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Published byHilary Conley Modified over 4 years ago

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Other Properties of Real Numbers

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Identity Properties Identity properties tell us how we can add or multiply and get an answer that is identical to the number we started with.

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Identity Property of Addition The identity property of addition tells us that we can add zero to any number and get that identical number as the answer. a + 0 = a That makes the identity element for addition:

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Identity Property of Multiplication The identity property of multiplication tells us that we can multiply any number by 1 and get that identical number as the answer. That makes the identity element for multiplication:

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Inverse Properties The inverse properties tell us how we can create the identity elements out of other numbers. Sort of like building a sand castle!

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Additive Inverse Property The identity element for addition is How can we add and get an answer equal to zero? Ah ha! - 5 + 5 = 0 In fact: - a + a = 0

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Additive Inverse Property -a + a = 0 Numbers that have the same magnitude but different signs are called opposites. Another term for opposite is additive inverse.

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Additive Inverse Property The additive inverse property tells us that when we add any number and its opposite the answer will be zero. - a + a = 0

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Double Negative Property Closely related to the concept of opposite is the double negative property. - ( - a ) = a We can think if that as two negative signs in a row convert to one positive sign. (signs are the same, replace with +)

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Double Negative Property Closely related to the concept of opposite is the double negative property. - ( - a ) = a Or we can think if it as ‘taking the opposite of an opposite gets you back where you started’!

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Multiplicative Inverse Property The identity element for multiplication is How can we multiply and get an answer equal to one? Ah ha! In fact:

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Reciprocals Reciprocals are the gymnasts of algebra. They just love to do headstands! Watch them flip!

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Multiplicative Inverse Property The multiplicative inverse property tells us that when we multiply any number by its reciprocal the answer will be one. Another term for reciprocal is multiplicative inverse.

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Multiplication Property of Zero Zero has a unique property that we will use a lot later in the semester. Any number multiplied by zero equals zero.

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Reduction Property When we reduce fractions, we are using the reduction property. In other words, as long as b and c are not equal to zero, we can cancel and reduce.

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More Properties of Real Numbers Identity properties a + 0 = a and Inverse properties – opposites and reciprocals Double negative property Multiplication property of zero Reduction property

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