0
By definition, every rational number x can be expressed as a ratio p/q where p and q are integers and q is not zero. Consider -p/q. Then by the properties of integers, -p is an integer and is the additive inverse of p. Therefore p + (-p) = 0
Then p/q + (-p/q) = [p + (-p)] /q = 0/q.
Also, -p/q is a ratio of two integers, with q non-zero and so -p/q is also a rational number. That is, -p/q is the additive inverse of x, expressed as a ratio.
Wiki User
∙ 6y ago
Add your answer:
Earn +20 pts
Does every integer has an additive inverse?
The additive inverse states that a number added to its opposite will equal zero. A + (-A) = 0. The "opposite" number here is the "negative" of the number. For any number n, the additive inverse is (-1)n. So therefore yes.
What is a number added to its additive inverse will always have a sum of zero?
It is a tautological description of one of the basic properties of numbers used in the branch of mathematics called Analysis: Property 2: there exists an additive identity, called 0; for every number n: n + 0 = 0 + n = n. Property 3: there exists an additive inverse, of every number n denoted by (-n) such that n + (-n) = (-n) + n = 0 (the additive identity).
What is the multiplication inverse of 8?
The multiplicative inverse is when you multiply a certain number, and the product is itself, the number. So, the multiplicative inverse of 8 is of course, 1. For every number, the multiplicative number is 1, because a certain number times 1 is equal to the certain number. It's simple!!
Every rational number is a real number?
Yes it is, but not every real number is a rational number
Properties of addition?
If 'a', 'b' and 'c' are any three numbers, then the properties of addition are:* Associative: the value of a + (b + c) is the same as (a + b) + c;* Additive identity: there exists zero (0) such that a + 0 = a;* Additive inverse: for every number a there is an additive inverse, denoted by (-a), such that a + (-a) = (-a) + a = 0;* Commutative: the value of a + b is the same as b + a;* Closed: the value of a + b is another number in the original set of a and b, for example, if aand b are both integers, then a + b will also be an integer.
Is a additive inverse of any rational number a negative number?
The additive inverse of EVERY positive rational number is a negative number.
Does every rational number have an additive inverse and why?
yes
Does every rational number have an additive inverse?
Yes.
Why does every rational number have a additive inverse?
The rational numbers form an algebraic structure with respect to addition and this structure is called a group. And it is the property of a group that every element in it has an additive inverse.
Why does every rational number have an additive inverse?
It is a fundamental requirement of algebraic structures called groups.
What is the aditive inverse property?
For every number, a,there exists a number called the additive inverse, -a, such that a + -a = 0.
Does every integer has an additive inverse?
The additive inverse states that a number added to its opposite will equal zero. A + (-A) = 0. The "opposite" number here is the "negative" of the number. For any number n, the additive inverse is (-1)n. So therefore yes.
Does every natural number have an additive inverse?
Yes. Just put a minus sign in front of it. Note that except for the zero, the additive inverse is no longer a natural number.
Does every integer have an additive inverse?
Yes.
When the additive inverse of a number equal to the absolute value of the number?
One example would be a Galois Field size 4 (ie GF(4)). Here, the elements are {0,1,2,3} and every element is its own additive inverse.
What is the additive inverse of the complex number 8 plus 3i?
To form the additive inverse, negate all parts of the complex number → 8 + 3i → -8 - 3i The sum of a number and its additive inverse is 0: (8 + 3i) + (-8 - 3i) = (8 + -8) + (3 + -3)i = (8 - 8) + (3 - 3)i = 0 + 0i = 0.
What is a number added to its additive inverse will always have a sum of zero?
It is a tautological description of one of the basic properties of numbers used in the branch of mathematics called Analysis: Property 2: there exists an additive identity, called 0; for every number n: n + 0 = 0 + n = n. Property 3: there exists an additive inverse, of every number n denoted by (-n) such that n + (-n) = (-n) + n = 0 (the additive identity).
