Subtracting Fractions Calculator
This subtracting fractions calculator takes two fractions or mixed numbers and subtracts, adds, multiplies or divides them. It finds the lowest common denominator, rewrites both fractions over it, combines the numerators and simplifies the result.
3/4, 2 1/2 and 0.75 all work.How to use the subtracting fractions calculator
- Type the first fraction.
3/4, the mixed number2 1/2and the decimal0.75are all read correctly. - Type the second fraction the same way.
- Choose the operation: subtract, add, multiply or divide. Subtract is selected to begin with.
- Read the answer as it updates. You get the lowest common denominator, both fractions rewritten over it, the combined numerator and the simplified result.
Every answer is given four ways: as a fraction in lowest terms, as a mixed number, as a decimal and as a percentage. If the result is negative — and subtraction often makes it negative — the sign is carried through all four.
Subtracting fractions with the same denominator
When the denominators match, the pieces are already the same size, so you just count how many are left.
Seven eighths minus three eighths is four eighths, for the same reason that seven apples minus three apples is four apples. The word “eighths” is a label, not a quantity to subtract.
Example: 7/8 − 3/8
Different denominators: finding the LCD properly
If the denominators differ, the pieces are different sizes and cannot be counted together yet. You need a common denominator: a number both denominators divide into. The best one to use is the lowest common denominator, which is the least common multiple of the two denominators.
Multiplying the denominators together always produces a common denominator, and plenty of people stop there. It works, but it makes the numbers bigger than they need to be and leaves more simplifying at the end. For 6 and 8, multiplying gives 48; the lowest common denominator is 24.
The quickest way to find it by hand is to list multiples of the larger denominator until one of them divides by the smaller. Multiples of 8 are 8, 16, 24 — and 24 divides by 6, so 24 is the LCD.
Example: 5/6 − 3/8
The LCD is 24. Scale each fraction so its denominator becomes 24, multiplying top and bottom by the same number so the value does not change.
Example: 7/10 − 1/4
Multiplying the denominators would give 40. The LCD is 20, which keeps the numbers half the size.
| Denominators | Product | Shared factor | Lowest common denominator |
|---|---|---|---|
| 3 and 5 | 15 | 1 | 15 |
| 4 and 6 | 24 | 2 | 12 |
| 6 and 8 | 48 | 2 | 24 |
| 10 and 4 | 40 | 2 | 20 |
| 6 and 9 | 54 | 3 | 18 |
| 8 and 12 | 96 | 4 | 24 |
| 9 and 12 | 108 | 3 | 36 |
| 5 and 15 | 75 | 5 | 15 |
| 7 and 21 | 147 | 7 | 21 |
When one denominator is already a multiple of the other, as in the last two rows, the larger denominator is the LCD and only one fraction needs rewriting.
Borrowing when you subtract mixed numbers
Subtracting mixed numbers goes wrong when the fraction you are taking away is bigger than the fraction you have. 3 1/4 − 1 3/4 is the classic case: you cannot take three quarters from one quarter. You borrow one whole from the 3 and turn it into quarters.
Example: 3 1/4 − 1 3/4, by borrowing
One whole is 4/4, so 3 1/4 becomes 2 wholes and 5 quarters.
The same subtraction without borrowing
Convert both to improper fractions and the borrowing disappears. This is usually the safer route.
Both methods give 1 1/2. Borrowing is faster on paper when the whole numbers are large, because you never build a huge numerator. Converting is more reliable when the denominators differ as well, since you would otherwise have to find the LCD and borrow in the same problem. The mixed number calculator handles the conversion on its own, and the improper fraction calculator converts the answer back.
Subtracting a fraction from a whole number
A whole number has an invisible denominator of 1, but that is not the useful move here. Instead, rewrite the whole number using the denominator you already have, then subtract normally.
Example: 5 − 2/3
Turn 5 into thirds. Each whole is 3 thirds, so 5 wholes are 15 thirds.
Example: 4 − 1 5/8
Convert both sides to eighths first.
A quick sanity check: the answer to 5 − 2/3 must be a little under 5, and 4 1/3 is. If you ever get an answer bigger than the number you started with, you have added instead of subtracted or dropped a sign somewhere.
