1. What is a Fraction Reciprocal?

The reciprocal of a fraction is obtained by interchanging the numerator and denominator. For any non-zero fraction a/b, its reciprocal is b/a. The product of a fraction and its reciprocal is always 1.

2. How Does the Calculator Work?

The calculator uses the reciprocal formula:

Where:

• \( a \) — Numerator of the original fraction
• \( b \) — Denominator of the original fraction

Explanation: The calculator first swaps the numerator and denominator, then simplifies the resulting fraction to its lowest terms.

3. Importance of Reciprocals

Details: Reciprocals are fundamental in mathematics, especially in division of fractions, solving equations, and working with rational expressions. They are essential in algebra, calculus, and many real-world applications.

4. Using the Calculator

Tips: Enter any non-zero numerator and denominator. The calculator will show the reciprocal in both fractional and decimal form. The fraction will be simplified to its lowest terms.

5. Frequently Asked Questions (FAQ)

Q1: What's the reciprocal of a whole number?
A: For any whole number n, the reciprocal is 1/n. For example, the reciprocal of 5 is 1/5.

Q2: What's the reciprocal of zero?
A: Zero has no reciprocal because division by zero is undefined.

Q3: What's the reciprocal of a mixed number?
A: First convert the mixed number to an improper fraction, then find its reciprocal.

Q4: How are reciprocals used in division?
A: Dividing by a fraction is the same as multiplying by its reciprocal (a/b ÷ c/d = a/b × d/c).

Q5: What's the reciprocal of a reciprocal?
A: The reciprocal of a reciprocal gives you back the original number (1/(1/x) = x).