1. **State the problem:** We need to represent each addition problem on a number line and find the sum. 2. **Formula and rules:** Addition on a number line means moving right for positive numbers and left for negative numbers. The sum is the final position after all moves. 3. **Solve each problem:** **a.** $(-2) + (-3)$ - Start at 0, move 2 units left to -2. - Then move 3 units left from -2 to -5. - So, $(-2) + (-3) = -5$. **b.** $(+4) + (+2)$ - Start at 0, move 4 units right to 4. - Then move 2 units right from 4 to 6. - So, $(+4) + (+2) = 6$. **c.** $(-5) + (+2)$ - Start at 0, move 5 units left to -5. - Then move 2 units right from -5 to -3. - So, $(-5) + (+2) = -3$. **d.** $(+5) + (-2)$ - Start at 0, move 5 units right to 5. - Then move 2 units left from 5 to 3. - So, $(+5) + (-2) = 3$. **e.** $(-4) + (+4)$ - Start at 0, move 4 units left to -4. - Then move 4 units right from -4 to 0. - So, $(-4) + (+4) = 0$. **f.** $(-3) + (+6) + (-1)$ - Start at 0, move 3 units left to -3. - Then move 6 units right from -3 to 3. - Then move 1 unit left from 3 to 2. - So, $(-3) + (+6) + (-1) = 2$. 4. **Summary of answers:** - a. $-5$ - b. $6$ - c. $-3$ - d. $3$ - e. $0$ - f. $2$