Subtraction can also run past zero, and that is fine. 1/4 − 3/4 is −1/2. Negative fractions behave like any other negative number, and if the expression has several operations in it, the order of operations calculator will resolve the sequence for you.
Common mistakes when subtracting fractions
- Subtracting the denominators.
5/6 − 3/8is not2/-2. Only the numerators are combined. - Scaling only the bottom. If you turn 5/6 into sixths of 24, the numerator has to be multiplied by 4 as well. Change one and you have changed the value.
- Subtracting the fraction parts of mixed numbers in the wrong order. In
3 1/4 − 1 3/4, taking 1/4 from 3/4 to get 2/4 gives 2 2/4, which is wrong by a whole unit. Borrow instead. - Using a common denominator that is not common. 18 is a multiple of 6 but not of 8, so it cannot hold both fractions.
- Forgetting the whole numbers after converting.
2 1/2is 5/2, not 1/2 with a 2 remembered separately. - Leaving the answer unsimplified.
4/8should be written as1/2. - Assuming a negative result is a mistake. Taking a bigger fraction from a smaller one gives a negative answer, exactly as it does with whole numbers.
Frequently asked questions
What is 3/4 minus 1/6?
7/12. The lowest common denominator of 4 and 6 is 12, so 3/4 becomes 9/12 and 1/6 becomes 2/12. Subtract the numerators: 9 − 2 = 7. The answer 7/12 has no common factor to cancel, so it is already in lowest terms. As a decimal that is about 0.5833, or 58.33%.
What is 3 1/4 minus 1 3/4?
1 1/2. You cannot take 3/4 from 1/4, so borrow one whole from the 3, which is 4/4, making the first number 2 5/4. Then 5/4 − 3/4 = 2/4 and 2 − 1 = 1, giving 1 2/4, which simplifies to 1 1/2. Converting to 13/4 − 7/4 = 6/4 gives the same answer.
Why do you never subtract the denominators?
The denominator names the size of the pieces, it does not count them. In 7/8 − 3/8 you have seven eighth-sized pieces and remove three of them, leaving four eighth-sized pieces. The size of a piece did not change, so the 8 stays. Subtracting the denominators would also produce 8 − 8 = 0, and a denominator of zero is undefined.
How do you subtract a fraction from a whole number?
Rewrite the whole number over the same denominator, then subtract. For 5 − 2/3, each whole is 3 thirds, so 5 is 15/3. Then 15/3 − 2/3 = 13/3, which is 4 1/3. The shortcut version is to take one whole off, convert just that one, and leave the rest alone: 5 becomes 4 and 3/3.
Do I have to use the lowest common denominator?
No. Any common denominator gives the correct value, and multiplying the two denominators together always produces one. Using the lowest keeps the numbers small and usually means less simplifying afterwards. For 5/6 − 3/8, multiplying gives 48ths and an answer of 22/48; the LCD of 24 gives 11/24 directly.
What is 7/8 minus 1/2?
3/8. Eight is already a multiple of 2, so the LCD is 8 and only the second fraction needs rewriting: 1/2 becomes 4/8. Then 7 − 4 = 3, giving 3/8. As a decimal that is 0.375, or 37.5%. Whenever one denominator divides into the other, the larger one is the common denominator.
Can the answer be negative?
Yes. If the second fraction is larger, the result drops below zero. 1/4 − 3/4 is −2/4, which simplifies to −1/2. Nothing about the method changes; the numerator subtraction simply comes out negative, and the minus sign is written in front of the finished fraction.
What is 5/6 minus 5/6?
Zero. The denominators already match, so subtract the numerators: 5 − 5 = 0, giving 0/6. Any fraction with a numerator of zero is zero, whatever the denominator, so the answer is written simply as 0. This is the one case where the fraction form of the answer disappears entirely.
Is subtracting mixed numbers easier by borrowing or by converting?
Converting to improper fractions is more reliable, especially when the denominators also differ, because it removes the borrowing step altogether. Borrowing is quicker on paper when the whole numbers are large, since it keeps the numerators small. Both give identical answers, so use whichever you can carry out without slipping.
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