Nell writes the expression

. She rewrites the expression using the associative property. Which expression could Nell have written using the associative property?
A
5.6x5.6x5.6x
B
9.6x−49.6x-49.6x−4
C
3.6x+(6−4)3.6x+(6-4)3.6x+(6−4)
D
3.6(x+6)−43.6(x+6)-43.6(x+6)−4

1 answer

The associative property states that the way in which numbers are grouped in addition or multiplication does not change their sum or product. In other words, for addition, \((a + b) + c = a + (b + c)\) and for multiplication, \((a \times b) \times c = a \times (b \times c)\).

From the options presented, we need to identify the expression that could have been rewritten using the associative property.

Let's analyze each option:

A. \(5.6 \times 5.6 \times 5.6 x\)
This expression is multiplication but does not change groups like \((a \times b) \times c\).

B. \(9.6x - 49.6x - 49.6x - 4\)
This expression involves subtraction and does not involve grouping that would allow for the associative property to apply.

C. \(3.6x + (6 - 4) \times 3.6x + (6 - 4) \times 3.6x + (6 - 4)\)
This could be rewritten to group terms involving \(3.6x\), but it's a mix with subtraction designed to simplify the expression. However, it doesn't show a clear use of the associative property.

D. \(3.6(x + 6) - 4\)
This expression can be grouped as \(3.6 \times (x + 6) - 4\), showing how you can group \(x + 6\) together before multiplying by \(3.6\).

Among the options, D clearly illustrates the associative property by showing that \(3.6\) can be distributed over the grouped terms.

Thus, the best answer is: D: \(3.6(x + 6) - 4\)