1. The problem involves understanding addition and subtraction of mixed numbers on a number line. 2. The number line ranges from -6 to 6, and the operations involve adding positive and negative mixed numbers. 3. The formula for adding mixed numbers is to convert them to improper fractions or decimals, perform the addition, then convert back if needed. 4. Important rules: - Adding a positive number moves right on the number line. - Adding a negative number moves left on the number line. 5. Example calculations: - For $-3 \frac{1}{4} + \frac{1}{4} = -4 \frac{3}{4}$: Convert $-3 \frac{1}{4}$ to $-\frac{13}{4}$ and $\frac{1}{4}$ stays $\frac{1}{4}$. $$-\frac{13}{4} + \frac{1}{4} = -\frac{12}{4} = -3$$ But the problem states $-4 \frac{3}{4}$, so this is likely a subtraction or a different operation. - For $-3 \frac{1}{4} + 4 \frac{3}{4} = 1 \frac{1}{2}$: Convert to improper fractions: $$-3 \frac{1}{4} = -\frac{13}{4}, \quad 4 \frac{3}{4} = \frac{19}{4}$$ Add: $$-\frac{13}{4} + \frac{19}{4} = \frac{6}{4} = 1 \frac{1}{2}$$ - For $3 \frac{1}{4} + (-1 \frac{1}{2}) = 4 \frac{3}{4}$: Convert: $$3 \frac{1}{4} = \frac{13}{4}, \quad -1 \frac{1}{2} = -\frac{3}{2} = -\frac{6}{4}$$ Add: $$\frac{13}{4} + (-\frac{6}{4}) = \frac{7}{4} = 1 \frac{3}{4}$$ The problem states $4 \frac{3}{4}$, so check the operation carefully. - For $3 \frac{1}{4} + (-4 \frac{3}{4}) = 1 \frac{1}{2}$: Convert: $$3 \frac{1}{4} = \frac{13}{4}, \quad -4 \frac{3}{4} = -\frac{19}{4}$$ Add: $$\frac{13}{4} + (-\frac{19}{4}) = -\frac{6}{4} = -1 \frac{1}{2}$$ The problem states $1 \frac{1}{2}$, so verify the signs. 6. The calculation modeled on the number line is addition of mixed numbers, including positive and negative values, showing movement left or right. 7. The curved arrows represent these additions visually: moving left for adding negatives, right for adding positives. Final answer: The number line models addition of mixed numbers with positive and negative values, showing how sums correspond to movements left or right on the line.