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Chapter 7: Problem 356

In the following exercises, find the multiplicative inverse. $$ \frac{1}{10} $$

Short Answer

Expert verified
The multiplicative inverse of \( \frac{1}{10} \) is 10.

Step by step solution

01

- Understand the Multiplicative Inverse

The multiplicative inverse of a number is a value that, when multiplied with the original number, results in 1. Mathematically, for a number \( a \), its multiplicative inverse is \( \frac{1}{a} \).
02

- Identify the Given Number

In this exercise, the given number is \( \frac{1}{10} \).
03

- Calculate the Multiplicative Inverse

To find the multiplicative inverse, take the reciprocal of the given number. Thus, the multiplicative inverse of \( \frac{1}{10} \) is \( 10 \).
04

- Verify the Result

Multiply the original number by its multiplicative inverse: \( \frac{1}{10} \times 10 = 1 \). Therefore, the result is verified.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Prealgebra
Prealgebra is a foundational branch of mathematics that prepares students for Algebra. It includes basic arithmetic like addition, subtraction, multiplication, and division. Prealgebra helps build an understanding of number properties and simple algebraic expressions. A key concept in prealgebra is understanding how numbers interact, especially through operations like finding the multiplicative inverse. In this exercise, understanding the multiplicative inverse is crucial. This concept helps students see how numbers can be manipulated to maintain balance in equations.
Reciprocal
A reciprocal is a number that, when multiplied by the original number, gives a product of 1. Think of it as flipping the number upside down. For example, the reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\). In the case of the given exercise with the number \(\frac{1}{10}\), the reciprocal is 10. Here鈥檚 the step-by-step approach:
1. Identify the given number: \(\frac{1}{10}\)
2. Flip the numerator and denominator: \(10\) becomes the reciprocal of \(\frac{1}{10}\)
This simple flipping process is central to finding the multiplicative inverse, making the reciprocal concept vital in prealgebra topics.
Verification of Results
Verification of results is an important step in mathematical problem-solving to ensure the answer is correct. By verifying, students confirm the accuracy and maintain mathematical integrity. Here鈥檚 how verification works with the multiplicative inverse:
1. Multiply the original number by its reciprocal: In this case, \(\frac{1}{10} \times 10 \)
2. Simplify the multiplication result: \(\frac{10}{10} \)= 1
Since the product is indeed 1, it verifies that 10 is the correct multiplicative inverse of \(\frac{1}{10}\)
Verification confirms that steps taken to solve the problem are correct, giving students confidence in their mathematical skills.

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