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Assuming that "x" and "y" are multiplicative inverses:
* The basic definition: x times x = 1
* "x" and "y" are either both positive or both negative.
* If they are positive, then if one is greater than 1, the other will be less than 1, and vice versa.
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What are all the properties of division?
Properties of division are the same as the properties of multiplication with one exception. You can never divide by zero. This is because in some advanced math courses division is defined as multiplication by the Multiplicative Inverse, and by definition zero does not have a Multiplicative Inverse.
What are some real life examples of multiplicative inverse?
Here is one example of a practical use of multiplicative inverses. If you want to convert from feet to meters, you multiply by 0.3048. If you want to convert the other way round, you either DIVIDE by the same number, or you MULTIPLY by its multiplicative inverse. The same applies to many similar conversions.
What are examples of inverse property of multiplication?
When multiplication is defined over some domains, for every non-zero element X, in the domain, there exists a unique element Y, also in the domain such that X*Y = Y*X = 1 where 1 is the multiplicative identity. Such a value Y is written as X-1 or 1/X. Note that a multiplicative inverse need not exist. For example, the set of integers is closed under multiplication, but most elements do not have an inverse within the set.
What is the opposite of an improper fraction?
The answer depends on what you mean by "opposite". Many users mean additive inverse - in which case it is a negative improper fraction. Some use the term to refer to the multiplicative inverse, in which case it is a proper fraction.
Which of the following sets of numbers contains multiplicative inverses for all its nonzero elements?
Please don't write "the following" if you don't provide a list. This is the situation for some common number sets:* Whole numbers / integers do NOT have this property. * Rational numbers DO have this property. * Real numbers DO have this property. * Complex numbers DO have this property. * The set of non-negative rational numbers, as well as the set of non-negative real numbers, DO have this property.
What does inverse property in multiplication mean?
Some one please tell me what inverse property is!!
Does every non-zero number have a multiplicative inverse?
Every non zero number has a multiplicative inverse, which is 1 divided by that number. This stands for both real and complex numbers. This can be proved by letting x=some non zero number. x*(1/x)=x/x=1, therefore the multiplicative inverse of x is 1/x.
What are all the properties of division?
Properties of division are the same as the properties of multiplication with one exception. You can never divide by zero. This is because in some advanced math courses division is defined as multiplication by the Multiplicative Inverse, and by definition zero does not have a Multiplicative Inverse.
What are some real life examples of multiplicative inverse?
Here is one example of a practical use of multiplicative inverses. If you want to convert from feet to meters, you multiply by 0.3048. If you want to convert the other way round, you either DIVIDE by the same number, or you MULTIPLY by its multiplicative inverse. The same applies to many similar conversions.
What are examples of inverse property of multiplication?
When multiplication is defined over some domains, for every non-zero element X, in the domain, there exists a unique element Y, also in the domain such that X*Y = Y*X = 1 where 1 is the multiplicative identity. Such a value Y is written as X-1 or 1/X. Note that a multiplicative inverse need not exist. For example, the set of integers is closed under multiplication, but most elements do not have an inverse within the set.
What is the definition of inverse property?
There are inverse properties for many things in math. Commonly, we talk about it for addition and multiplication. So for addition, take any number a, there is an additive inverse -a such that a+ (-a) =0 For example, the additive inverse of 2 is -2 since 2+ -2=0 Similiarly for multiplication, for any number a, we have some number, 1/a such that a(1/a)=1. We call 1/a the multiplicative inverse. In a more abstract sense, we look at sets of objects in math and having an inverse is one of the properties a set needs to be a group. Other things, such as functions have inverses too. In fact, the inverse property is a big topic in math.
The equation 3 4x 4x 3 illustrates which property 1 Commutative 2 Associative 3 Distributive 4 Multiplicative inverse?
3 + 4x = 4x + 3 is an example of the commutative property of addition.
What is a mathamatical unit?
