Subtracting Fractions Calculator

Subtracting fractions runs into the same problem as adding them: you cannot subtract the pieces until they are the same size. A third and a quarter are different-sized slices, so this subtracting fractions calculator first rewrites both over a common denominator, then subtracts. It handles proper fractions, improper fractions, mixed numbers, and negative results, and shows the answer three ways: as a simplified fraction, as a mixed number, and as a decimal.

Quick answer: to subtract fractions, convert any mixed numbers to improper fractions, rewrite both fractions over the least common denominator (LCD), subtract the numerators only, keep the denominator, then reduce. Example: 1/3 − 1/4 = 4/12 − 3/12 = 1/12.

How to Subtract Fractions (step by step)

Step One: Convert mixed numbers to improper fractions

Multiply the whole number by the denominator, then add the numerator. The denominator never changes here.

improper numerator = (whole × denominator) + numerator

With defaults (0 and 1/3, minus 0 and 1/4), both are already improper:

First:  (0 × 3) + 1 = 1  →  1/3
Second: (0 × 4) + 1 = 1  →  1/4

Why this step exists: 2 1/2 is really 2 + 1/2, two separate numbers glued together. You cannot borrow or subtract reliably while a whole number is sitting outside the fraction, so the calculator flattens it into a single numerator over a single denominator first (2 1/2 → 5/2).

Step Two: Find the least common denominator

The LCD is the least common multiple of the two denominators. It is the smallest slice size that both fractions can be cut into evenly.

LCD = lcm(3, 4) = 12
lcm(a, b) = (a × b) / gcd(a, b)

gcd(3, 4) = 1  →  lcm = (3 × 4) / 1 = 12

Shortcut worth knowing: if one denominator already divides the other (like 4 and 8), the larger one is the LCD. If the two denominators share no common factor (like 3 and 4), the LCD is simply their product.

Step Three: Rewrite both fractions over the LCD

Multiply the top and bottom of each fraction by whatever it takes to reach the LCD. Multiplying top and bottom by the same number does not change the value, only the way it is written.

12 ÷ 3 = 4  →  1/3 = (1 × 4) / (3 × 4) = 4/12
12 ÷ 4 = 3  →  1/4 = (1 × 3) / (4 × 3) = 3/12

Step Four: Subtract the numerators

Denominators do not get subtracted. They are the unit label, like “twelfths,” and the unit stays put.

4/12 − 3/12 = (4 − 3)/12 = 1/12

Step Five: Reduce to lowest terms and convert to decimal

Divide the numerator and denominator by their greatest common divisor, then divide out for the decimal.

gcd(1, 12) = 1  →  already lowest
decimal = 1 ÷ 12 = 0.08333...

Worked examples (with explanations)

Example 1: Same denominators, nothing to convert

5/8 − 3/8

denominators already match  →  LCD = 8
5/8 − 3/8 = 2/8
gcd(2, 8) = 2  →  2/8 = 1/4
decimal = 0.25

Explanation: the slices are already the same size, so you just count how many are left. Notice the answer still needed reducing, which is the step people skip most often.

Example 2: One denominator divides the other

3/4 − 1/8

8 ÷ 4 = 2  →  LCD = 8 (no need for 4 × 8 = 32)
3/4 = 6/8
6/8 − 1/8 = 5/8
gcd(5, 8) = 1  →  already lowest
decimal = 0.625

Explanation: you only had to rewrite one of the two fractions. Using 32 as the denominator would also work (24/32 − 4/32 = 20/32), it just forces you to reduce back down to 5/8 afterward.

Example 3: Coprime denominators (the default case)

1/3 − 1/4

LCD = 3 × 4 = 12
4/12 − 3/12 = 1/12
decimal = 0.08333...

Explanation: this is the classic result that surprises people. A third and a quarter look close, and the gap between them is a single twelfth, the thinnest slice in the problem.

Example 4: Mixed numbers that require borrowing

3 1/4 − 1 2/3

Step 1: 3 1/4 = (3 × 4) + 1 = 13/4
        1 2/3 = (1 × 3) + 2 = 5/3
Step 2: LCD = lcm(4, 3) = 12
Step 3: 13/4 = 39/12
        5/3  = 20/12
Step 4: 39/12 − 20/12 = 19/12
Step 5: gcd(19, 12) = 1  →  lowest terms
        mixed = 1 7/12   (19 ÷ 12 = 1 remainder 7)
        decimal = 1.58333...

