What is the multiplicative identity of 1/2?
The multiplicative identity of a real number is 1. When we multiply 1 by any real number then we get the same number. Examples are 3 x 1 = 3, -9 x 1 = -9, ½ x 1 = ½.
Is 0.5 the multiplicative inverse of 1 2?
Answer: multiplicative inverse of 1/2 is 2/1 or 2. because in multiplicative inverse we have to write the reciprocal of the fraction that means in reverse order. but not to divide it.
What is multiplicative inverse of a fraction?
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number.
What is the multiplicative inverse of /- 5?
So, the multiplicative inverse of -5 is -1 / 5. Therefore, the solution is 74/7.
What is the multiplicative inverse of 1 2?
The multiplicative inverse of 1/2 is 2. To determine the multiplicative inverse of a number, we use the following rule: The multiplicative inverse of a number a/b is b/a.
How to find multiplicative inverse?
The multiplicative inverse of a number is defined as a number that when multiplied by the original number gives the product as 1. The multiplicative inverse of ‘a’ is denoted by a–1 or 1/a. In other words, when the product of two numbers is 1, they are said to be multiplicative inverses of each other.
Is 0.2 the multiplicative inverse of?
The multiplicative inverse of any number is its reciprocal. Therefore, the multiplicative inverse of 0.2 is 1/0.2.
What is the multiplicative inverse of 6?
Multiplicative inverse of a natural number For example, the multiplicative inverse of 6 is 1/6 or 6-1. The multiplicative inverse of a positive natural number will be positive only. For example, the multiplicative inverse of 1/7 is 7.
What is the multiplicative inverse of 10?
Answer and Explanation: The multiplicative inverse of 10 is 1/10. In general, the multiplicative inverse of a number is the reciprocal of that number.
Is the multiplicative inverse of 2?
The multiplicative inverse of 2 is 1/2, which is written as one-half. To find the multiplicative inverse of a whole number, simply form a fraction with a numerator of 1 and the original number as the denominator.
How to invert a fraction?
To find the inverse of a fraction, switch the numerator and the denominator. If the fraction is a whole number, then it can be written as the whole number over 1, and its inverse is 1 over the whole number.
What is the multiplicative inverse of /- 8?
The multiplicative inverse of a natural number -Y is -Y⁻¹ or 1/-X. For example, the multiplicative inverse of -8 is 1/-8 because -8×1/-8=1.
Is 0.5 the multiplicative inverse of 2?
The multiplicative inverse of a number is the number which when multiplied to the number gives 1. Here, 0.5*2 = 1, Hence 0.5 is the multiplicative inverse of 2. Usually the reciprocal of a number will be its multiplicative inverse. ie, herein case of 2, the multiplicative inverse will be 1/2 = 0.5.
What is 4 multiplicative inverse?
The multiplicative inverse of 4 is 1/4. (One-fourth is 1/4 in written form.) In order to find the multiplicative inverse of a number, just make a fraction with 1 on top and the number you want to find the multiplicative inverse of on the bottom. So, for example, the multiplicative inverse of 15 is 1/15.
What is the multiplicative inverse of 7?
The multiplicative inverse of 7 is 1/7. A number’s multiplicative inverse is its reciprocal. To get the multiplicative inverse of a number, just put that number as the denominator of a fraction with one as the numerator. In other words, 1/7 is the multiplicative inverse of 7.
What is the multiplicative inverse of 5?
The multiplicative inverse of 5 is 1/5. The multiplicative inverse property states that any number a multiplies with its reciprocal, 1/a, to give 1. Therefore, the multiplicative inverse of a number a is 1/a. Applying this property to the number 5, we get that the multiplicative inverse of 5 is 1/5.
What is the inverse of 1/4?
Reciprocal is a number that when multiplied to the given number gives the product 1. To find the reciprocal of a fraction, interchange the numerator and denominator. Hence, reciprocal of 1/4 is 4. Note: Reciprocal is another word for the multiplicative inverse.
What is the multiplicative inverse of 12?
Answer and Explanation: The multiplicative inverse of 12 is 1/12. In general, we have the following rule for finding the multiplicative inverse of a number. The multiplicative inverse of a number, a/b, is b/a.
What is the multiplicative inverse of 11?
Another name for it is the reciprocal of the number. In symbols n * 1/n = 1. If n = 2 Its multiplicative inverse is 1/2 so that 2 * 1/2 = 1. The multiplicative inverse of 11 is 1/11 so that 11 * 1/11 = 1.
What is the multiplicative inverse of 3?
Consider the number 3. The multiplicative inverse property gives that the multiplicative inverse of 3 is equal to its reciprocal, 1/3, and this is verified as follows: 3 × (1/3) = (3 × 1) / 3 = 3 / 3 = 1.
Is 0.3 the multiplicative inverse of 3?
0.3 can be written as 3/10. We know that, 313 3 1 3 can be written as 10/3. Yes, 0.3 is the multiplicative inverse of 313 3 1 3 since 3/10 × 10/3 is equal to 1.
What is the multiplicative inverse of 1 0?
Zero doesn’t have a reciprocal because it is undefined. Thus looking into each option we can figure out the pair whose multiplicative inverse is the same as that of the number. In (1, 0) = In multiplicative inverse of 1 is 1 and zero’s reciprocal is undefined.
