Subtracting Fractions Calculator
Enter two fractions or mixed numbers to find their difference, simplified to lowest terms, with every step shown.
Updated
Subtracting Fractions Calculator
Our Subtracting Fractions Calculator subtracts one fraction or mixed number from another and gives the difference in lowest terms. Type the numerators and denominators and the answer appears straight away as a simplified fraction, a mixed number and a decimal, with every step shown: the least common denominator, the rewritten fractions, the subtracted numerators and the simplification. It works with negative answers and very large numbers, always exactly.
Quick answer
To subtract fractions, rewrite them over a common denominator, subtract the numerators and simplify. For example, 3/4 − 1/6 = 9/12 − 2/12 = 7/12. Enter any two fractions above and the calculator shows the difference instantly.
- Same denominator: subtract the numerators, 5/8 − 3/8 = 2/8 = 1/4
- Different denominators: use the least common denominator (LCD)
- Formula: a/b − c/d = (a × d − b × c) / (b × d), then simplify
- Order matters: 1/2 − 1/3 = 1/6, but 1/3 − 1/2 = −1/6
How to Subtract Fractions
You can only take away pieces of the same size, so subtracting fractions works just like adding them, in three steps:
- Find a common denominator, ideally the least common denominator (LCD).
- Rewrite each fraction over it, multiplying the top and bottom by the same number.
- Subtract the numerators, keep the denominator, and simplify the result.
Subtracting Fractions With the Same Denominator
When the denominators already match, subtract the numerators and keep the denominator:
= 2/8 = 1/4
Five eighths of a pizza minus three eighths leaves two eighths, which is a quarter.
Subtracting Fractions With Different Denominators
Rewrite both fractions over the least common denominator first. For 3/4 − 1/6 the LCD is 12:
1/6 = 2/12 (× 2)
9/12 − 2/12 = 7/12
The shortcut formula multiplies the denominators instead:
3/4 − 1/6 = (18 − 4)/24
= 14/24 = 7/12
It always works, but gives bigger numbers that need simplifying. The LCD is the least common multiple of the denominators; for 10 and 15 it is 30, so 7/10 − 4/15 = 21/30 − 8/30 = 13/30.
Subtracting Mixed Numbers
The surest way is to turn each mixed number into an improper fraction (whole × denominator + numerator). For 4 1/4 − 1 5/8:
17/4 − 13/8 = 34/8 − 13/8
= 21/8 = 2 5/8
Or subtract the parts, borrowing 1 from the whole number when the first fraction is too small: 4 2/8 becomes 3 10/8, and 3 10/8 − 1 5/8 = 2 5/8. Choose Mixed in the calculator to type a whole number for each fraction.
Subtracting Fractions From Whole Numbers
Write the whole number as a fraction with the same denominator. In the calculator, type the whole number as the numerator and 1 as the denominator.
= 5/8
5 − 2/3 = 15/3 − 2/3
= 13/3 = 4 1/3
Negative Answers and Negative Fractions
When the second fraction is bigger, the answer is negative:
= −1/6
Subtracting a negative fraction is the same as adding it:
= 8/20 + 15/20
= 23/20
For a negative mixed number such as −1 1/2, the minus sign applies to the whole thing, so it is −3/2.
Common Fraction Differences
| Difference | LCD | Answer |
|---|---|---|
| 1/2 − 1/3 | 6 | 1/6 |
| 2/3 − 1/4 | 12 | 5/12 |
| 3/4 − 2/3 | 12 | 1/12 |
| 5/6 − 1/4 | 12 | 7/12 |
| 5/12 − 3/8 | 24 | 1/24 |
| 3/8 − 5/16 | 16 | 1/16 |
Common Mistakes
- Subtracting the denominators. 1/2 − 1/3 is 1/6, not (1 − 1)/(2 − 3) = 0.
- Changing only the denominator. When 3/4 becomes twelfths, the numerator is multiplied too: 9/12, not 3/12.
