The reciprocal of 6/2 is 3/1.

Verified step by step guidance

1. Understand the concept of a reciprocal: The reciprocal of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \).
2. Identify the given fraction: The fraction provided is \( \frac{6}{2} \).
3. Find the reciprocal: Swap the numerator and the denominator of \( \frac{6}{2} \) to get its reciprocal.
4. Write the reciprocal: The reciprocal of \( \frac{6}{2} \) is \( \frac{2}{6} \).
5. Simplify the reciprocal: Simplify \( \frac{2}{6} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

Key Concepts

Reciprocal

The reciprocal of a number is defined as 1 divided by that number. For a fraction, the reciprocal is obtained by swapping its numerator and denominator. For example, the reciprocal of 6/2 is 2/6, which simplifies to 1/3. Understanding reciprocals is essential for operations involving division and fractions.

Fractions

A fraction represents a part of a whole and consists of a numerator (the top number) and a denominator (the bottom number). In the case of 6/2, 6 is the numerator and 2 is the denominator, indicating that 6 is divided into 2 equal parts. Mastery of fractions is crucial for performing arithmetic operations and understanding ratios.

Simplification

Simplification involves reducing a fraction to its simplest form, where the numerator and denominator have no common factors other than 1. For instance, the fraction 6/2 simplifies to 3/1, as both 6 and 2 can be divided by 2. This concept is vital for making calculations easier and clearer in algebra.