Higher Order Thinking Is it necessary to rename \( 4 \frac{1}{4} \) to subtract \( \frac{3}{4} \) ? Explain.

No, it is not necessary to **rename** \( 4 \frac{1}{4} \) in order to subtract \( \frac{3}{4} \). However, understanding different methods can make the subtraction process clearer and more intuitive. ### Direct Subtraction Method You can directly subtract the fractions from the mixed number without renaming: \[ 4 \frac{1}{4} - \frac{3}{4} \] 1. **Separate the Whole Number and the Fraction:** \[ 4 + \frac{1}{4} - \frac{3}{4} \] 2. **Subtract the Fractions:** \[ \frac{1}{4} - \frac{3}{4} = -\frac{2}{4} = -\frac{1}{2} \] 3. **Combine with the Whole Number:** \[ 4 - \frac{1}{2} = 3 \frac{1}{2} \] ### Renaming (Alternative) Method Renaming involves adjusting the mixed number to simplify the subtraction. Here's how you can do it: 1. **Convert \( 4 \frac{1}{4} \) to an Improper Fraction:** \[ 4 \frac{1}{4} = \frac{17}{4} \] 2. **Subtract \( \frac{3}{4} \):** \[ \frac{17}{4} - \frac{3}{4} = \frac{14}{4} = \frac{7}{2} = 3 \frac{1}{2} \] ### Conclusion While renaming (or converting to an improper fraction) is a valid method and can sometimes make calculations easier, it is **not necessary** for this subtraction. You can successfully subtract \( \frac{3}{4} \) directly from \( 4 \frac{1}{4} \) by handling the whole number and the fractional parts separately. Understanding both methods enhances flexibility in problem-solving and deepens comprehension of fraction operations.