- Swapping the order. Subtraction is not commutative: 1/3 − 1/2 is negative.
- Forgetting to borrow. In 4 1/4 − 1 5/8, 1/4 is less than 5/8, so borrow 1 from the 4.
- Forgetting to simplify. 14/24 is correct but not finished; it reduces to 7/12.
Key Terms
- Difference
- The answer to a subtraction.
- Minuend
- The fraction you subtract from, the first one.
- Subtrahend
- The fraction being taken away, the second one.
- LCD
- Least common denominator, the smallest shared denominator.
- Mixed number
- A whole number and a fraction, such as 2 5/8.
- Borrowing
- Turning 1 from the whole number into a fraction, such as 4 2/8 = 3 10/8.
How to Use the Subtracting Fractions Calculator
- Choose the fraction type. Pick Simple for fractions such as 3/4 or 7/2, or Mixed to add a whole-number box for mixed numbers such as 4 1/4.
- Enter the two fractions. Type the fraction you subtract from on the left and the fraction to take away on the right, with the numerator in the top box and the denominator in the bottom box. For a whole number, use 1 as the denominator. Negative numbers work; put the minus sign on the numerator, or on the whole number of a mixed number.
- Read and copy the difference. The difference appears as you type, in lowest terms. The table shows it as a fraction, a mixed number and a decimal, with the steps: the least common denominator, the rewritten fractions, the subtracted numerators and the simplification. Press Copy to copy it, or Clear or Esc to start again.
Example: enter 3/4 and 1/6. The difference is 7/12, with the working 3/4 − 1/6 = 9/12 − 2/12 = 7/12, the decimal ≈ 0.5833333333 = 0.58(3) and the steps LCD of 4 and 6 = 12, 9 − 2 = 7.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
How do you subtract fractions?
Rewrite the fractions over a common denominator, subtract the numerators, keep the denominator and simplify. For example 3/4 − 1/6 = 9/12 − 2/12 = 7/12.
How do you subtract fractions with different denominators?
Find the least common denominator (the least common multiple of the denominators), rewrite each fraction over it, then subtract the numerators. For 2/3 − 1/4 the LCD is 12: 8/12 − 3/12 = 5/12.
What is the formula for subtracting fractions?
a/b − c/d = (a × d − b × c) / (b × d). Simplify the answer afterwards: 3/4 − 1/6 = (18 − 4)/24 = 14/24 = 7/12.
Do you subtract the denominators when subtracting fractions?
No. The denominator gives the size of the pieces, which stays the same. 5/8 − 3/8 = 2/8 = 1/4, and the denominator stays 8 until you simplify.
How do you subtract mixed numbers?
Turn each mixed number into an improper fraction, subtract, and turn the answer back. 4 1/4 − 1 5/8 = 17/4 − 13/8 = 34/8 − 13/8 = 21/8 = 2 5/8. Or subtract the parts, borrowing 1 from the whole number when the first fraction is smaller.
How do you subtract a fraction from a whole number?
Write the whole number with the same denominator as the fraction. 1 − 3/8 = 8/8 − 3/8 = 5/8, and 5 − 2/3 = 15/3 − 2/3 = 13/3 = 4 1/3.
What is 1/2 − 1/3?
1/2 − 1/3 = 3/6 − 2/6 = 1/6, or about 0.1667.
What is 3/4 − 2/3?
3/4 − 2/3 = 9/12 − 8/12 = 1/12, or about 0.0833.
Can the answer be negative?
Yes. When the second fraction is bigger than the first, the difference is negative: 1/3 − 1/2 = 2/6 − 3/6 = −1/6. Subtracting a negative fraction adds it: 2/5 − (−3/4) = 23/20.
Is the Subtracting Fractions Calculator free?
Yes. It is completely free, needs no sign-up, and can be used as many times as you like.
Try our Subtracting Fractions Calculator to subtract any two fractions or mixed numbers, with every step shown.