Simplify 6/9

Reduce the fraction 6/9 to its lowest terms with a complete step-by-step solution.

Answer: 6/9 = \frac{2}{3}

Step-by-Step Solution

Step 1 Identify the Fraction

We need to simplify the fraction 6/9 to its lowest terms.

A fraction is in lowest terms when the numerator and denominator have no common factors other than 1.

\frac{6}{9} = ?

Step 2 Find Factors of the Numerator

First, let's find all factors of 6 (the numerator).

Factors are numbers that divide evenly into 6.

\text{Factors of } 6: 1, 2, 3, 6

Step 3 Find Factors of the Denominator

Now let's find all factors of 9 (the denominator).

\text{Factors of } 9: 1, 3, 9

Step 4 Find the Greatest Common Factor (GCF)

The common factors of 6 and 9 are: 1, 3

The Greatest Common Factor (GCF) is the largest of these: 3

We will divide both the numerator and denominator by 3.

\text{GCF}(6, 9) = 3

Step 5 Divide Both by the GCF

Divide the numerator by 3: 6 ÷ 3 = 2

Divide the denominator by 3: 9 ÷ 3 = 3

\frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}

Step 6 Final Answer

The simplified fraction is 2/3

We can verify: 2 × 3 = 6 and 3 × 3 = 9 ✓

2 and 3 have no common factors, so this is fully simplified.

\frac{6}{9} = \frac{2}{3}