Compare the whole against the mixed number
A whole number has no fraction part, so there is nothing to take the mixed number’s fraction from directly. That missing part is what the regrouping solves.
Subtracting mixed numbers
How to Subtract a Mixed Number from a Whole Number
A whole number has no fraction part to take the mixed number’s fraction from — so one whole is unbundled into fraction parts first. One move, and the problem becomes an ordinary two-column subtraction.
- borrow from the whole
- rewrite the whole as a fraction
- no fraction part to take from
- same answer, two methods
Visual subtraction tool
See how fraction parts become ready to subtract
Make the parts match, regroup one whole when you need more pieces, then take away the second amount.
Type the full expression
Examples: 3/4 - 1/6, 2 - 3/4, or 2 1/4 - 1 2/3.
Visual explanation
Notice the matching parts
These fractions already name pieces of the same size.
First amount5/1
5 wholes
Amount to take away7/3
2 wholes
Quick answer
Break one whole open, then subtract
To compute 5 - 2 1/3, rewrite the 5 as 4 3/3: one whole drops out of the whole column and reappears as three thirds. Then subtract in columns — 4 - 2 = 2 wholes and 3/3 - 1/3 = 2/3 — for an answer of 2 2/3.
The improper-fraction route agrees: 5 = 15/3 and 2 1/3 = 7/3, and 15/3 - 7/3 = 8/3 = 2 2/3. Two methods, one answer — which is what makes the check trustworthy.
The method
Four steps: spot, unbundle, subtract, or convert
Unbundle one whole
Rewrite the whole number one whole smaller, and attach one whole’s worth of parts: 5 becomes 4 3/3, 7 becomes 6 5/5. The denominator copies the mixed number’s fraction part.
Subtract wholes and parts separately
Now both numbers have whole and fraction parts: 4 3/3 - 2 1/3 subtracts to 2 2/3 with no further regrouping needed.
Or convert everything to improper fractions
5 = 15/3 and 2 1/3 = 7/3, so 15/3 - 7/3 = 8/3 = 2 2/3. One procedure, the same answer — a useful check and a clean path for harder problems.
Worked example
The base case: 5 - 2 1/3
5 - 2 1/3 = 4 3/3 - 2 1/3 = 2 2/3
Five wholes become four wholes plus three thirds. Taking 2 wholes and 1 third leaves 2 wholes and 2 thirds. The unbundled whole contributed exactly the 3/3 that the fraction subtraction needed.
Worked example
Eighths: 4 - 1 5/8
4 - 1 5/8 = 3 8/8 - 1 5/8 = 2 3/8
One whole is 8/8, so 4 rewrites as 3 8/8. Subtracting 1 5/8 leaves 2 wholes and 3 eighths. The improper-fraction check agrees: 32/8 - 13/8 = 19/8 = 2 3/8.
Worked example
Fifths with a simplify: 7 - 3 2/5
7 - 3 2/5 = 6 5/5 - 3 2/5 = 3 3/5
Seven becomes 6 5/5, and 5/5 - 2/5 = 3/5 with 6 - 3 = 3 wholes. Nothing here simplifies because 3 and 5 share no common factor.
Worked example
Improper-fraction method: 10 - 4 1/2
10 - 4 1/2 = 20/2 - 9/2 = 11/2 = 5 1/2
Ten wholes are 20 halves, and 4 1/2 is 9 halves. The difference 11/2 regroups to 5 1/2. Both methods are worth running once so the regrouping is visibly verified.
Why unbundling works
Rewriting 5 as 4 3/3 changes the writing, not the value: 4 wholes plus 3/3 is 4 wholes plus exactly one whole, which is 5. The regrouping moves one whole from the unit you have plenty of (wholes) into the unit the subtraction needs (thirds). It is the same idea as breaking a dollar into four quarters to pay a 75-cent debt.
The denominator of the new fraction part always copies the mixed number’s fraction part, because that is the unit the subtraction will happen in. In 7 - 3 2/5 the whole opens into fifths (6 5/5); in 10 - 4 1/2 it opens into halves (9 2/2). Once both numbers speak the same fraction language, the two-column subtraction runs without further decisions.
See the mixed-by-mixed version of this methodCommon mistakes to avoid
- Subtracting the fraction from nothing: Writing 5 - 2 1/3 as 3 1/3 treats the 1/3 as if it disappeared. The fraction part must be taken from a whole that has been broken open — 4 3/3 — not ignored.
- Borrowing 1 instead of one whole’s parts: The regroup moves one whole, which equals a full denominator of parts: 5 becomes 4 3/3 (adding 3/3), not 4 1/3. Adding only 1/3 breaks the value and every line after it.
- Using the wrong denominator when unbundling: The new fraction part copies the mixed number’s denominator. In 7 - 3 2/5, the rewrite is 6 5/5 — fifths, not 6 1/2 or 6 2/2 — because the subtraction happens in fifths.
Keep learning
Related fraction topics
Common questions
Subtracting a Mixed Number from a Whole Number FAQ
Unbundle one whole first. Rewrite the whole number as one-less whole plus one whole’s worth of fraction parts, then subtract: 5 - 2 1/3 = 4 3/3 - 2 1/3 = 2 2/3. Converting everything to improper fractions — 15/3 - 7/3 = 8/3 — reaches the same answer.