Simplify Fraction Calculator
Reduce one fraction to lowest terms with the Euclidean GCD steps used on paper, then read it as a mixed number and a decimal.
6/15 = 2/5
- Find gcd(6, 15) with the Euclidean algorithm, using absolute values.
- 15 = 2 × 6 + 3.
- 6 = 2 × 3 + 0.
- The last non-zero remainder is 3, so the GCD is 3.
- Divide both parts by 3: (6 ÷ 3) / (15 ÷ 3) = 2/5.
- As a mixed number: Proper fraction. As a decimal: 0.4.
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How to Use the Simplify Fraction Calculator
Enter one fraction — or a mixed number — and select Simplify Fraction. The tool finds the greatest common divisor with Euclid’s remainder steps, divides both parts by that divisor, and reports the mixed number and decimal.
- Leave Whole blank unless you are reducing a mixed number such as 1 4/8.
- Type integer numerator and denominator. A negative sign belongs on the numerator.
- Select Simplify Fraction and read the Euclidean steps.
The Fraction Calculator adds, subtracts, multiplies, and divides two fractions and then reduces the answer. This page only reduces one fraction. A decimal such as 0.75 belongs on the Decimal to Fraction Calculator. Two whole numbers, not a fraction, belong on the GCD and LCM Calculator. An algebraic expression in x belongs on the Simplify Calculator.
Lowest Terms and the Euclidean Algorithm
A fraction is in lowest terms when the numerator and denominator share no common factor other than 1. The greatest common divisor is that shared factor. Once you have g, you divide both parts by it.
Euclid’s algorithm finds g without listing all factors. Divide the larger absolute value by the smaller, replace the pair with (smaller, remainder), and stop when the remainder is 0. The last non-zero remainder is the GCD. For 6 and 15: 15 = 2 × 6 + 3, then 6 = 2 × 3 + 0, so g = 3 and 6/15 = 2/5.
The sign is kept on the numerator. A negative denominator is rewritten first: a/(−b) = (−a)/b. Zero over a nonzero denominator is 0.
Simplify Fraction Examples
A proper fraction that reduces
6/15. Euclid: 15 = 2 × 6 + 3, then 6 = 2 × 3 + 0. GCD 3, so 2/5. Decimal 0.4.
Already in lowest terms
15/8. gcd(15, 8) = 1, so the improper fraction stays 15/8. The mixed number is 1 7/8. Decimal 1.875.
A common classroom reduction
8/12. gcd(8, 12) = 4, so 2/3.
A negative fraction
−18/24. Work with 18 and 24: gcd 6, then restore the sign. The result is −3/4.
A mixed number
1 4/8 is the improper fraction 12/8. gcd(12, 8) = 4, so 3/2, which is the mixed number 1 1/2.
Zero
0/5 is 0. gcd(0, 5) = 5, and 0 ÷ 5 over 5 ÷ 5 is 0/1.
Mixed Numbers and Improper Fractions
A mixed number w n/d means |w| + n/d, then the original sign. Rewrite it as (|w| × d + n) / d before reducing. After you have the reduced improper fraction, divide again to get the mixed form: the quotient is the whole number and the remainder is the new numerator.
15/8 is already lowest terms and still has a mixed form 1 7/8. 6/15 reduces to a proper fraction 2/5, so the mixed-number line reads Proper fraction.
Common Simplify-Fraction Mistakes
Canceling matching digits instead of factors
16/64 is not 1/4 by crossing out the 6s. The GCD of 16 and 64 is 16, so the reduced form is 1/4 — but only because 16 really is a common factor, not because a digit disappeared.
Stopping at 6/15
6/15 is equivalent, not lowest terms. Divide both parts by 3.
Thinking every improper fraction must reduce
15/8 is already lowest terms. Improper means the numerator is at least the denominator; it does not mean the GCD is greater than 1.
Using 0 as a denominator
5/0 is undefined. There is no reduced form.
Typing a decimal in the numerator
This page wants integers. Convert 0.75 on the Decimal to Fraction Calculator, then reduce here only if you still have an unreduced fraction.
Entering an expression in x
3x + 6 is algebra. Use the Simplify Calculator on the Algebra hub.
Simplify Fraction FAQs
How do you simplify 6/15?
gcd(6, 15) = 3, so divide both parts by 3 to get 2/5.
What if the fraction is already in lowest terms?
The GCD is 1 and the fraction is unchanged. 15/8 stays 15/8 and is also shown as 1 7/8.
Can I simplify a mixed number?
Yes. Enter the whole number plus the fraction. 1 4/8 becomes 12/8, then 3/2, then 1 1/2.
How is this different from the Fraction Calculator?
That page operates on two fractions. This page only reduces one fraction and shows the Euclidean GCD steps.
Does this convert a decimal to a fraction?
No. Use the Decimal to Fraction Calculator for 0.75 or 0.333…
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
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Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
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Disclaimer
This calculator is for general educational use. It reduces one integer fraction to lowest terms. It is not a computer-algebra system and does not simplify algebraic expressions.