Fraction simplifying
Calculator for simplifying proper and improper fractions and simplify fractions. Please enter one fraction, decimal or mixed number (mixed fraction). Reduction of fraction is done by dividing numerator and denominator by gcf (greatest common factor).
This calculator also simplifies proper fractions by reducing to lowest terms. Show fraction simpliflying steps.
This calculator also simplifies proper fractions by reducing to lowest terms. Show fraction simpliflying steps.
Simplifying fractions means reducing them to their simplest form, where the numerator (top number) and denominator (bottom number) have no common divisors other than 1. Here’s a step-by-step guide:
Method 1:
Divide by the Greatest Common Divisor (GCD)1. Find the GCD of the numerator and denominator.
- The GCD is the largest number that divides both evenly.
- Example: For 8/12, the GCD of 8 and 12 is 4.
2. Divide both numerator and denominator by the GCD.
8 ÷ 412 ÷ 4 = 23 .
Method 2:
Divide by Common Factors (Step-by-Step)If you don’t know the GCD, divide by common factors until no more exist:
1. Check for small divisors (2, 3, 5, etc.).
- Example: Simplify 18/24.
2. Divide by 2 (both are even):
18 ÷ 224 ÷ 2 = 912 .
3. Divide by 3 (next common factor):
9 ÷ 312 ÷ 3 = 34 .
Now, 3/4 is simplified (no common factors left).
Special Cases
1. Improper fractions (numerator ≥ denominator):
Convert to a mixed number if needed.
Example: 104 simplifies to 52 (or 212 ).
2. Fractions with variables:
Factor algebraic expressions first.
Example: 6x29x = 2x3 (divide by 3x ).
Key Rule
Always ensure the fraction is fully reduced by checking for any remaining common factors.
Example:
Simplify 1545 :
1. GCD of 15 and 45 is 15.
2. 15 ÷ 1545 ÷ 15 = 13
