How to Simplify Fractions? (+FREE Worksheet!)

Simplify fractions by dividing the numerator and denominator by their greatest common factor.

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 2027 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 4.34 out of 5 based on 106 customer ratings

Satisfied 92 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. \(\color{blue}{\frac{3}{4}}\) (\(\color{blue}{\text{ GCF } = 15}\))

Frequently Asked Questions

What does simplifying fractions mean?

Simplifying a fraction means rewriting it as an equal fraction with the smallest possible numbers, so the numerator and denominator share no common factor except 1. This is also called writing it in lowest terms. For example, 12/18 simplifies to 2/3 because both numbers divide by 6. The value stays the same; 2/3 of a pizza is the same amount as 12/18 of it.

How do you simplify fractions step by step?

Step 1: find the greatest common factor (GCF) of the numerator and denominator. Step 2: divide both numbers by it. Step 3: check that no common factor remains. For 45/60, the common factors are 1, 3, 5 and 15, and 15 is the greatest. Since 45 ÷ 15 = 3 and 60 ÷ 15 = 4, 45/60 = 3/4. If the GCF is hard to spot, divide by 2, 3 or 5 repeatedly instead.

Is simplifying fractions the same as reducing fractions?

Yes. Simplifying, reducing and writing in lowest terms all mean the same thing: dividing the numerator and denominator by a common factor until none is left. The word reducing can sound like the fraction gets smaller, but its value never changes. 18/24 and 3/4 are exactly equal; the reduced form just uses smaller numbers, which makes later steps on GED math questions easier.

Is simplifying fractions the same as equivalent fractions?

They are related but not identical. Equivalent fractions are any fractions with the same value, like 1/2, 2/4, 5/10 and 50/100. Simplifying finds the one equivalent fraction with the smallest whole numbers. So 6/9 and 2/3 are equivalent, and 2/3 is the simplified form. You make equivalent fractions by multiplying or dividing top and bottom by the same number; simplifying always divides.

How do you simplify fractions with variables and exponents?

Simplify the numbers first, then cancel matching variables by subtracting exponents. For 14x⁵y² over 21x²y³, the GCF of 14 and 21 is 7, which gives 2/3. For x, x⁵ ÷ x² = x³ stays in the numerator. For y, the larger power is on the bottom, so one y is left in the denominator. The answer is 2x³/(3y).

Can you simplify fractions on a calculator?

Yes, many calculators can. On a TI-84 Plus, type the fraction and choose ►Frac from the MATH menu, and many scientific calculators show a fraction in reduced form automatically. The TI-30XS MultiView, the calculator used on the GED test, can display fractions in simplest form too. It is still worth simplifying by hand, since knowing your factors makes fraction questions faster.

Related Topics

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