The way in which you dry throw rugs after laundering is vital to its longevity and usefulness. If you throw a rubber non-skid backed rug into the dryer, you will shorten its lifespan. Instead, plan on washing and air drying.
Remove the old backing. Scraping with a spackling trowel or edge of a metal spatula may work. If you heat the rug in the dryer, the warm backing may be easier to remove.
If the rugs slide on the floor, purchase non-slip rug padding at a store and place under the rugs. You could also glue/sew rubber canning jar rings to the bottoms of the rugs. Always air dry these types of rugs.
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I had an old off white throw rug size 5x10 feet. I took 3 spray bottles. I filled one spray bottle with green RIT dye and a tablespoon of salt, and a tablespoon of laundry detergent.
The backing on throw rugs can deteriorate over time. Proper storage can help slow this process down. This is a page about storing rubber backed rugs.