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Chapter 10: Problem 23

Find the reciprocal. $$ 13 $$

Short Answer

Expert verified
The reciprocal of 13 is \( \frac{1}{13} \).

Step by step solution

01

- Understand the Concept of a Reciprocal

The reciprocal of a number is defined as 1 divided by that number. This means if you have a number 'a', the reciprocal is given by \( \frac{1}{a} \).
02

- Write the Given Number

Write down the given number, which in this case is 13.
03

- Calculate the Reciprocal

To find the reciprocal, calculate \( \frac{1}{13} \).
04

- Confirm the Result

Ensure that the calculation is correct. The reciprocal of 13 is \( \frac{1}{13} \).

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Key Concepts

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

headline of the respective core concept
In mathematics, understanding the basics is crucial to solving more complex problems. The concept of a reciprocal is fundamental in many areas, including algebra and calculus. The reciprocal of a number is essentially what you multiply that number by to get the product of 1. For example, if you have the number 13, the reciprocal is found by dividing 1 by 13, resulting in \( \frac{1}{13} \). This concept holds true for all non-zero numbers, as these are the only numbers that have reciprocals.
  • Basic understanding of reciprocal: 1 divided by the number.
  • Only non-zero numbers have reciprocals.
  • It's a core concept in algebra and higher mathematics.
Good grasp of reciprocals can make other mathematical concepts easier to handle.
headline of the respective core concept
Fractions represent parts of a whole and are written as one number over another, like \( \frac{1}{13} \) in this case. Understanding fractions is essential since reciprocals themselves are expressed as fractions. When dealing with fractions:
  • The numerator (top number) represents how many parts we have.
  • The denominator (bottom number) shows how many parts make a whole.
  • A fraction less than 1 is a proper fraction, while more than 1 is an improper fraction.
To find the reciprocal of a whole number, convert the whole number to a fraction by placing it over 1, then flip the numerator and the denominator. For instance, 13 can be written as \( \frac{13}{1} \), and its reciprocal is \( \frac{1}{13} \).
headline of the respective core concept
Division is the process of splitting a number into equal parts. When we talk about finding a reciprocal, we're essentially performing division since a reciprocal is found by dividing 1 by the given number. In division:
  • The number being divided is the dividend.
  • The number you are dividing by is the divisor.
  • The result of the division is called the quotient.
So, to find the reciprocal of 13, we treat it as dividing 1 (the dividend) by 13 (the divisor) to get the quotient of \( \frac{1}{13} \). This process is a fundamental part of learning division and reciprocals.

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