6/20 simplified

Simplifying the Fraction $\frac{6}{20}$

Answer:

The simplified form of $\frac{6}{20}$ is $\frac{3}{10}$.

Method: Simplification by Finding the Greatest Common Divisor (GCD)

To simplify a fraction, we need to divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of two numbers is the largest number that divides both of them without leaving a remainder.

Step-by-Step Calculation:

1. Identify the Numerator and Denominator:

   • Numerator: 6
   • Denominator: 20

2. Find the GCD of 6 and 20:

   • The divisors of 6 are: 1, 2, 3, 6
   • The divisors of 20 are: 1, 2, 4, 5, 10, 20
   • The common divisors of 6 and 20 are: 1, 2
   • The greatest common divisor is 2.

3. Divide Both Numerator and Denominator by the GCD:

   • $\frac{6 \div 2}{20 \div 2} = \frac{3}{10}$

4. Write the Simplified Fraction:

   • The simplified fraction is $\frac{3}{10}$.

Verification:

To ensure that the fraction has been simplified correctly, we can check that:

• The numerator and denominator have no common divisors other than 1.
• No further simplification is possible.

Since 3 and 10 have no common divisors other than 1, the fraction $\frac{3}{10}$ is indeed in its simplest form.

Related Knowledge Points:

• Greatest Common Divisor (GCD): The largest positive integer that divides two or more integers without a remainder.
• Simplifying Fractions: The process of reducing the numerator and denominator of a fraction to their smallest possible values while keeping the value of the fraction unchanged.
• Divisors: Numbers that divide another number completely without leaving a remainder.

Detailed Explanation:

When simplifying fractions, it is important to find the GCD of the numerator and denominator. This ensures that the fraction is reduced to its simplest form. In the case of $\frac{6}{20}$, the GCD is 2, which means both the numerator and the denominator can be divided by 2 to reduce the fraction.

The simplified fraction $\frac{3}{10}$ represents the same value as $\frac{6}{20}$ but with smaller, more manageable numbers. Simplifying fractions makes them easier to work with, especially when performing arithmetic operations such as addition, subtraction, multiplication, or division with other fractions.

In conclusion, the fraction $\frac{6}{20}$ simplifies to $\frac{3}{10}$ by dividing both the numerator and the denominator by their GCD, which is 2. This process is a fundamental skill in mathematics that aids in the clear and concise representation of numerical values.