Simplify 18/24

Reduce the fraction 18/24 to its lowest terms with a complete step-by-step solution.

Answer: 18/24 = \frac{3}{4}

Step-by-Step Solution

Step 1 Identify the Fraction

We need to simplify the fraction 18/24 to its lowest terms.

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

\frac{18}{24} = ?

Step 2 Find Factors of the Numerator

First, let's find all factors of 18 (the numerator).

Factors are numbers that divide evenly into 18.

\text{Factors of } 18: 1, 2, 3, 6, 9, 18

Step 3 Find Factors of the Denominator

Now let's find all factors of 24 (the denominator).

\text{Factors of } 24: 1, 2, 3, 4, 6, 8, 12, 24

Step 4 Find the Greatest Common Factor (GCF)

The common factors of 18 and 24 are: 1, 2, 3, 6

The Greatest Common Factor (GCF) is the largest of these: 6

We will divide both the numerator and denominator by 6.

\text{GCF}(18, 24) = 6

Step 5 Divide Both by the GCF

Divide the numerator by 6: 18 ÷ 6 = 3

Divide the denominator by 6: 24 ÷ 6 = 4

\frac{18}{24} = \frac{18 \div 6}{24 \div 6} = \frac{3}{4}

Step 6 Final Answer

The simplified fraction is 3/4

We can verify: 3 × 6 = 18 and 4 × 6 = 24 ✓

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

\frac{18}{24} = \frac{3}{4}