Question

Sandra used the distributive property to simplify the following problem. Did she correctly use the distributive property? If so, explain why or how you know. If not, explain her mistake and how you would fix it.

3(4 + 6) = 4 + 18

Answer 1

Sandra incorrectly simplified the expression 3(4 + 6) as 4 + 18. The correct use of the distributive property gives 3(4 + 6) = 12 + 18 = 30.

Step-by-step explanation:

Sandra did not use the distributive property correctly when simplifying the expression 3(4 + 6). The distributive property states that you must multiply the number outside the parentheses by each term inside the parentheses. The correct simplification should involve multiplying 3 by both 4 and 6 separately and then adding the products. The correct steps are:

Multiply the outer term by each term inside the parentheses: 3 × 4 = 12 and 3 × 6 = 18.Add the products together: 12 + 18 = 30.

Thus, the correct expression should be 3(4 + 6) = 3 × 4 + 3 × 6 = 12 + 18 = 30. Sandra's mistake was adding the 3 only to the 6 (yielding 18), and leaving the 4 unchanged, which is incorrect. To fix this, she needs to apply the distributive property properly as shown above.

After simplifying the algebra, it's crucial to check the answer to see if it is reasonable. In this case, 30 is the correct solution, showing that the algebra has been simplified correctly.