Scanned images, especially those scanned as gray scale or color, can be very large. When confronted with a file that is too big, there are several ways to reduce its size. 

Draw a smaller selection frame 
Only select the part of the image that is needed. Including areas not necessary in the final output needlessly increase image file size. 

Scan the image at a lower resolution 
Using a lower resolution will significantly reduce the size of your files. For example, in some cases scanning a gray scale image at 150 dpi, with software sharpening, can result in an image that is as good as a 300 dpi scan. 

Be careful with color image 
Images scanned as color will be large because so much data is captured during the scan. Unless a color monitor to display or edit the image is available, scanning the image as color is unnecessary.