[Music] now let's discuss the third property of integer identity property identity property has two kinds we have identity property of addition and identity property of multiplication first identity property of addition this property states that if a is a real number then a plus 0 is equal to a examples number 1 nine plus zero is equal to nine this property states that when zero is added to any real number the answer is the given number the number zero is called the additive property number two zero plus negative one hundred is equal to negative 100 again this property states that when you add 0 to any real number the answer is always the given number the second kind of identity property is the identity property of multiplication this property states that if a is a real number then a times one is equal to a examples number one negative 21 times one is equal to negative 21. this property states that when one is multiplied to any real number the answer is always the given number the number one is called the multiplicative property number two one times fifty is equal to fifty again this property tells us that when you multiply one to any real number the answer is always the given number now let's discuss the fourth property of integer inverse property first let's have the inverse property of addition this states that if a is a real number then there exists another real number negative a such that a plus negative a is equal to zero examples number one five plus negative five is equal to zero this property states that when a real number five is added to its additive inverse negative five their sum is zero number two negative two over three plus two over three is equal to zero in this example two over three is the additive inverse of negative two over three because their sum is zero so when you add the additive inverse to any given number the sum is always zero inverse property of multiplication it states that if a is a real number and a is not equal to zero then there exists another real number one over a such that a times one over eight is equal to one examples number one twelve times one over 12 is equal to 1. this property states that when a real number 12 is multiplied to its multiplicative inverse 1 over 12 their product is one number two negative two over three times negative three over two is equal to one in this example negative three over two is the multiplicative inverse of negative two over three because as you can see their product is one [Music] always remember the only way to learn mathematics is to do mathematics