Simplify 10/15

Reduce the fraction 10/15 to its lowest terms with a complete step-by-step solution.

Answer: 10/15 = \frac{2}{3}

Step-by-Step Solution

Step 1 Identify the Fraction

We need to simplify the fraction 10/15 to its lowest terms.

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

\frac{10}{15} = ?

Step 2 Find Factors of the Numerator

First, let's find all factors of 10 (the numerator).

Factors are numbers that divide evenly into 10.

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

Step 3 Find Factors of the Denominator

Now let's find all factors of 15 (the denominator).

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

Step 4 Find the Greatest Common Factor (GCF)

The common factors of 10 and 15 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}(10, 15) = 5

Step 5 Divide Both by the GCF

Divide the numerator by 5: 10 ÷ 5 = 2

Divide the denominator by 5: 15 ÷ 5 = 3

\frac{10}{15} = \frac{10 \div 5}{15 \div 5} = \frac{2}{3}

Step 6 Final Answer

The simplified fraction is 2/3

We can verify: 2 × 5 = 10 and 3 × 5 = 15 ✓

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

\frac{10}{15} = \frac{2}{3}