A number that has a multiplicative inverse. That is, x is a unit iff there exists some y such that x*y = y*x = 1.
What is the opposite of an improper fraction?
The answer depends on what you mean by "opposite". Many users mean additive inverse - in which case it is a negative improper fraction. Some use the term to refer to the multiplicative inverse, in which case it is a proper fraction.
Why does the fact 0 has no multiplicative inverse still mean R is still a field?
In the definition of a field it is only required of the non-zero numbers to have a multiplicative inverse. If we want 0 to have a multiplicative inverse, and still keep the other axioms we see (for example by the easy to prove result that a*0 = 0 for all a) that 0 = 1, now if that does not contradict the axioms defining a field (some definitions allows 0 = 1), then we still get for any number x in the field that x = 1*x = 0*x = 0, so we would get a very boring field consisting of only one element.
Why 0 does not have a multiplicative inverse?
As n gets very small, 1/n goes towards infinity. A multiplicative inverse of 0 would be some number x, such that 0x=1. This is impossible with the real numbers we use, since 0x=0 for any number x. One might be tempted to invent a new number (calling it "infinity", "nullity", or any other name) that would be the inverse of 0. Of course, then you're not dealing with real numbers anymore, you're dealing with real numbers plus this invented number. There are serious issues even with this approach. Again, let x be this "multiplicative inverse of 0". Then 0*1=0 and 0*2=0. So 0*1 = 0*2. Multiply both sides by x to get x*0*1 = x*0*2. Since x*0 is 1, this means 1*1 = 1*2. So 1=2, which is an absurd conclusion. As you can see, there are good reasons not to allow a multiplicative inverse for 0 - it breaks all the laws of multiplication we're accustomed to.
What is the Inverse Property of Subtraction?
Generally there are only two inverse properties. The inverse property of addition, also known as the additive inverse property, and the inverse property of multiplication, also known as the multiplicative inverse property. The additive inverse property for say the the integer -5 (integer is a fancy word for number) is the same number but with the opposite sign. So if you are asked to find the additive inverse for -5 it is asking you to find it's opposite. So the what is the opposite of -5? +5, also written as just plain old 5 without the + sign! If you are asked to find the additive inverse of 5 what would you write? -5 of course! If you are asked to state in words and numbers the definition of the additive inverse property you would say that "the additive inverse property states that -a+a=0=a+-a". Here is another example. Say you are asked "what number can be used to make the following equation true? -5+?=0". What is the inverse of -5? 5 of course. So -5+5=0! ****If you know how to add/subtract positive and negative integers**** The inverse properties deal with negatives and positive integers. If you don't know how to add or subtract and divide and multiply negative and positive integers you should really learn to help you to better understand inverse properties. If you have studied integers then you know there cannot really be a inverse property of subtraction because the rule for subtracting integers is "Keep, Change, Change". Technically there can be a inverse subtraction property because ( -5)-5=0=(-5)5=0 BUT 5-(-5)=0=5+5 is false because 5+5=10 not 0! When subtracting integers the Keep, Change, Change rule means that if you were given the problem 5-(-5) you would KEEP the first number and sign exactly the same but CHANGE the sign, the minus sign, to a plus sign and then CHANGE the second number (in this case -5) to it's opposite. This changing the second number, (-5), is inverting it to it's opposite (5). So there can technically be a inverse subtraction property but it would be one that isn't reliable in making an equation true because depending on how the numbers are arranged you could get a completely different answer then you would if the numbers were arranged a different way. ( -5)-5=0=(-5)5=0 BUT 5-(-5)=0=5+5 is false because 5+5=10 not 0! But with addition (-5)+5 is the same as 5+(-5) making the following equation true: (-5)+5=0=5+(-5). I know this is a lot of reading to do but it really is quite simple. I was never any good at math but if I can do it so can you! It may be helpful to learn about integers before you learn about properties. This is found in the pre-algebra section. I hope this does some good for you. Xoxo
