Simplify 15/20

Reduce the fraction 15/20 to its lowest terms with a complete step-by-step solution.

Answer: 15/20 = \frac{3}{4}

Step-by-Step Solution

Step 1 Identify the Fraction

We need to simplify the fraction 15/20 to its lowest terms.

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

\frac{15}{20} = ?

Step 2 Find Factors of the Numerator

First, let's find all factors of 15 (the numerator).

Factors are numbers that divide evenly into 15.

\text{Factors of } 15: 1, 3, 5, 15

Step 3 Find Factors of the Denominator

Now let's find all factors of 20 (the denominator).

\text{Factors of } 20: 1, 2, 4, 5, 10, 20

Step 4 Find the Greatest Common Factor (GCF)

The common factors of 15 and 20 are: 1, 5

The Greatest Common Factor (GCF) is the largest of these: 5

We will divide both the numerator and denominator by 5.

\text{GCF}(15, 20) = 5

Step 5 Divide Both by the GCF

Divide the numerator by 5: 15 ÷ 5 = 3

Divide the denominator by 5: 20 ÷ 5 = 4

\frac{15}{20} = \frac{15 \div 5}{20 \div 5} = \frac{3}{4}

Step 6 Final Answer

The simplified fraction is 3/4

We can verify: 3 × 5 = 15 and 4 × 5 = 20 ✓

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

\frac{15}{20} = \frac{3}{4}