Subtracting Fractions Calculator
Type two fractions or mixed numbers to subtract the second from the first, with the working shown line by line.
2 1/3 − 5/6 =
1 1/2
2 1/3 − 5/6 = 1 1/2 (3/2), 1.5 as a decimal.
- As a fraction
- 3/2
- As a decimal
- 1.5
How this works: Method, 1 source, Checked against 1 worked example,
How this works
Method
Subtraction works like addition: give both fractions the same denominator, then subtract the numerators. For 5/6 − 1/4 the least common denominator is 12, so 10/12 − 3/12 = 7/12. Full method
How it’s tested
One worked example for this page is checked by automated tests before every release: given the inputs, the tool must show the expected answer.
Privacy
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Changes
- First published, with nine pages: adding, subtracting, multiplying, dividing and simplifying fractions, fraction to decimal and back, mixed numbers and ratios.
How to subtract fractions
Subtraction works like addition: give both fractions the same denominator, then subtract the numerators. For 5/6 − 1/4 the least common denominator is 12, so 10/12 − 3/12 = 7/12.
Mixed numbers are where most mistakes happen. In 2 1/3 − 5/6 the fraction part 1/3 (2/6) is smaller than 5/6, so by hand you would borrow one whole: 2 1/3 = 1 8/6, and 1 8/6 − 5/6 = 1 3/6 = 1 1/2. Converting to improper fractions first avoids the borrowing altogether: 7/3 − 5/6 = 14/6 − 5/6 = 9/6 = 3/2.
If the second fraction is bigger, the answer is negative, which is fine: 1/4 − 2/3 = 3/12 − 8/12 = −5/12. Subtracting a negative fraction is the same as adding its positive.
a/b − c/d = (a × (L ÷ b) − c × (L ÷ d)) / L, where L = lcm(b, d)
- Grade 4 standards start with subtracting fractions that have the same denominator, including mixed numbers, by thinking of them as joining and separating parts of the same whole (4.NF.B.3). Source: Common Core State Standards, Grade 4 Number and Operations: Fractions.
Fraction differences, worked
Each subtraction with its least common denominator, the rewritten fractions and the simplified answer; some come out negative.
| Difference | LCD | Rewritten | Answer |
|---|---|---|---|
| 1/2 − 1/3 | 6 | 3/6 − 2/6 | 1/6 |
| 3/4 − 1/2 | 4 | 3/4 − 2/4 | 1/4 |
| 5/6 − 1/4 | 12 | 10/12 − 3/12 | 7/12 |
| 2/3 − 1/6 | 6 | 4/6 − 1/6 | 1/2 |
| 7/8 − 3/4 | 8 | 7/8 − 6/8 | 1/8 |
| 4/5 − 1/2 | 10 | 8/10 − 5/10 | 3/10 |
| 5/8 − 1/3 | 24 | 15/24 − 8/24 | 7/24 |
| 9/10 − 2/5 | 10 | 9/10 − 4/10 | 1/2 |
| 1/4 − 2/3 | 12 | 3/12 − 8/12 | −5/12 |
| 1 − 3/8 | 8 | 8/8 − 3/8 | 5/8 |
Show all 14 rowsShow fewer
| 3 1/2 − 1 3/4 | 4 | 14/4 − 7/4 | 1 3/4 |
| 2 1/3 − 5/6 | 6 | 14/6 − 5/6 | 1 1/2 |
| 5 − 2 2/7 | 7 | 35/7 − 16/7 | 2 5/7 |
| 11/12 − 7/18 | 36 | 33/36 − 14/36 | 19/36 |
Frequently Asked Questions
How do I subtract a fraction from a whole number?
Write the whole number as a fraction with the same denominator: 3 − 2/5 = 15/5 − 2/5 = 13/5 = 2 3/5. Or take one whole and split it: 3 − 2/5 = 2 + (5/5 − 2/5) = 2 3/5.
What is borrowing in mixed-number subtraction?
When the first fraction part is smaller than the second, take 1 from the whole number and add it to the fraction as d/d. 4 1/5 − 2 3/5 becomes 3 6/5 − 2 3/5 = 1 3/5.
Does the order matter?
Yes. Subtraction is not commutative: 3/4 − 1/2 = 1/4 but 1/2 − 3/4 = −1/4. The calculator always takes the second fraction away from the first.