Simplify 25/100

Reduce the fraction 25/100 to its lowest terms with a complete step-by-step solution.

Answer: 25/100 = \frac{1}{4}

Step-by-Step Solution

Step 1 Identify the Fraction

We need to simplify the fraction 25/100 to its lowest terms.

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

\frac{25}{100} = ?

Step 2 Find Factors of the Numerator

First, let's find all factors of 25 (the numerator).

Factors are numbers that divide evenly into 25.

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

Step 3 Find Factors of the Denominator

Now let's find all factors of 100 (the denominator).

\text{Factors of } 100: 1, 2, 4, 5, 10, 20, 25, 50, 100

Step 4 Find the Greatest Common Factor (GCF)

The common factors of 25 and 100 are: 1, 5, 25

The Greatest Common Factor (GCF) is the largest of these: 25

We will divide both the numerator and denominator by 25.

\text{GCF}(25, 100) = 25

Step 5 Divide Both by the GCF

Divide the numerator by 25: 25 ÷ 25 = 1

Divide the denominator by 25: 100 ÷ 25 = 4

\frac{25}{100} = \frac{25 \div 25}{100 \div 25} = \frac{1}{4}

Step 6 Final Answer

The simplified fraction is 1/4

We can verify: 1 × 25 = 25 and 4 × 25 = 100 ✓

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

\frac{25}{100} = \frac{1}{4}