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There are many properties and it is impossible to name them all. The question needs to be more specific.
how to do mental math useing propertys
Grouping symbols are parentheses such as {}, (), []. They need to be evaluated before other operations. If there are a number of nested parentheses, they must be evaluated starting with the innermost.
Grouping symbols are symbols such as parentheses or brackets, that indicate that the operations within them should be done first. When an expression contains more than one pair of grouping symbols, the computations in the innermost grouping should be done first.
Dimensional grouping is exactly what it sounds like, grouping numbers and problems in terms of how many dimensions they have. For instance there are two dimensional and three dimensional groupings.