### Identity Elements

An**identity element**is a number which, when combined with a mathematical operation on a number, leaves that number unchanged. For example, the

**identity element**for addition and subtraction is

**zero**, because adding or subtracting zero to a number doesn’t change the number. And zero is also what you get when you add together a number and its opposite, like 3 and -3.

The

**inverse operation**of addition is subtraction—when you add a number and then subtract that same number, you end up back where you started. Also, adding a number’s opposite is the same as subtracting it—for example, is the same as .Multiplication and division are also inverse operations to each other—when you multiply by a number and then divide by the same number, you end up back where you started. Multiplication and division also have an identity element: when you multiply or divide a number by

**one**, the number doesn’t change.

Just as the

**opposite**of a number is the number you can add to it to get zero, the**reciprocal**of a number is the number you can multiply it by to get one. And finally, just as adding a number’s opposite is the same as subtracting the number, multiplying by a number’s reciprocal is the same as dividing by the number.
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