Simplify Fractions

Reduce fractions to lowest terms and convert improper fractions to mixed numbers. Shows step-by-step GCF calculation.

Reduce fractions to lowest terms by finding the GCF. See step-by-step prime factorization and division process.

Max 9 digits

Simplified

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help_outlineHow to Useexpand_more

This calculator reduces fractions to their lowest terms and converts improper fractions to mixed numbers. It shows each step of the simplification process so you can follow along.

When Can a Fraction Be Simplified?

A fraction can be reduced when:

A number divides evenly into both the numerator and denominator
The GCF (Greatest Common Factor) is greater than 1

Improper Fractions:

When the numerator is larger than the denominator (like 16/3), the calculator also converts it to a mixed number (5 1/3).

infoWhat is Simplify Fractions?expand_more

Simplifying a fraction means reducing it to its smallest equivalent form. This is done by dividing both the numerator and denominator by their Greatest Common Factor (GCF). A fraction is fully simplified when no number except 1 divides both parts evenly.

What is an Improper Fraction?

An improper fraction has a numerator larger than its denominator.

Examples: 16/3, 81/9, 45/10

These can be written as mixed numbers: 5 1/3, 9, 4 1/2

Proper Fractions

Numerator smaller than denominator

3/4, 2/5, 7/12

Improper Fractions

Numerator larger than denominator

16/3, 9/4, 45/10

functionsFormulaexpand_more

How to Simplify a Fraction:

1. Find the GCF of numerator and denominator

2. Divide both numbers by the GCF

3. The result is the simplified fraction

Example: Simplify 45/10

Step 1: Find GCF of 45 and 10

Factors of 45: 1, 3, 5, 9, 15, 45

Factors of 10: 1, 2, 5, 10

GCF = 5

Step 2: Divide both by 5

45 ÷ 5 = 9

10 ÷ 5 = 2

Step 3: Simplified fraction is 9/2

Converting 9/2 to a Mixed Number:

1. Divide 9 by 2: 9 ÷ 2 = 4 remainder 1

2. The whole number is 4

3. The remainder 1 becomes the new numerator

Result: 45/10 = 9/2 = 4 1/2

lightbulbExamplesexpand_more

Proper Fraction

12/18 = 2/3

GCF = 6

Proper Fraction

25/100 = 1/4

GCF = 25

Improper to Mixed

16/3 = 5 1/3

16 ÷ 3 = 5 r 1

Simplify then Convert

45/10 = 9/2 = 4 1/2

GCF = 5, then divide

Reduces to Whole Number

81/9 = 9

GCF = 9

Already Simplified

7/12 = 7/12

GCF = 1

quizFAQexpand_more

How do I know if a fraction is already simplified?expand_more

A fraction is fully simplified when the GCF of the numerator and denominator equals 1. This means no number other than 1 divides both evenly. For example, 7/12 is already simplified because 7 is prime and doesn't share factors with 12.

What is an improper fraction?expand_more

An improper fraction has a numerator larger than its denominator, like 16/3 or 9/4. These fractions represent values greater than 1 and can be converted to mixed numbers (5 1/3 or 2 1/4).

How do I convert an improper fraction to a mixed number?expand_more

Divide the numerator by the denominator. The quotient is the whole number part, and the remainder becomes the new numerator over the original denominator. For 16/3: 16 ÷ 3 = 5 remainder 1, so the mixed number is 5 1/3.

Should I simplify before or after converting to a mixed number?expand_more

Always simplify first if possible. Reducing 45/10 to 9/2 before converting gives you 4 1/2, which is cleaner than working with larger numbers. The calculator does this automatically.

What if my fraction has negative numbers?expand_more

Simplify as usual, then place the negative sign in front. By convention, negative fractions are written with the minus sign in the numerator: -3/4 rather than 3/-4 or -(-3/-4).

Why is simplifying fractions important?expand_more

Simplified fractions are easier to compare, add, subtract, and understand. They also make calculations faster and help identify equivalent fractions. In real life, 1/2 is much clearer than 17/34.