Commutative Property 3Fedfc

1. **State the problem:** Determine if Maggie correctly applied the commutative property to the expression $$\frac{4}{5} + 6.9y - 8$$ by rewriting it as $$6.9y + 8 - \frac{4}{5}$$. 2. **Recall the commutative property:** The commutative property of addition states that terms can be rearranged in any order without changing the sum, i.e., $$a + b = b + a$$. 3. **Analyze the original expression:** The original expression is $$\frac{4}{5} + 6.9y - 8$$, which can be seen as $$\frac{4}{5} + 6.9y + (-8)$$. 4. **Analyze Maggie's expression:** Maggie wrote $$6.9y + 8 - \frac{4}{5}$$, which is $$6.9y + 8 + (-\frac{4}{5})$$. 5. **Compare the terms:** The original expression has terms $$\frac{4}{5}$$, $$6.9y$$, and $$-8$$. Maggie's expression has terms $$6.9y$$, $$8$$, and $$-\frac{4}{5}$$. 6. **Check signs:** The sign of the constant term changed from $$-8$$ to $$+8$$, and the fraction term changed from positive $$\frac{4}{5}$$ to negative $$-\frac{4}{5}$$. 7. **Conclusion:** Since the signs of some terms changed, Maggie did **not** apply the commutative property correctly. The commutative property only allows rearranging terms, not changing their signs. **Final answer:** No, some of the terms changed signs, so Maggie's application of the commutative property is incorrect.