How to Simplify Fractions? (+FREE Worksheet!)

Simplifying fractions is a core skill for the GED Mathematical Reasoning test. A fraction is in simplest form (also called lowest terms) when the numerator and denominator share no common factor other than 1. Knowing how to reduce fractions quickly will help you on every section of GED Math that involves fractions, ratios, and proportions.

What Does It Mean to Simplify a Fraction?

Simplifying a fraction means dividing both the numerator (top number) and the denominator (bottom number) by their Greatest Common Factor (GCF) — the largest number that divides evenly into both. The result is an equivalent fraction in lowest terms. For example, \(\color{blue}{\frac{12}{18}}\) simplifies to \(\color{blue}{\frac{2}{3}}\) because the GCF of 12 and 18 is 6.

GED Math for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the GED Math Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.33 out of 5 based on 105 customer ratings

Satisfied 91 Students

How to Simplify a Fraction

Method 1: Find the GCF and divide

List the factors of the numerator and denominator, identify the greatest common factor, then divide both by it.

• Simplify \(\color{blue}{\frac{8}{24}}\): factors of 8 are 1, 2, 4, 8; factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. \(\color{blue}{\text{ GCF } = 8}\). So \(\color{blue}{8 \div 8 = 1}\) and \(\color{blue}{24 \div 8 = 3}\). Result: \(\color{blue}{\frac{1}{3}}\).

Method 2: Divide by small primes repeatedly

If the GCF is not obvious, divide numerator and denominator by 2, then 3, then 5, and so on until they share no common factors.

• Simplify \(\color{blue}{\frac{36}{48}}\): both even, divide by 2 → \(\color{blue}{\frac{18}{24}}\); both even again, divide by 2 → \(\color{blue}{\frac{9}{12}}\); both divisible by 3, divide by 3 → \(\color{blue}{\frac{3}{4}}\). Result: \(\color{blue}{\frac{3}{4}}\).

Step-by-Step Summary

1. Find the GCF of the numerator and denominator.
2. Divide both the numerator and denominator by the GCF.
3. Check: the new numerator and denominator should share no common factors (other than 1).
4. If the fraction is negative, keep the negative sign in the numerator or in front of the fraction.

Watch: Simplifying Fractions (Video Lesson)

Math Antics demonstrates how to find the GCF and reduce fractions to lowest terms:

Simplifying Fractions – Worked Examples

Example 1: Simplify \(\color{blue}{\frac{12}{18}}\).

\(\color{blue}{\text{ GCF }(12, 18) = 6}\). Divide: \(\color{blue}{12 \div 6 = 2}\), \(\color{blue}{18 \div 6 = 3}\).
\(\color{blue}{\frac{12}{18} = \frac{2}{3}}\)

Example 2: Simplify \(\color{blue}{\frac{15}{25}}\).

\(\color{blue}{\text{ GCF }(15, 25) = 5}\). Divide: \(\color{blue}{15 \div 5 = 3}\), \(\color{blue}{25 \div 5 = 5}\).
\(\color{blue}{\frac{15}{25} = \frac{3}{5}}\)

Example 3: Simplify \(\color{blue}{\frac{36}{48}}\).

\(\color{blue}{\text{ GCF }(36, 48) = 12}\). Divide: \(\color{blue}{36 \div 12 = 3}\), \(\color{blue}{48 \div 12 = 4}\).
\(\color{blue}{\frac{36}{48} = \frac{3}{4}}\)

Example 4: Simplify \(\color{blue}{\frac{9}{12}}\).

\(\color{blue}{\text{ GCF }(9, 12) = 3}\). Divide: \(\color{blue}{9 \div 3 = 3}\), \(\color{blue}{12 \div 3 = 4}\).
\(\color{blue}{\frac{9}{12} = \frac{3}{4}}\)

More Practice: Fractions in Lowest Terms (Video)

Khan Academy reinforces simplifying fractions with additional examples and explains why equivalent fractions are equal:

Exercises for Simplifying Fractions

Reduce each fraction to lowest terms.

1. \(\color{blue}{\frac{6}{9}}\)
2. \(\color{blue}{\frac{10}{25}}\)
3. \(\color{blue}{\frac{14}{21}}\)
4. \(\color{blue}{\frac{20}{30}}\)
5. \(\color{blue}{\frac{8}{32}}\)
6. \(\color{blue}{\frac{45}{60}}\)

Answers

1. \(\color{blue}{\frac{2}{3}}\) (\(\color{blue}{\text{ GCF } = 3}\))
2. \(\color{blue}{\frac{2}{5}}\) (\(\color{blue}{\text{ GCF } = 5}\))
3. \(\color{blue}{\frac{2}{3}}\) (\(\color{blue}{\text{ GCF } = 7}\))
4. \(\color{blue}{\frac{2}{3}}\) (\(\color{blue}{\text{ GCF } = 10}\))
5. \(\color{blue}{\frac{1}{4}}\) (\(\color{blue}{\text{ GCF } = 8}\))
6. \(\color{blue}{\frac{3}{4}}\) (\(\color{blue}{\text{ GCF } = 15}\))

The Ultimate Middle School Math Bundle Grades 6-8

Download

$109.99 Original price was: $109.99.$54.99Current price is: $54.99.

Frequently Asked Questions

How do I know when a fraction is fully simplified?

A fraction is fully simplified (in lowest terms) when the GCF of the numerator and denominator is 1 — that is, the only number that divides both evenly is 1. You can check by testing small primes (2, 3, 5, 7) to see if any divide both numbers.

Does simplifying a fraction change its value?

No. Simplifying a fraction creates an equivalent fraction — the same value written with smaller numbers. For example, \(\color{blue}{\frac{12}{18} = \frac{2}{3} = 0.&\#773;6}\); all three represent the same quantity.

How does simplifying fractions appear on the GED?

GED questions often require you to express answers in simplest form, compare fractions by first reducing them, or simplify the result of adding, subtracting, multiplying, or dividing fractions. Always check if your answer can be reduced further.

Related Topics

• Convert Between Fractions and Decimals
• Word Problems Fractions
• Convert Between Improper Fractions and Mixed Numbers
• Multiplying Mixed Numbers
• Dividing Mixed Numbers