accommodate the fraction with the largest denominator, which is 12. Therefore, you would divide the number line into **12 parts**.