Explanation: doing this by hand the “columns” way requires borrowing, because 1/4 is smaller than 2/3. Converting to improper fractions first removes the borrowing entirely, which is exactly why the calculator does it in Step One.

Example 5: A negative result

1/5 − 3/4

LCD = 20
4/20 − 15/20 = −11/20
decimal = −0.55

Explanation: subtraction is not commutative. 1/5 − 3/4 and 3/4 − 1/5 have the same size but opposite signs. The sign lives on the numerator, so you get -11/20, never 11/-20.

Example 6: A whole number minus a fraction

2 − 5/6

2 = 2/1 = 12/6
12/6 − 5/6 = 7/6
mixed = 1 1/6
decimal = 1.1666...

Explanation: any whole number is already a fraction with a denominator of 1, so the same five steps apply with no special case.

Example 7: A measurement subtraction

7/8" − 5/16"

16 ÷ 8 = 2  →  LCD = 16
7/8 = 14/16
14/16 − 5/16 = 9/16
decimal = 0.5625"

Explanation: shop and tape-measure fractions almost always share a power-of-two denominator (2, 4, 8, 16, 32), so the LCD is just the largest denominator in the problem. Handy when you are trimming a board or checking a tolerance.

What your results mean

Fraction form is exact: subtraction never introduces rounding error, so 1/12 is the true answer down to the last digit.

Decimal form approximates the fraction whenever it repeats (like twelfths, thirds, sixths, and sevenths). 1/12 = 0.08333... is truncated for display, so avoid chaining rounded decimals through several steps if precision matters.

Mixed form rewrites an improper result (numerator larger than denominator) as a whole number plus a fraction: 19/12 → 1 7/12. Divide the numerator by the denominator; the quotient is the whole number and the remainder becomes the new numerator.

If the first fraction is smaller than the second, the result is negative. The calculator keeps that sign on the numerator, e.g. -1/12, rather than the denominator.

LCD vs. cross multiplication: two valid routes

You do not strictly need the least common denominator. Any common denominator gets the right answer, it just leaves more reducing to do at the end.

Cross multiplication:  a/b − c/d = (a×d − c×b) / (b×d)
1/3 − 1/4 = (1×4 − 1×3) / (3×4) = 1/12
5/6 − 1/4 = (5×4 − 1×6) / 24 = 14/24 = 7/12   ← needed reducing

Use cross multiplication when you want one formula you never have to think about. Use the LCD when you want the smallest numbers and the cleanest final answer, which is what this calculator reports.

Common mistakes when subtracting fractions

• Subtracting the denominators too. 3/4 − 1/4 is 2/4, not 2/0. The denominator is a unit, not a quantity.
• Forgetting to scale the numerator. Turning 1/3 into ?/12 means multiplying the top by 4 as well, giving 4/12, not 1/12.
• Reversing the order. 1/4 − 1/3 is not the same as 1/3 − 1/4. Order matters and flips the sign.
• Leaving the answer unreduced. 2/8 is correct but not finished; 1/4 is the expected form on most homework and tests.
• Losing the whole number in mixed subtraction. Convert to improper fractions first and the borrowing problem disappears.

Common pairs and their results

Frequently asked questions

Do I have to use the least common denominator? No. Any common denominator produces the correct value, including the simple product of the two denominators. The LCD just keeps the numbers small and usually saves you a reducing step.

What is 1/2 minus 1/3? 1/6. Rewrite both over 6: 3/6 − 2/6 = 1/6, or about 0.1667.

How do you subtract fractions with the same denominator? Subtract the numerators and keep the denominator, then reduce. 7/10 − 3/10 = 4/10 = 2/5.

How do you subtract a fraction from a whole number? Write the whole number over 1, convert it to the shared denominator, then subtract. 3 − 1/4 = 12/4 − 1/4 = 11/4 = 2 3/4.

Can the answer be negative? Yes, whenever the second fraction is larger than the first. The calculator returns the sign on the numerator, like -11/20.

Why does the decimal keep repeating? A fraction terminates as a decimal only when its reduced denominator has no prime factors other than 2 and 5. Twelfths, thirds, sixths, and sevenths repeat forever, so the decimal shown is rounded while the fraction stays exact.

How do you subtract three or more fractions? Find one common denominator for all of them, then subtract left to right: 1 − 1/2 − 1/3 = 6/6 − 3/6 − 2/6 = 1/6.

For addition instead, switch to the adding fractions calculator. For multiplication or division, try the fraction calculator, which also handles rounding to the nearest 1/16” or 1/32” for measurements.