Overview
Mixed Number Arithmetic
Add, subtract, multiply, or divide two mixed numbers in one place. Pick an operation, type your values, and watch the result and the full working update instantly — no button required. Use this page to see how the four operations relate to each other, then jump to a dedicated page for a deeper dive into any one of them.
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
The Universal Method
One Workflow Handles All Four Operations
Convert, Operate, Simplify
Whichever operation a problem calls for, the same four-step shape gets you to the answer. Only the middle step changes.
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Convert to improper fractions
2 1/2 → 5/2, and 1 1/3 → 4/3
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Match denominators — addition and subtraction only
5/2 → 15/6, and 4/3 → 8/6 — multiplication and division skip this step
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Apply the operation
+, −, ×, or ÷
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Simplify and convert back
reduce with the GCF, then rewrite as a mixed number
Every operation ends the same way: a simplified mixed number.
Side by Side
How the Four Operations Compare
Each operation starts from the same improper-fraction form but treats the numerator and denominator differently from there. Here is what changes, and what stays the same, for each one.
Addition
Needs a common denominator. Add the numerators once the denominators match.
2 1/4 + 1 1/2 = 3 3/4
Subtraction
Needs a common denominator. Subtract the numerators once matched, borrowing if needed.
3 1/4 − 1 1/2 = 1 3/4
Multiplication
No common denominator needed. Multiply numerators together and denominators together.
2 1/4 × 1 1/2 = 3 3/8
Division
No common denominator needed. Multiply by the reciprocal of the second fraction instead.
2 1/4 ÷ 1 1/2 = 1 1/2
Notice the pattern: addition and subtraction are the two operations that actually combine amounts of the same size, so they're the only two that ever require a common denominator. Multiplication and division reshape the fraction itself rather than combining like parts, so the original denominators never need to match at all.
Why It Matters
Where Each Operation Shows Up in Real Life
Addition and subtraction of mixed numbers appear anywhere amounts get combined or compared: totaling the lengths of boards cut from a longer piece, tracking how much of a recipe's flour is left after using some, or figuring out how much time remains in a project after several partial-hour tasks. Anywhere the question is "how much altogether" or "how much is left," one of these two operations is doing the work.
Multiplication shows up whenever a fractional amount gets scaled — doubling a recipe that calls for 2 1/2 cups of flour, calculating the total distance of 3 1/2 laps around a 1/4-mile track, or finding the area of a rug that measures 4 1/2 feet by 3 feet. Any time a mixed number is being repeated or resized by another quantity, multiplication is the tool.
Division of mixed numbers answers "how many portions fit" or "how much is each share." Splitting 7 1/2 yards of fabric into pieces 1 1/4 yards long, or working out how many 3/4-cup servings come out of a 6-cup batch, both come down to dividing one mixed number by another — and in both cases, the reciprocal step is what makes the calculation possible.
Most real problems don't announce which operation they need — they describe a situation and leave the arithmetic to you. Recognizing the action underneath the words is the actual skill; once the right operation is identified, the convert-operate-simplify method above handles the rest the same way every time.
Common Mistakes
Where Mixed Number Arithmetic Goes Wrong
Questions
Frequently Asked Questions
Questions about choosing the right operation and combining several in one expression.