1. **Stating the problem:** Use the associative property of addition to show that the expressions are equal. 2. **Recall the associative property:** For any numbers $a$, $b$, and $c$, the associative property states: $$ (a + b) + c = a + (b + c) $$ This means that when adding three numbers, the way in which they are grouped does not change the sum. 3. **Example given:** $$(2 + 3) + 4 = 2 + (3 + 4)$$ Calculate both sides: $$(2 + 3) + 4 = 5 + 4 = 9$$ $$2 + (3 + 4) = 2 + 7 = 9$$ Both sides equal 9, confirming the property. 4. **Solve part 1:** **a.** $$(2 + 5) + 3 = 2 + (5 + 3)$$ Calculate both sides: $$(2 + 5) + 3 = 7 + 3 = 10$$ $$2 + (5 + 3) = 2 + 8 = 10$$ **b.** $$(4 + 6) + 2 = 4 + (6 + 2)$$ Calculate both sides: $$(4 + 6) + 2 = 10 + 2 = 12$$ $$4 + (6 + 2) = 4 + 8 = 12$$ **c.** $$(7 + 8) + 1 = 7 + (8 + 1)$$ Calculate both sides: $$(7 + 8) + 1 = 15 + 1 = 16$$ $$7 + (8 + 1) = 7 + 9 = 16$$ 5. **Solve part 2:** Use variables to show the associative property. **a.** $$(m + n) + p = m + (n + p)$$ **b.** $$(x + y) + z = x + (y + z)$$ **c.** $$(c + d) + e = c + (d + e)$$ These equalities hold true by the associative property of addition for any numbers or variables. **Final answers:** 1.a. $10$ 1.b. $12$ 1.c. $16$ 2.a. $ (m + n) + p = m + (n + p) $ 2.b. $ (x + y) + z = x + (y + z) $ 2.c. $ (c + d) + e = c + (d + e) $