### Instruction: The area of a rectangle is 432 square centimeters. What would the new area be if the length of the rectangle was decreased by $10\%$ and the width of the rectangle was increased by $10\%$? Express your answer to the nearest whole number.### Response: To find the area of a rectangle, I need to multiply the length by the width.
Let me call the original length L and the original width W.
Then I have that LW = 432.
I want to find the new area after changing the length and the width by $10\%$.
To decrease something by $10\%$, I need to multiply it by $0.9$.
To increase something by $10\%$, I need to multiply it by $1.1$.
So the new length is $0.9L$ and the new width is $1.1W$.
The new area is then $0.9L \times 1.1W$.
To simplify this expression, I can use the distributive property and get $0.9L \times 1.1W = 0.99LW$.
But I already know that LW = 432, so I can substitute that and get $0.99LW = 0.99 \times 432$.
This is equal to 427.68, but the problem asks me to round to the nearest whole number.
So the final answer is 428 square centimeters.