50 % of toothpase is made up of a substance called abrassives, which help in the removal of plaque. This ais made of bases like hydroxipatite, alluminum hydroxide etc. Hence toothpase is basic..
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50% of toothpastes are basic in nature because they are used to prevent tooth decay.
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Toothpaste is often basic (or alkaline) in order to counteract acidity in the mouth. Two types that I have in my bathroom contain sodium hydroxide (NaOH) a well known alkali.