Addition properties

There are three properties of addition of numbers,which are used to solve mathematical problems, both in simple and in complex mathematics. The traveling, combining and distributing properties have their own peculiarities and are used only when the numbers are combined and multiplied, and in no case, under any other arithmetic operations.

• The combining property of adding numbers means(x + y) + c = x + (y + c) is true for any of the numbers x, y, and c that must be added. The combining property used in multiplying numbers means that for any of the numbers x, y and c, the equality (xy) c = x (yc) is true.
• The movable property used foraddition of any of the numbers x and y, indicates that these numbers can be rearranged in any direction, to group them in groups in a way that is acceptable in a particular case, and the result will not change. The displacement property of addition indicates that the sum obtained when two numbers are added does not change if these numbers are interchanged. The following equation is used: x + y = y + x.
• The distribution property of addition allowsadd numbers, according to this equation: (x + y) + c = x + (y + c). The same property is used in multiplication in accordance with the following equation: (xy) c = x (yc). The distributive property is applicable not only when it is necessary to multiply the sum by two summands, but also by the sum of three or more terms. In this case, the equality holds: x (y + c + d) = xy + xc + xd, regardless of what the numbers x, y, c and d are.