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Chapter 1: Problem 80

Find the reciprocal of each number, if it exists. $$ -\frac{13}{11} $$

Short Answer

Expert verified
The reciprocal of \(-\frac{13}{11}\) is \(-\frac{11}{13}\).

Step by step solution

01

Understand Reciprocals

The reciprocal of a number is 1 divided by that number. If the original number is a fraction, its reciprocal is obtained by swapping the numerator and the denominator.
02

Identify the Given Fraction

The given number is \(-\frac{13}{11}\). Identify the numerator (top part) and the denominator (bottom part) of the fraction.
03

Swap Numerator and Denominator

To find the reciprocal, swap the numerator and the denominator. This changes the fraction from \(-\frac{13}{11}\) to \(-\frac{11}{13}\).
04

Interpret the Negative Sign

Since the original number is negative, the reciprocal will also be negative. Therefore, the reciprocal of \(-\frac{13}{11}\) is \(-\frac{11}{13}\).

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Key Concepts

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

fraction
A fraction represents a part of a whole and is composed of two parts: the numerator and the denominator. The numerator is the top part of the fraction and indicates how many parts we have.
The denominator is the bottom part and shows how many equal parts the whole is divided into.
For example, in the fraction \(\frac{13}{11}\), 13 is the numerator and 11 is the denominator.
Fractions can represent values less than 1, equal to 1, or greater than 1, depending on the relationship between the numerator and the denominator.
numerator and denominator
The numerator and denominator are the two main components of a fraction. The numerator, located on the top, tells us how many parts we are considering.
The denominator, found on the bottom, tells us the total number of equal parts in the whole.
When finding the reciprocal of a fraction, you simply swap the numerator and the denominator.
For example, the reciprocal of \-\(\frac{13}{11}\) would involve switching the numerator (13) and the denominator (11), resulting in \-\(\frac{11}{13}\).
This is a crucial step to remember when working with fractions, as it helps in various mathematical operations and problem-solving.
negative numbers
Negative numbers are numbers less than zero and are represented with a minus sign (鈭�).
They are found to the left of zero on the number line. When dealing with fractions, if either the numerator or the denominator is negative, the entire fraction is negative.
In our example, \-\(\frac{13}{11}\), the fraction is negative because the numerator is negative.
When we find the reciprocal, the negative sign stays with the fraction, so the reciprocal of \-\(\frac{13}{11}\) is \-\(\frac{11}{13}\).
Understanding how to handle negative numbers when finding reciprocals ensures accuracy in mathematical operations.

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