Final answer:
The query seeks to correct Sarah's application of operation properties on mathematical expressions, which involves the Distributive, Associative, Commutative, and Transitive Properties, as well as rules of multiplication and division concerning signs. Without seeing the exact expressions, we cannot specifically point out errors, but we can confirm how each property should be applied and how to handle the signs in calculations.
Step-by-step explanation:
The question is looking to identify errors in the application of properties of operations to equivalent expressions. Let's address each claim:
- B. Expression 1: Sarah can use the Distributive Property even if there are three addends by grouping them as needed before distribution.
- C. Expression 2: Sarah can indeed combine numbers with the same sign; in this case, combining -4 and -6 is correct if her expression allows for it.
- D. Expression 3: For the Distributive Property to be correctly applied with a fraction, Sarah must ensure she multiplies 1/2 by -6 correctly. Remember, multiplying a positive number by a negative number results in a negative product.
Without the exact expressions Sarah wrote, we cannot definitively identify any specific errors, but we can clarify how the properties should be used:
- The Associative Property allows us to group addends or factors and add or multiply in any order.
- The Commutative Property states that the order of addition or multiplication does not change the result.
- The Distributive Property allows us to multiply a single term by each term within a parenthesis separately.
- The Transitive Property states that if one quantity equals another, and the second quantity equals a third, then the first equals the third.
When dealing with multiplication and division of numbers, rules for the resulting signs must be followed:
- Positive multiplied by positive equals positive (e.g., 2x3 = 6).
- Negative multiplied by negative equals positive (e.g., (-4) x (-3) = 12).
- Positive multiplied by negative, or negative by positive, results in a negative (e.g., (-3) x 2 = -6).
- Division follows the same sign rules as multiplication.