Simplify 12/16

Reduce the fraction 12/16 to its lowest terms with a complete step-by-step solution.

Answer: 12/16 = \frac{3}{4}

Step-by-Step Solution

Step 1 Identify the Fraction

We need to simplify the fraction 12/16 to its lowest terms.

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

\frac{12}{16} = ?

Step 2 Find Factors of the Numerator

First, let's find all factors of 12 (the numerator).

Factors are numbers that divide evenly into 12.

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

Step 3 Find Factors of the Denominator

Now let's find all factors of 16 (the denominator).

\text{Factors of } 16: 1, 2, 4, 8, 16

Step 4 Find the Greatest Common Factor (GCF)

The common factors of 12 and 16 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}(12, 16) = 4

Step 5 Divide Both by the GCF

Divide the numerator by 4: 12 ÷ 4 = 3

Divide the denominator by 4: 16 ÷ 4 = 4

\frac{12}{16} = \frac{12 \div 4}{16 \div 4} = \frac{3}{4}

Step 6 Final Answer

The simplified fraction is 3/4

We can verify: 3 × 4 = 12 and 4 × 4 = 16 ✓

3 and 4 have no common factors, so this is fully simplified.

\frac{12}{16} = \frac{3}{4}