Simplify 8/12

Reduce the fraction 8/12 to its lowest terms with a complete step-by-step solution.

Answer: 8/12 = \frac{2}{3}

Step-by-Step Solution

Step 1 Identify the Fraction

We need to simplify the fraction 8/12 to its lowest terms.

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

\frac{8}{12} = ?

Step 2 Find Factors of the Numerator

First, let's find all factors of 8 (the numerator).

Factors are numbers that divide evenly into 8.

\text{Factors of } 8: 1, 2, 4, 8

Step 3 Find Factors of the Denominator

Now let's find all factors of 12 (the denominator).

\text{Factors of } 12: 1, 2, 3, 4, 6, 12

Step 4 Find the Greatest Common Factor (GCF)

The common factors of 8 and 12 are: 1, 2, 4

The Greatest Common Factor (GCF) is the largest of these: 4

We will divide both the numerator and denominator by 4.

\text{GCF}(8, 12) = 4

Step 5 Divide Both by the GCF

Divide the numerator by 4: 8 ÷ 4 = 2

Divide the denominator by 4: 12 ÷ 4 = 3

\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}

Step 6 Final Answer

The simplified fraction is 2/3

We can verify: 2 × 4 = 8 and 3 × 4 = 12 ✓

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

\frac{8}{12} = \frac{2}{3}