Subtracting Fractions Calculator
Enter two fractions (or mixed numbers) and this calculator finds their difference in one step. It shows the least common denominator, converts each fraction, subtracts the numerators, and reduces the result to lowest terms - with a full step-by-step breakdown so you can follow every part of the working.
How to subtract fractions
Subtracting fractions follows four steps. First, check whether the denominators match. If they do, subtract the numerators directly and keep the denominator unchanged. If they differ, find the least common denominator (LCD), rewrite each fraction so it has the LCD as its denominator, subtract the numerators, then reduce the result by dividing both the numerator and denominator by their greatest common factor (GCF). For example, 3/4 - 1/4 = 2/4 = 1/2 (same denominator), while 1/2 - 1/3 requires an LCD of 6: 3/6 - 2/6 = 1/6.
Subtracting fractions with different denominators
When the denominators differ, the fractions must be converted to equivalent fractions that share a common denominator before any subtraction can occur. The most efficient choice is the least common denominator, which is the least common multiple (LCM) of the two denominators. Multiply the numerator and denominator of each fraction by the factor needed to reach the LCD, then subtract the new numerators. Example: 5/6 - 1/4. LCM(6, 4) = 12. Rewrite: 10/12 - 3/12 = 7/12. Because GCD(7, 12) = 1, the fraction is already in lowest terms.
Subtracting mixed numbers
To subtract mixed numbers (such as 2 3/4 - 1 1/2), convert each to an improper fraction first. Multiply the whole-number part by the denominator and add the numerator: 2 3/4 becomes (2 x 4 + 3)/4 = 11/4, and 1 1/2 becomes (1 x 2 + 1)/2 = 3/2. Then follow the standard steps: find the LCD (4), rewrite 3/2 as 6/4, subtract: 11/4 - 6/4 = 5/4. Convert back to a mixed number: 1 1/4. Switching the input format selector above to "Mixed numbers" lets this calculator do all of these conversion steps for you automatically.
Simplifying the result
A fraction is in its simplest form (lowest terms) when 1 is the only number that divides both the numerator and denominator evenly - in other words, when GCD(numerator, denominator) = 1. To simplify, find the GCF of the numerator and denominator and divide both by it. For instance, 6/8 reduces to 3/4 because GCD(6, 8) = 2. This calculator performs simplification automatically. The decimal output lets you cross-check: divide the simplified numerator by the denominator and the decimal should match.
Common fraction subtraction reference
| First fraction | Second fraction | Difference | Decimal |
|---|---|---|---|
| 1/2 | 1/4 | 1/4 | 0.25 |
| 3/4 | 1/4 | 1/2 | 0.5 |
| 1/2 | 1/3 | 1/6 | 0.1667 |
| 2/3 | 1/6 | 1/2 | 0.5 |
| 3/4 | 1/2 | 1/4 | 0.25 |
| 5/6 | 1/3 | 1/2 | 0.5 |
| 7/8 | 3/8 | 1/2 | 0.5 |
| 1/1 | 1/2 | 1/2 | 0.5 |
Frequently encountered differences, simplified to lowest terms.
Frequently asked questions
Why can I not subtract the denominators?
Denominators tell you the size of each piece. Subtracting them would change what unit you are measuring, giving a nonsense result. Only the numerators - the number of pieces you have - can be subtracted, and only after the pieces are the same size (same denominator).
What is the least common denominator?
The least common denominator (LCD) is the smallest positive integer that is a multiple of both denominators. For example, the LCD of 4 and 6 is 12, because 12 is the smallest number divisible by both 4 and 6. Using the LCD keeps the numbers as small as possible and avoids extra simplification at the end.
How do I subtract a fraction from a whole number?
Treat the whole number as a fraction with denominator 1 (for example, 3 = 3/1), or switch to the mixed-number mode and enter the whole number in the "Whole number" field while leaving the numerator at 0. The calculator will handle the rest. For instance, 3 - 1/4 = 3/1 - 1/4 = 12/4 - 1/4 = 11/4 = 2 3/4.
Can the result be negative?
Yes. If the second fraction is larger than the first, the numerator after subtraction will be negative, and the result will be a negative fraction. This calculator handles negative results correctly and shows the minus sign in front of the numerator.
What if the result is an improper fraction?
An improper fraction has a numerator larger than (or equal to) its denominator, such as 7/4. It is mathematically correct and fully simplified if the GCD is 1. The "Result (mixed number)" output converts it to the equivalent mixed number (1 3/4 in that example) for easier reading.
How do I subtract fractions with negative values?
Enter a negative numerator to make a fraction negative. For example, entering numerator -3 and denominator 4 represents -3/4. The calculator treats the minus sign as part of the numerator and applies it throughout all steps.