MATHEMATICS · SUBTRACTION

Subtracting Fractions Calculator

Subtract two fractions with unlike denominators. This calculator finds the LCD, converts both fractions to equivalent fractions over that LCD, then subtracts the numerators. Every step is visible as you type.

SUBTRACTION CALCULATOR LIVE

Enter two fractions to subtract. Switch to Mixed Numbers for whole-number parts.

01 · METHOD

How to Subtract Fractions with Unlike Denominators

Subtracting fractions with different denominators takes three steps: find the LCD of the two denominators, rewrite each fraction as an equivalent fraction over that LCD, then subtract the numerators and keep the shared denominator.

Step 1: Find the LCD

Find the least common denominator of the two denominators, the same way you would for addition.

Step 2: Convert

Rewrite each fraction as an equivalent fraction with the LCD as its new denominator.

Step 3: Subtract

Subtract the second numerator from the first, keep the denominator, then simplify if possible.

02 · MATCHING DENOMINATORS

Subtracting Fractions with Matching Denominators

When two fractions already share a denominator, subtraction is immediate: subtract the numerators and keep the denominator. For example, 5/8 − 3/8 = 2/8, which simplifies to 1/4. No LCD step is needed because the denominators already match. That is exactly why finding a common denominator first matters for fractions that don't already share one.

03 · MIXED NUMBERS

Subtracting Mixed Numbers

Mixed-number subtraction sometimes requires borrowing, just like regular column subtraction. Consider 3 1/4 − 1 3/4: the fractional part of the second number (3/4) is larger than the fractional part of the first (1/4), so you can't subtract them directly. Borrow one whole unit from the 3, turning it into 2 and adding that whole (as 4/4) to the 1/4, giving 2 5/4 − 1 3/4. Now the fractional parts subtract cleanly: 5/4 − 3/4 = 2/4 = 1/2, and the whole numbers give 2 − 1 = 1, so the final answer is 1 1/2. The safest way to avoid borrowing mistakes is to convert both mixed numbers to improper fractions first, subtract as ordinary fractions, then convert the result back to a mixed number at the end.

04 · EXAMPLES

Worked Fraction Subtraction Examples

Six subtraction problems from simple fractions to mixed numbers.

Example 1
3/4 − 1/6
= 7/12

LCD of 4 and 6 is 12; 3/4 becomes 9/12 and 1/6 becomes 2/12.

Example 2
5/8 − 1/3
= 7/24

LCD of 8 and 3 is 24; 5/8 becomes 15/24 and 1/3 becomes 8/24.

Example 3
2/3 − 1/4
= 5/12

LCD of 3 and 4 is 12; 2/3 becomes 8/12 and 1/4 becomes 3/12.

Example 4
2 1/2 − 1 3/4
= 3/4

Convert to improper fractions (5/2 and 7/4), find the LCD of 4, then subtract.

Example 5
7/8 − 3/5
= 11/40

LCD of 8 and 5 is 40; 7/8 becomes 35/40 and 3/5 becomes 24/40.

Example 6
1/2 − 1/3
= 1/6

LCD of 2 and 3 is 6; 1/2 becomes 3/6 and 1/3 becomes 2/6.

05 · CHECKING

How to Check a Subtraction Answer

A subtraction answer should always be checked by adding it back to the fraction you subtracted. The result should return the original first fraction. For 3/4 − 1/6 = 7/12, check by adding 7/12 + 1/6: convert 1/6 to 2/12, and 7/12 + 2/12 = 9/12, which simplifies to 3/4, matching the original first fraction and confirming the subtraction was done correctly. This same check works for mixed-number subtraction once both numbers are back in mixed form: add the difference to the fraction subtracted and confirm you land back on the number you started with.

06 · COMPARISON

Subtraction vs Addition

Adding and subtracting fractions share the exact same first two steps: find the LCD, then rewrite both fractions as equivalents over that LCD. The only difference is the final operation: addition sums the numerators, subtraction takes the difference. Once you're comfortable finding the LCD for addition, subtraction is the same skill applied one step further.

07 · FAQ

Frequently Asked Questions About Subtracting Fractions

How do you subtract fractions with different denominators?
Find the LCD of the two denominators, rewrite both fractions as equivalent fractions over that LCD, then subtract the numerators and keep the shared denominator. Simplify the result if possible. For example, subtracting 1/4 from 3/4 needs no conversion since they already share a denominator, but most problems require this extra rewriting step first.
What is 3/4 − 1/6?
The LCD of 4 and 6 is 12. 3/4 becomes 9/12 and 1/6 becomes 2/12. 9/12 − 2/12 = 7/12, which is already in lowest terms. Since 9 and 12 share no common factor other than 1, the fraction 7/12 cannot be simplified any further.
How do you subtract mixed numbers?
Convert each mixed number to an improper fraction first, find the LCD of the denominators, subtract the improper fractions, then convert the result back to a mixed number if needed. If the second fraction part is larger than the first, borrow one whole unit from the first mixed number before subtracting.
What is 5/8 − 1/3?
The LCD of 8 and 3 is 24. 5/8 becomes 15/24 and 1/3 becomes 8/24. 15/24 − 8/24 = 7/24, already in lowest terms. Because 7 and 24 share no common factor besides 1, this result cannot be reduced further, so 7/24 is the final answer.
What happens when the result of subtracting fractions is negative?
If the first fraction is smaller than the second, the difference is negative. The calculator shows the sign clearly, e.g. −1/6, meaning the second fraction was actually larger than the first. For instance, subtracting 3/4 from 1/2 produces −1/4, since 1/2 is the smaller value in that pair.