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Chapter 4: Problem 133

Find the reciprocal. \(-19\)

Short Answer

Expert verified
The reciprocal of -19 is \( \frac{1}{-19} \).

Step by step solution

01

- Understand Reciprocals

The reciprocal of a number is defined as 1 divided by that number. Recognize that the reciprocal of any non-zero number 'a' is \( \frac{1}{a} \).
02

- Apply the Definition

To find the reciprocal of \(-19\), use the definition of a reciprocal. This means you need to calculate \( \frac{1}{-19} \).
03

- Simplify the Expression

Since \( \frac{1}{-19} \) is already in its simplest form, the result can be left as it is. The reciprocal of \(-19\) is \( \frac{1}{-19} \).

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Key Concepts

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

Understanding Reciprocals
Reciprocals are a fundamental concept in prealgebra that you will encounter frequently. When we talk about the reciprocal of a number, we're referring to dividing 1 by that number. For example, for any non-zero number 'a', the reciprocal is written as \( \frac{1}{a} \).
Here's how you find a reciprocal:
  • If you have a whole number, like 5, its reciprocal is \ \frac{1}{5} \.
  • If you have a fraction, such as \ \frac{3}{4} \, its reciprocal is simply flipping the numerator and the denominator to get \ \frac{4}{3} \.
  • Always remember, zero does not have a reciprocal because division by zero is undefined.
Working with Negative Numbers
Negative numbers can be a challenging concept initially, but with practice, they become much easier to handle. When finding the reciprocal of a negative number, like \ -19 \ in our exercise, the negative sign remains in place.
So, the reciprocal of \ -19 \ is formulated as follows: \( \frac{1}{-19} \).
Let's break this down:
  • The negative sign doesn't disappear; it stays with the number.
  • When dividing 1 by a negative number, the result will always be a negative fraction.
Simplifying Fractions
Simplifying fractions means making them as simple as possible, usually by dividing the numerator and the denominator by their greatest common divisor. However, in the case of reciprocals, sometimes the fraction is already in its simplest form, like \( \frac{1}{-19} \).
When simplifying:
  • Check if the numerator and the denominator can be divided by the same number.
  • If they can鈥檛 be divided by the same number besides 1, then the fraction is already in its simplest form.
In our case, \( \frac{1}{-19} \) is already simplified because the numerator is 1, and 1 doesn't have any divisors other than itself.

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Most popular questions from this chapter

In the following exercises, simplify. $$ \frac{5}{20} $$

In the following exercises, simplify. $$ -\frac{3}{13}+\left(-\frac{4}{13}\right) $$

In the following exercises, subtract. $$\frac{8}{11}-\frac{6}{11}$$

In the following exercises, subtract. $$\frac{11}{15}-\frac{5}{15}-\left(-\frac{2}{15}\right)$$

In the following exercises, simplify. $$ \frac{3}{5} \cdot 15 $$
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