What is the multiplicative inverse of 1 6?
Multiplicative inverse of a number, a = 1/a. So, in this way, multiplicative inverse of 1/6 is 1/(1/6) = 6. Example 3: Find the multiplicative inverse of 81.
What is the inverse of 2?
Answer and Explanation: The additive inverse of 2 is -2. In general, the additive inverse of a number, x, is -x because of the following: x + (-x) = x – x = 0.
What is the multiplicative inverse of 5 4 3 4 7 2?
To find the multiplicative inverse of a number or expression, we simply need to take the reciprocal of it. Therefore, the multiplicative inverse of (5/4)^3 × (4/7)^2 is 392/250.
What is the multiplicative inverse of the minus 13?
Answer: Multiplicative inverse of -13 = 1/-13.
What is the multiplicative identity of negative 1?
For positive integers, multiplicative identity is 1 and for negative integers, multiplicative identity is 1.
What is the multiplicative identity of a fraction?
The multiplicative identity of a rational number is 1 as the product of a number and its multiplicative inverse is 1. For example, the multiplicative inverse of the rational number 4/5 is 5/4, their product is (4/5). (5/4) = 1.
Is the multiplicative inverse of 2?
The multiplicative inverse of 2 is 1/2, which is written as one-half. To find the multiplicative inverse of a whole number, simply form a fraction with a numerator of 1 and the original number as the denominator.
What is the formula for the multiplicative identity?
The multiplicative identity formula is expressed as a × 1 = a, where ‘a’ is any real number. This shows that when any number is multiplied by 1, the product is the number itself. For example, if we multiply 65 with 1 we get 65 as the product.
What is multiplicative inverse calculator?
What is the multiplicative inverse of a reciprocal number?
When a number is multiplied by its own multiplicative inverse?
What is the multiplicative inverse of a 2 x 1/3?
Understanding Multiplicative Inverses
First, let’s break down what a multiplicative inverse even is. It’s simply a number that, when multiplied by the original number, gives you 1. Think of it like finding a partner in crime, but instead of pulling off a heist, you’re aiming for a specific mathematical outcome.
Here’s the official definition:
The multiplicative inverse of a number ‘a’ (where ‘a’ is not equal to zero) is a number denoted by 1/a that satisfies the equation:
a * (1/a) = 1
Example:
The multiplicative inverse of 5 is 1/5 because 5 * (1/5) = 1.
Finding the Multiplicative Inverse of 1/2
Now, let’s get back to our main event – 1/2. Finding its multiplicative inverse means we’re looking for a number that, when multiplied by 1/2, will give us 1.
The easiest way to find the multiplicative inverse of a fraction is to simply flip it over. So, the multiplicative inverse of 1/2 is 2/1, which simplifies to 2.
Let’s confirm this:
(1/2) * 2 = 1
And there you have it! The multiplicative inverse of 1/2 is 2.
Beyond the Basics: Understanding Why This Works
Let’s explore why flipping the fraction works.
Think of 1/2 as a fraction representing a division operation: 1 divided by 2. To find its multiplicative inverse, we’re essentially trying to reverse this division operation.
When you multiply 1/2 by 2, you’re effectively doing:
(1 / 2) * 2 = (1 / 2) * (2 / 1)
The two ‘2’s in the denominator and numerator cancel each other out, leaving you with:
(1 * 1) / (2 * 1) = 1/1 = 1
This process essentially undoes the original division, resulting in 1.
Key Concepts Related to Multiplicative Inverses
Here are some key concepts related to multiplicative inverses:
Zero: Zero doesn’t have a multiplicative inverse. You can’t find any number that, when multiplied by zero, results in one.
Reciprocal: The multiplicative inverse is also known as the reciprocal of a number. So, the reciprocal of 1/2 is 2.
Identity Element: In multiplication, 1 is the identity element. When you multiply any number by 1, the number remains unchanged. The concept of the multiplicative inverse is closely related to the identity element.
Real-World Applications of Multiplicative Inverses
Multiplicative inverses are not just abstract mathematical concepts; they have real-world applications in various fields.
Solving Equations: Multiplicative inverses are crucial for solving algebraic equations. For example, to solve an equation like 2x = 8, you would multiply both sides by 1/2, the multiplicative inverse of 2, to isolate ‘x’.
Computer Programming: Multiplicative inverses are used in computer programming for tasks like matrix inversion and solving systems of linear equations.
Engineering: In fields like electrical engineering, multiplicative inverses are used in calculations involving resistance, capacitance, and inductance.
FAQs
Q: What is the multiplicative inverse of a whole number?
A: The multiplicative inverse of a whole number is simply its reciprocal, written as 1 over the whole number. For example, the multiplicative inverse of 3 is 1/3.
Q: Can a number have more than one multiplicative inverse?
A: No, each number (except for zero) has only one unique multiplicative inverse.
Q: What is the multiplicative inverse of a negative number?
A: The multiplicative inverse of a negative number is its reciprocal, but with the opposite sign. For example, the multiplicative inverse of -4 is -1/4.
Q: Why is zero excluded from having a multiplicative inverse?
A: Zero doesn’t have a multiplicative inverse because any number multiplied by zero is always zero, not one.
Let me know if you have any more questions about multiplicative inverses. I’m here to help you unlock the secrets of this fascinating mathematical concept!
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