How do you subtract fractions with different denominators?

Find the least common denominator, rewrite both fractions over it, subtract the numerators, and reduce. For 5/6 − 3/4 the least common denominator is 12: 10/12 − 9/12 = 1/12.

How do you subtract fractions with the same denominator?

Subtract the numerators and keep the denominator, then reduce. For 3/4 − 1/4 the result is 2/4, which reduces to 1/2.

What if the second fraction is larger than the first?

The difference is negative. For 1/3 − 1/2 the least common denominator is 6, giving 2/6 − 3/6 = −1/6. To get the positive amount, subtract in the other order.

How do you subtract mixed numbers?

Convert each mixed number to an improper fraction, subtract over the least common denominator, then convert back if you want a mixed answer. For 3 1/2 − 1 3/4: 7/2 − 7/4 = 14/4 − 7/4 = 7/4 = 1 3/4.

Do I have to use the least common denominator?

No. Any common denominator works, such as the product of the two denominators, but the result must then be reduced. The least common denominator keeps the numbers smaller and the reduction shorter.

Sumivo · Mathematics

Fraction Subtraction Calculator

Subtract the second fraction from the first. For a mixed number, add a whole part and a nonnegative proper fraction with positive denominator; the whole-part sign applies to the entire value.

01 / inputs

First whole part (optional mixed number)

integer

First numerator

integer

First denominator (nonzero)

integer

Second whole part (optional mixed number)

integer

Second numerator

integer

Second denominator (nonzero)

integer

02 / result

FIRST MINUS SECOND

1/12

Least common denominator: 12
Before reducing: 1/12
Mixed number: 1/12
Exact decimal (parentheses repeat): 0.08(3)
Sign of the result: Positive

Calculation trace

lcm(6, 4) = (6 × 4) / gcd(6, 4) = 12
Least common denominator = lcm of the denominators
5/6 = 10/12; 3/4 = 9/12
Rewrite both fractions over the least common denominator
(10 − (9))/12 = 1/12
Subtract the numerators and keep the denominator
gcd(1, 12) = 1; 1/12 = 1/12
Reduce by the greatest common divisor of the numerator and denominator

Rewrite both fractions over their least common denominator 12, subtract the numerators (10 − 9 = 1), then divide the numerator and denominator by their greatest common divisor 1. A mixed-number minus sign applies to the entire value.

How it works

Each mixed number is converted to an improper fraction first, and a negative denominator moves its sign to the numerator. The least common denominator is lcm(b, d) = (b × d) / gcd(b, d). Both fractions are rewritten over that denominator, the numerators are subtracted (a·(L/b) − c·(L/d)), and the result is reduced by dividing the numerator and denominator by their greatest common divisor. All arithmetic uses exact integers, so large numerators and denominators do not lose precision.

Assumptions & limits

Enter signed integers for the numerators and nonzero signed integers for the denominators. Each field is limited to 1024 characters and 1000 digits; decimal points, E notation and expressions are rejected.
For a mixed number, the fraction part must have a nonnegative numerator smaller than a positive denominator. Put the sign on the whole part: −2 with 1/3 means −(2 + 1/3) = −7/3. Use -0 with 1/2 for −1/2. A blank whole part means a single fraction.
The order matters: the result is the first fraction minus the second. If the second is larger the answer is negative, and the tool says so instead of swapping the order.
The decimal preview is limited to 2000 fractional digits. An ellipsis marks an incomplete, unrounded preview; the exact fraction stays valid. Parentheses mark a complete repeating block.
This tool subtracts two fractions. The Fraction Calculator adds two fractions; use the Fraction Simplifier to reduce a single fraction.

FAQ

How do you subtract fractions with different denominators?: Find the least common denominator, rewrite both fractions over it, subtract the numerators, and reduce. For 5/6 − 3/4 the least common denominator is 12: 10/12 − 9/12 = 1/12.
How do you subtract fractions with the same denominator?: Subtract the numerators and keep the denominator, then reduce. For 3/4 − 1/4 the result is 2/4, which reduces to 1/2.
What if the second fraction is larger than the first?: The difference is negative. For 1/3 − 1/2 the least common denominator is 6, giving 2/6 − 3/6 = −1/6. To get the positive amount, subtract in the other order.
How do you subtract mixed numbers?: Convert each mixed number to an improper fraction, subtract over the least common denominator, then convert back if you want a mixed answer. For 3 1/2 − 1 3/4: 7/2 − 7/4 = 14/4 − 7/4 = 7/4 = 1 3/4.
Do I have to use the least common denominator?: No. Any common denominator works, such as the product of the two denominators, but the result must then be reduced. The least common denominator keeps the numbers smaller and the reduction shorter.

Related calculators

SOURCES

OpenStax, Rice University
Prealgebra 2e — 4.5 Add and Subtract Fractions with Different Denominators ↗
Section 4.5, Add and Subtract Fractions with Different Denominators: find the least common denominator, rewrite each fraction over it, subtract, and write the result in simplest form. Signed-input conventions and display limits are calculator choices.
Accessed 2026-10-04
OpenStax, Rice University
Prealgebra 2e — 4.6 Add and Subtract Mixed Numbers ↗
Section 4.6, Add and Subtract Mixed Numbers: subtract mixed numbers by converting the fractional parts to equivalent fractions over the least common denominator. This tool converts each mixed number to an improper fraction first, which gives the same value.
Accessed 2026-10-04