0
No, the multiplicative inverse is a number that when multiplied by the original gives 1 as the product. Also called the reciprocal.
For example the multiplicative inverse of 2/3 is 3/2, because (2/3) x (3/2) = 1. Another example: If the number is -2, then the reciprocal is -1/2, so (-2) x (-1/2) = 1.
Add your answer:
Earn +20 pts
What is multiplictive inverse?
The multiplicative inverse of a number is that number which when multiplied by the original number gives 1.
What is the difference between multiplicative inverse and additive inverse?
The multiplicative inverse of a non-zero element, x, in a set, is an element, y, from the set such that x*y = y*x equals the multiplicative identity. The latter is usually denoted by 1 or I and the inverse of x is usually denoted by x-1 or 1/x. y need not be different from x. For example, the multiplicative inverse of 1 is 1, that of -1 is -1.The additive inverse of an element, p, in a set, is an element, q, from the set such that p+q = q+p equals the additive identity. The latter is usually denoted by 0 and the additive inverse of p is denoted by -p.
How do you prove the multiplicative inverse is unique?
You can multiply each side of the multiplicative inverse equation by the other inverse to show that any two multiplicative inverses are equal. Here it is more formally. Theorem: For all x in R, there exists y in R s.t. x * y = 1. If there is a y' in R such that x * y' = 1, then y = y'. Proof: - Start with x * y = 1. - y * x = 1 (commutative) - (y * x) * y' = 1 * y' = y' - y * (x * y') = y' (associative) - y * 1 = y' (because x*y' = 1) - y = y'
How could you turn any fraction into one using a single multiplication operation?
A fraction can be expressed as two expressions, a and b, in the form a/b. The multiplicative inverse is b/a. Just flip the numerator and denominator. Multiplying the original and the result of this always gives one, which is the definition of the multiplicative inverse.
Why does zero have no multiplicative inverse?
The multiplicative inverse is defined as: For every number a ≠ 0 there is a number, denoted by a⁻¹ such that a . a⁻¹ = a⁻¹ . a = 1 First we need to prove that any number times zero is zero: Theorem: For any number a the value of a . 0 = 0 Proof: Consider any number a, then: a . 0 + a . 0 = a . (0 + 0) {distributive law) = a . 0 {existence of additive identity} (a . 0 + a . 0) + (-a . 0) = (a . 0) + (-a . 0) = 0 {existence of additive inverse} a . 0 + (a . 0 + (-a . 0)) = 0 {Associative law for addition} a . 0 + 0 = 0 {existence of additive inverse} a . 0 = 0 {existence of additive identity} QED Thus any number times 0 is 0. Proof of no multiplicative inverse of 0: Suppose that a multiplicative inverse of 0, denoted by 0⁻¹, exists. Then 0 . 0⁻¹ = 0⁻¹ . 0 = 1 But we have just proved that any number times 0 is 0; thus: 0⁻¹ . 0 = 0 Contradiction as 0 ≠ 1 Therefore our original assumption that there exists a multiplicative inverse of 0 must be false. Thus there is no multiplicative inverse of 0. ---------------------------------------------------- That's the mathematical proof. Logically, the multiplicative inverse undoes multiplication - it is the value to multiply a result by to get back to the original number. eg 2 × 3 = 6, so the multiplicative inverse is to multiply by 1/3 so that 6 × 1/3 = 2. Now consider 2 × 0 = 0, and 3 × 0 = 0 There is more than one number which when multiplied by 0 gives the result of 0. How can the multiplicative inverse of multiplying by 0 get back to the original number when 0 is multiplied by it? In the example, it needs to be able to give both 2 and 3, and not only that, distinguish which 0 was formed from which, even though 0 is a single "number".
Does every real numbers have a multiplicative inverse?
You can invert almost any number by dividing 1 by that number. Zero is an exception since division by zero yields the equivalent of infinity, which is difficult to deal with by the usual rules of arithmetic. We cannot really know what the product of zero and infinity is. All other real numbers can be inverted.
What is the multiplicative inverse and where is an example?
Multiplicative inverse is also called the reciprocal for a number. You will probably hear reciprocal more often since it much easier to say than multiplicative inverse. They both mean the same thing and what they mean is a number that multiplied to your original number gives a product of 1. In order to find the reciprocal of a number you can just flip the fraction over. If your number is not in fraction form, just pretend it is by making it a fraction with a denominator by 1. If you flip it over then you get 1/your number. Examples: 1/2's reciprocal = 2/1 Test: 1/2 * 2 = 1 5.6's reciprocal = 1/5.6=0.17857142... Test 5.6*0.17857142... = 1 Etc. etc.
What is the multiplication inverse of -4?
inverse means one over the number. i.e. the inverse of 4 is 1/4. These multiplied together gives 1 (4/4)
What is additive inverse in math terms?
negative of a number gives its additive inverse
What is inverse in algebra?
Given a set and a binary operation defined on the set, the inverse of any element is that element which, when combined with the first, gives the identity element for the binary operation. If the set is integers and the binary operation is addition, then the identity is 0, and the inverse of an integer k is -k. If the set is rational numbers and the binary operation is multiplication, then the identity element is 1 and the inverse of any member of the set, x (other than 0) is 1/x.
What is -8(-5) as an integer?
Just multiply the two numbers. Remember that multiplying two negative numbers gives a positive result.
Additive inverse of a number?
The additive inverse of a number is that which when added to the number gives 0. If n is a number then the additive inverse of it (-n) is that number such that: n + -n = 0 For example, the additive inverse of '4' is '-4'.
