What is the reciprocal of 20 as a fraction?
The Correct Answer and Explanation is :
The reciprocal of 20, expressed as a fraction, is ( \frac{1}{20} ).
Explanation:
The concept of a reciprocal refers to the inverse of a number. In mathematical terms, the reciprocal of a number is found by flipping the fraction or dividing 1 by that number. If a number is represented as a fraction, say ( \frac{a}{b} ), then its reciprocal is ( \frac{b}{a} ). For a whole number, like 20, you can express it as a fraction by writing it as ( \frac{20}{1} ). The reciprocal of ( \frac{20}{1} ) is ( \frac{1}{20} ), as the numerator and denominator are swapped.
Here’s a breakdown:
- Definition: The reciprocal of a number ( x ) is ( \frac{1}{x} ). This operation “flips” the number or fraction.
- Example:
- For a number like 5, its reciprocal is ( \frac{1}{5} ).
- For a number like 20, represented as ( \frac{20}{1} ), its reciprocal is ( \frac{1}{20} ).
- Mathematical Property: When you multiply a number by its reciprocal, the result is always 1:
[
20 \times \frac{1}{20} = 1
]
This holds true for any non-zero number, meaning every non-zero number has a reciprocal. If a number is 0, it does not have a reciprocal, since division by zero is undefined. - Real-world Applications: Reciprocals are commonly used in various fields, including algebra, calculus, and physics. For example, the reciprocal of a resistance in electronics can determine conductance. Reciprocals also appear in formulas for rates, such as speed and time.
In summary, the reciprocal of 20 as a fraction is ( \frac{1}{20} ), and this concept plays an important role in various areas of mathematics and practical applications.