Simplify 20/25

Reduce the fraction 20/25 to its lowest terms with a complete step-by-step solution.

Answer: 20/25 = \frac{4}{5}

Step-by-Step Solution

Step 1 Identify the Fraction

We need to simplify the fraction 20/25 to its lowest terms.

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

\frac{20}{25} = ?

Step 2 Find Factors of the Numerator

First, let's find all factors of 20 (the numerator).

Factors are numbers that divide evenly into 20.

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

Step 3 Find Factors of the Denominator

Now let's find all factors of 25 (the denominator).

\text{Factors of } 25: 1, 5, 25

Step 4 Find the Greatest Common Factor (GCF)

The common factors of 20 and 25 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}(20, 25) = 5

Step 5 Divide Both by the GCF

Divide the numerator by 5: 20 ÷ 5 = 4

Divide the denominator by 5: 25 ÷ 5 = 5

\frac{20}{25} = \frac{20 \div 5}{25 \div 5} = \frac{4}{5}

Step 6 Final Answer

The simplified fraction is 4/5

We can verify: 4 × 5 = 20 and 5 × 5 = 25 ✓

4 and 5 have no common factors, so this is fully simplified.

\frac{20}{25} = \frac{4}{5}