How to solve it
- Find the least common multiple (LCM) of the denominators.
- Rewrite each fraction with that common denominator.
- Add or subtract the numerators and keep the common denominator.
- Simplify the result.
3/4 − 1/6 = 9/12 − 2/12 = 7/12
Result: 7/12
Common mistake:Wrong: 5/6 − 1/3 = 4/3.Right: 5/6 − 1/3 = 1/2.Subtracting numerators and denominators separately mixes parts of different sizes and gives a result larger than 5/6, which is impossible when you subtract. The parts must be the same size before you subtract.
Full guide: Why denominators are not added
The first thing to do when subtracting is look at the denominators. If they match, subtract the numerators. If they differ, rewrite each fraction with a common denominator and then subtract. Here is the method with a full example, the cases that change the procedure, and the most common mistake. Making the denominators equal works the same way as when you add fractions; this page covers what only happens with subtraction: the order, negative results and what is left over.
Worked example: 5/6 − 1/4
A bottle holds 5/6 of a liter of water and you pour out 1/4 of a liter. How much water is left?
- Find the common denominator. The least common multiple of 6 and 4 is 12.
- Convert each fraction. Multiply the first by 2 on top and bottom and the second by 3: they become 10/12 and 3/12.
- Subtract the numerators. 10/12 − 3/12 = 7/12, and 7 and 12 share no divisor other than 1, so the fraction is already in lowest terms.
Answer: 7/12 of a liter is left.
Check: if you add what you poured out to what is left, you should get the total back. 7/12 + 3/12 = 10/12, which is 5/6.
What changes from case to case
With the same denominator, you subtract directly. The table lists the cases that change something and the calculation for each one.
| Case | What you do | Calculation |
|---|---|---|
| One denominator divides the other | Use the larger one as the common denominator | 7/9 − 2/3 = 7/9 − 6/9 = 1/9 |
| Denominators with no common factor | Use their product | 3/5 − 2/7 = 21/35 − 10/35 = 11/35 |
| The first fraction is smaller | Subtract as usual; the result is negative, so keep the minus sign | 2/5 − 3/4 = 8/20 − 15/20 = −7/20 |
| Mixed numbers | Convert to improper fractions | 3 1/5 − 1 3/5 = 16/5 − 8/5 = 8/5 = 1 3/5 |
| Whole number minus a fraction | Write the whole number with denominator 1 | 2 − 3/8 = 16/8 − 3/8 = 13/8 |
With mixed numbers you do not need to “borrow” if you work with improper fractions: the calculation is direct, and you convert the result back to a mixed number at the end. For help with the common denominator, see the least common denominator. If the result has common factors, the calculator reduces it, and you can repeat that by hand with simplify fractions.
Subtracting several fractions in a row
A subtraction with three values goes from left to right: first the first two, then you subtract the third from that result. It is the natural way to find “what is left” after taking several parts away from a whole. With 1 − 1/3 − 1/5, you write 1 as 15/15 and get 15/15 − 5/15 − 3/15 = 7/15. The order of the fractions you take away can change, because removing 1/3 and then 1/5 leaves the same amount as the other way around. What cannot change is which fraction comes first.
If the problem mixes subtraction with products or parentheses, the fraction expression calculator follows the order of operations.
When to use another page
When the problem asks for “what is left” of a fraction of a quantity, the fraction of the remainder problems guide walks through the setup. To practice by hand, the add and subtract worksheets have exercises with solutions. OpenStax Prealgebra covers subtraction with like denominators, unlike denominators and mixed numbers (accessed October 16, 2026). The calculator accepts up to 100 digits per number and rejects any denominator equal to zero.
Frequently asked questions
Can I subtract a fraction and a decimal?
Yes, in the Mixed numbers and decimals mode. The decimal is converted to a fraction before subtracting, so 0.6 − 1/4 is the same as 3/5 − 1/4 = 12/20 − 5/20 = 7/20. The result is an exact fraction, with no rounding.
What happens when the result is zero?
It means the two fractions have the same value, even though they are written differently. For example, 4/10 − 2/5 gives 0, because 4/10 simplifies to 2/5. The calculator shows 0 and leaves no fraction waiting to be simplified.
How do you subtract a negative number?
Subtracting a negative is the same as adding its opposite. In 4/5 − (−1/10), the problem becomes 4/5 + 1/10 = 8/10 + 1/10 = 9/10. The result is larger than the first fraction, which never happens when you subtract a positive value. For signs in general, see the guide on negative fractions.