Multiplicative Inverse Of -2/3 Is.
Introduction
In mathematics, the multiplicative inverse of a number is another number that, when multiplied together, gives a product of 1. For fractions, the multiplicative inverse is also known as the reciprocal. In this article, we will explore the concept of the multiplicative inverse of a fraction, with a focus on finding the multiplicative inverse of -2/3.
What is a Multiplicative Inverse?
A multiplicative inverse is a number that, when multiplied by the original number, gives a product of 1. In other words, if we have a number 'a', its multiplicative inverse is a number 'b' such that:
a × b = 1
For example, the multiplicative inverse of 2 is 1/2, because:
2 × 1/2 = 1
Multiplicative Inverse of a Fraction
When it comes to fractions, the multiplicative inverse is also known as the reciprocal. To find the multiplicative inverse of a fraction, we simply flip the numerator and denominator. For example, the multiplicative inverse of 3/4 is 4/3.
Finding the Multiplicative Inverse of -2/3
Now, let's find the multiplicative inverse of -2/3. To do this, we simply flip the numerator and denominator:
-2/3 × ? = 1
Flipping the numerator and denominator, we get:
? = -3/2
Therefore, the multiplicative inverse of -2/3 is -3/2.
Properties of Multiplicative Inverse
The multiplicative inverse of a number has several important properties:
- The product of a number and its multiplicative inverse is always 1.
- The multiplicative inverse of a number is unique.
- The multiplicative inverse of a negative number is also negative.
Real-World Applications of Multiplicative Inverse
The concept of multiplicative inverse has several real-world applications, including:
- Finance: In finance, the multiplicative inverse is used to calculate interest rates and investment returns.
- Physics: In physics, the multiplicative inverse is used to calculate forces and energies.
- Engineering: In engineering, the multiplicative inverse is used to calculate stresses and strains in materials.
Conclusion
In conclusion, the multiplicative inverse of a fraction is another fraction that, when multiplied together, gives a product of 1. Finding the multiplicative inverse of a fraction involves simply flipping the numerator and denominator. The concept of multiplicative inverse has several important properties and real-world applications.
Frequently Asked Questions
- What is the multiplicative inverse of 2/3?
- The multiplicative inverse of 2/3 is 3/2.
- What is the multiplicative inverse of -1/2?
- The multiplicative inverse of -1/2 is -2.
- What is the multiplicative inverse of 1/4?
- The multiplicative inverse of 1/4 is 4.
References
- Khan Academy: Multiplicative Inverse of a Fraction
- Math Is Fun: Multiplicative Inverse
- Wikipedia: Multiplicative Inverse
Multiplicative Inverse of a Fraction: Q&A =============================================
Introduction
In our previous article, we explored the concept of the multiplicative inverse of a fraction, with a focus on finding the multiplicative inverse of -2/3. In this article, we will answer some frequently asked questions related to the multiplicative inverse of a fraction.
Q&A
Q: What is the multiplicative inverse of 2/3?
A: The multiplicative inverse of 2/3 is 3/2.
Q: What is the multiplicative inverse of -1/2?
A: The multiplicative inverse of -1/2 is -2.
Q: What is the multiplicative inverse of 1/4?
A: The multiplicative inverse of 1/4 is 4.
Q: How do I find the multiplicative inverse of a fraction?
A: To find the multiplicative inverse of a fraction, you simply flip the numerator and denominator. For example, the multiplicative inverse of 3/4 is 4/3.
Q: What is the difference between the multiplicative inverse and the reciprocal?
A: The multiplicative inverse and the reciprocal are the same thing. The term "reciprocal" is often used to refer to the multiplicative inverse of a fraction.
Q: Can the multiplicative inverse of a fraction be a negative number?
A: Yes, the multiplicative inverse of a fraction can be a negative number. For example, the multiplicative inverse of -2/3 is -3/2.
Q: What is the product of a number and its multiplicative inverse?
A: The product of a number and its multiplicative inverse is always 1. For example, the product of 2 and its multiplicative inverse (1/2) is 1.
Q: Can the multiplicative inverse of a fraction be a decimal number?
A: Yes, the multiplicative inverse of a fraction can be a decimal number. For example, the multiplicative inverse of 1/2 is 2, which is a decimal number.
Q: How do I use the multiplicative inverse in real-world applications?
A: The multiplicative inverse is used in various real-world applications, including finance, physics, and engineering. For example, in finance, the multiplicative inverse is used to calculate interest rates and investment returns.
Q: Can the multiplicative inverse of a fraction be a complex number?
A: Yes, the multiplicative inverse of a fraction can be a complex number. For example, the multiplicative inverse of 1 + i is 1 - i, where i is the imaginary unit.
Conclusion
In conclusion, the multiplicative inverse of a fraction is a fundamental concept in mathematics that has several important properties and real-world applications. We hope that this Q&A article has helped to clarify any questions you may have had about the multiplicative inverse of a fraction.
Frequently Asked Questions (FAQs)
- What is the multiplicative inverse of 2/3?
- The multiplicative inverse of 2/3 is 3/2.
- What is the multiplicative inverse of -1/2?
- The multiplicative inverse of -1/2 is -2.
- What is the multiplicative inverse of 1/4?
- The multiplicative inverse of 1/4 is 4.
- How do I find the multiplicative inverse of a fraction?
- To find the multiplicative inverse of a fraction, you simply flip the numerator and denominator.
- What is the difference between the multiplicative inverse and the reciprocal?
- The multiplicative inverse and the reciprocal are the same thing.
References
- Khan Academy: Multiplicative Inverse of a Fraction
- Math Is Fun: Multiplicative Inverse
- Wikipedia: Multiplicative Inverse