Work backward from your frame
Effective PPI is the number of source pixels assigned to an inch of printed image. A 2,400 × 3,000 portrait at 8 × 10 inches has 300 pixels per inch on both axes. At 12 × 15 inches, it has 200 PPI on each axis.
The width calculation is pixel width divided by width in inches; the height calculation uses height. Different values indicate a shape mismatch. Crop uses the lower density to fill the target without stretching. Fit uses the higher density because the whole image occupies a smaller area with borders.
Use the pixels that actually remain
A calculation based on the original dimensions can overstate the detail available after cropping. If you remove half the image width, use the retained pixel width when checking the cropped picture.
Do not confuse effective image PPI with your printer’s advertised DPI. A printer may use multiple dots to reproduce a pixel’s color. Higher printer DPI does not replace missing source pixels, and a PPI result alone cannot assess focus, motion blur, or color.