Properties

Addition Terms

The values added in addition are called 'addends', and the result of the addition is the 'sum'.

Additive Identity

Any value added to the additive identity (0) is the value itself.

Additive Inverse

A value added to the additive inverse (the negative of itself) equals the additive identity (0).

Negative Addends

Negative addends are subtracted instead of added.

Double Negatives

Subtracting a negative addend reverses the operation upon itself and turns it into addition.

Commutative Law of Addition

Order does not matter when adding elements together, as long as the final sum reflects all addends.

Associative Law of Addition

Grouping does not matter when adding elements together, as long as the final sum reflects all addends.

Example Problems

Long Addition

Additive Identity

The additive identity property states that any value added to 0 (or the 'additive identity') is equal to the value itself.

Additive Inverse

The additive inverse property states that any value added to its additive inverse (itself multiplied by -1) is equal to zero.

Negative Addends

Negative addends are subtracted instead of added.

Double Negatives

Subtracting negatives addends reverses the operation upon itself, changing the operation from subtraction to addition.

Commutative and Associative Laws of Addition

Neither grouping nor order matters when adding addends, only that they are all added together in the final sum and the negatives are handled correctly.

Exercises

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