Heat 1/2 cup of vinegar in the microwave for about 30 seconds. It doesn't need to be boiling or extremely hot.
Apply the warm vinegar to the jeans with an old toothbrush. Cover the area where the gum is stuck.
Allow the vinegar to set for 15 to 20 minutes, to allow it to dissolve the gum.
Rinse the vinegar out of the jeans, removing as much of the gum as possible.
Apply a stain pretreater to the area, to help remove any stains left behind by the gum.
Wash the jeans through the washing machine, using your regular laundry detergent and warm water.
Check the jeans for any sign of gum stains before placing the jeans in the dryer again. If some of the stain remains, re-treat the stain and wash it again. Don't put your jeans in the dryer until the stain is completely removed.