Operation
Subtracting Mixed Numbers
Subtract one mixed number or fraction from another and watch the result, and the full working, update as you type. This calculator handles matching denominators, finding a common denominator when they differ, borrowing a whole unit when the second fraction is larger than the first, and simplifying the final answer — all in real time, no button required.
Type the whole number, numerator, and denominator into their own fields. For a negative value such as −2 3/4, use the sign toggle or type −2 in the whole-number field.
Result
View step-by-step working
Formula
The Subtracting Fractions Formula
Subtracting fractions formula
This formula always works, whatever the two denominators are, because multiplying each fraction by the other's denominator (top and bottom) rewrites both over the same shared denominator, bd, before subtracting. The order matters here in a way it doesn't for addition — a/b − c/d and c/d − a/b land on opposite signs of the same value, so the numerator that comes first in the formula has to be the one you're subtracting from.
Method
Subtracting Mixed Numbers Without Borrowing
Worked Example — 5 3/4 − 2 1/4
When the first fraction part is already large enough to subtract from, no borrowing is needed — subtract the whole numbers and the numerators separately.
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Check the denominators match
both fractions are already over 4
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Subtract the whole numbers
5 − 2 = 3
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Subtract the numerators
3/4 − 1/4 = 2/4 — the denominator stays at 4
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Simplify the fraction
2/4 → 1/2
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Combine
3 + 1/2 = 3 1/2
5 3/4 − 2 1/4 = 3 1/2
Method
Subtracting Mixed Numbers That Require Borrowing
Worked Example — 5 1/4 − 2 3/4
When the fraction being subtracted is larger than the fraction you're starting with, you have to borrow a whole from the first number's whole-number part before you can subtract.
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Compare the numerators
1/4 is smaller than 3/4, so borrowing is needed
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Borrow one whole from 5
5 1/4 → 4 + 4/4 + 1/4 = 4 5/4
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Subtract the whole numbers
4 − 2 = 2
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Subtract the numerators
5/4 − 3/4 = 2/4 → 1/2
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Combine
2 + 1/2 = 2 1/2
5 1/4 − 2 3/4 = 2 1/2
Method
Subtracting Fractions with Different Denominators
Worked Example — 4 5/6 − 1 1/3
Different denominators need a common denominator before the numerators can be compared or subtracted at all.
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Find the common denominator
of 6 and 3: the LCD is 6
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Rewrite each fraction over 6
5/6 stays 5/6, and 1/3 → 2/6
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Subtract the whole numbers
4 − 1 = 3
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Subtract the numerators
5/6 − 2/6 = 3/6 → 1/2
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Combine
3 + 1/2 = 3 1/2
4 5/6 − 1 1/3 = 3 1/2
Special Case
When the Result Is Negative
Unlike addition, subtracting mixed numbers can legitimately produce a negative answer, whenever the second mixed number is larger than the first. Converting both values to improper fractions first lets the sign travel through the formula on its own, with no separate borrowing step to manage.
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Convert to improper fractions
2 1/3 → 7/3, and 2 2/3 → 8/3
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Subtract the numerators
7/3 − 8/3 = −1/3
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Read off the result
−1/3
2 1/3 − 2 2/3 = −1/3
Why It Matters
Where Subtracting Mixed Numbers Actually Gets Used
Subtracting mixed numbers shows up anywhere a quantity gets reduced by a smaller amount that isn't a whole number itself — cutting 1 3/4 feet off a board that started at 6 1/2 feet, figuring out how much flour is left in a 5-pound bag after using 2 1/3 pounds, or working out how much time remains in a task once 1 1/4 hours of a 3-hour block have already passed.
It's also the operation behind checking a running total. If a recipe calls for 3 1/2 cups of a dry ingredient split across two bowls, and one bowl already holds 2 1/4 cups, subtraction tells you exactly how much belongs in the second — no guessing required.
The borrowing step in particular mirrors something everyone already does with whole numbers — regrouping a ten into ones when subtracting 42 − 17, say — just applied one level down, to fractions instead of ones and tens. Recognising that parallel is often what makes the fraction version click for the first time.
The calculator above always shows the full working, whichever method you reach for, so you can check a by-hand borrowing calculation against the improper-fraction shortcut and confirm both land on the same mixed number.
Common Mistakes
Where Subtraction Calculations Go Wrong
Quick Reference
Subtraction Results for Common Mixed Numbers
Search or scroll this table for the result of subtracting common mixed-number pairs — useful for checking homework or double-checking a mental calculation, including a few pairs that land on a negative result.
Questions
Frequently Asked Questions
Questions specific to subtracting fractions, not already covered elsewhere on the site.