Presentation on theme: "Other Properties of Real Numbers. Identity Properties Identity properties tell us how we can add or multiply and get an answer that is identical to the."— Presentation transcript:
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.
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:
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:
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!
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
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.
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
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 +)
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’!
Multiplicative Inverse Property The identity element for multiplication is How can we multiply and get an answer equal to one? Ah ha! In fact:
Reciprocals Reciprocals are the gymnasts of algebra. They just love to do headstands! Watch them flip!
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.
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.
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.
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