4) Look at this square:
(1) If the side lengths are halved, then which of the following statements about its area will be true?
(1) The ratio of the new area to the old area will be $1: 4$.
The ratio of the new area to the old area will be $1: 8$.
The ratio of the new area to the old area will be $9: 1$.
The ratio of the new area to the old area will be $1: 2$.

Answer

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Answer

$\boxed{1:4}$ is the ratio of the new area to the old area.

Steps

Step 1 ：Let the original side length be $s$, then the new side length is $\frac{s}{2}$.

Step 2 ：Calculate the area of the original square and the new square: $s^2$ and $\left(\frac{s}{2}\right)^2$.

Step 3 ：Find the ratio between the new area and the old area: $\frac{\left(\frac{s}{2}\right)^2}{s^2}$.

Step 4 ：Simplify the ratio: $\frac{\frac{s^2}{4}}{s^2}$ = $\frac{1}{4}$.

Step 5 ：$\boxed{1:4}$ is the ratio of the new area to the old area.