1. What is a Reciprocal of a Fraction?

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. Multiplying a fraction by its reciprocal always gives 1.

2. How Does the Calculator Work?

The calculator uses the reciprocal formula:

Where:

• \( a \) — Numerator (any real number)
• \( b \) — Denominator (any non-zero real number)

Explanation: The calculator simply swaps the numerator and denominator and optionally simplifies the resulting fraction.

3. Importance of Reciprocals

Details: Reciprocals are fundamental in mathematics, especially in division of fractions, solving equations, and working with ratios and proportions.

4. Using the Calculator

Tips: Enter any numerator and any non-zero denominator. The calculator will show the reciprocal and its simplified form if possible.

5. Frequently Asked Questions (FAQ)

Q1: What's the reciprocal of a whole number?
A: A whole number n can be written as n/1, so its reciprocal is 1/n.

Q2: What's the reciprocal of zero?
A: Zero (0/1) has no reciprocal because division by zero is undefined.

Q3: What's the reciprocal of a mixed number?
A: First convert to improper fraction (e.g., 2¾ = 11/4), then take reciprocal (4/11).

Q4: What's the reciprocal of a negative fraction?
A: The reciprocal keeps the same sign. Reciprocal of -a/b is -b/a.

Q5: How are reciprocals used in real life?
A: They're used in calculating parallel resistances, harmonic means, converting units, and solving rate problems.