To make it easier to clean under the stove burners, cover the plates under the burners with foil. Just change the foil occasionally when dirty rather than try to scrub the plates themselves.
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Use baking soda to put out grease fires. (Jennifer)
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Coat the wall behind the stove with furniture polish. It will make it easier to wipe clean.
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To avoid food splatters, sprinkle a little salt in the pan or cover it with an upside down colander. Make sure also that the heat isn't too high.