Convert a mixed number to an improper fraction (or back), and add, subtract, multiply or divide mixed numbers with full step-by-step work — including borrowing and carrying. Instant, no signup.
Enter a value and click Convert to see the result
Enter two mixed numbers and choose an operation to see the result
This free mixed fraction calculator is built specifically around whole-number-plus-fraction values like 2 3/4 — the form most measurements, recipes, and everyday quantities are written in. It converts a mixed number to an improper fraction (or an improper fraction back to a mixed number), and it adds, subtracts, multiplies, and divides two mixed numbers directly, showing the whole-and-fraction-parts method — including carrying for addition and borrowing for subtraction — rather than silently converting everything to improper fractions behind the scenes. A mixed number combines a whole quantity with a leftover part, and this mixed number calculator shows every step so you can see exactly how the whole and fractional parts interact.
The tool has two modes: a Convert mode that turns a mixed number into its improper-fraction equivalent, or an improper fraction into its mixed-number equivalent, with the full division-and-remainder working shown; and a Mixed Number Operations mode that adds, subtracts, multiplies, or divides two mixed numbers, using carrying/borrowing for addition and subtraction and the standard convert-then-multiply approach for multiplication and division.
Students and teachers learning the whole-and-fraction-parts method (rather than always converting to improper fractions first), cooks scaling recipes written as mixed numbers like 1 1/2 cups, carpenters and tradespeople combining tape-measure readings such as 3 3/8 inches, and anyone who wants to see borrowing and carrying demonstrated explicitly can all use this mixed number calculator.
Most arithmetic curricula teach mixed-number addition and subtraction by combining whole parts and fraction parts separately, borrowing a whole unit when the fraction being subtracted is larger — the same logic used in column subtraction with regular numbers. This is often the first method students learn, before they're introduced to converting everything to improper fractions. Seeing both the whole-and-fraction-parts steps and the final simplified answer builds a stronger, more transferable understanding of what a mixed number actually represents.
Recipes are almost always written in mixed numbers (1 1/2 cups flour, 2 1/4 teaspoons salt). Tape measures and rulers are read in mixed numbers (5 3/8 inches). Fabric, lumber, and pipe are cut and combined in mixed-number lengths. Fitness and nutrition logs often track quantities like 2 1/2 servings. Any time two such measurements need to be combined or compared, mixed-number arithmetic — not decimal rounding — keeps the result exact.
How this mixed fraction calculator converts and combines whole-number-plus-fraction values
If the added fraction parts reach or exceed a whole unit (numerator ≥ denominator), that whole unit is moved into the whole-number total — exactly like carrying a 1 in column addition.
Borrowing rewrites one whole unit from the first number as an equivalent fraction (denominator/denominator), added to its existing fraction part, so the subtraction can proceed without a negative fraction.
A mixed number's whole and fraction parts don't distribute cleanly across multiplication, so both numbers are converted to improper fractions before multiplying or dividing — the universally taught method.
From picking a tool to verifying the answer
Pick Convert (Mixed ↔ Improper) to change form, or Mixed Number Operations to combine two mixed numbers.
For Convert, type the whole number, numerator and denominator (or the improper numerator and denominator). For Operations, enter both mixed numbers in the whole/numerator/denominator boxes.
Choose +, −, ×, or ÷ for the two mixed numbers.
The calculator applies the matching method instantly, including any borrowing or carrying needed.
See the mixed number, the equivalent improper fraction, and the decimal value, plus the full worked steps.
Convert the result back through the opposite operation, or re-check the improper fraction form, to confirm it's correct.
Adding 1½ cups of flour to ⅔ cup of sugar in a recipe
A recipe calls for 1 1/2 cups of flour and 2/3 cup of sugar. What is the combined amount, using the whole-and-fraction-parts (carrying) method?
Explanation: The combined dry ingredients equal 2 1/6 cups. Notice the whole numbers were added first (1+0=1), and only the fractional parts (1/2 and 2/3) needed a common denominator — the carry step then moved the "extra" whole unit hiding inside 7/6 into the whole-number total. The final answer, 2 1/6, matches exactly what you'd get by converting both numbers to improper fractions first (3/2 + 2/3 = 13/6 = 2 1/6) — the two methods always agree, they just show different working.
What each result field actually represents
| Result Field | What It Means | Example Reading |
|---|---|---|
| Mixed Number | The primary answer as a whole number plus a proper fraction, always reduced to lowest terms | 2 1/6 |
| Improper Fraction | The same value written as a single fraction, useful for further calculation | 2 1/6 = 13/6 |
| Decimal | The value converted to base-10, useful for comparing with other decimal figures | 13/6 ≈ 2.166667 |
| Negative result (subtraction only) | Shown with a leading minus sign when the first mixed number is smaller than the second | 1 1/2 − 2 3/4 = −1 1/4 |
Reading a carry or borrow: the step list explicitly shows when a carry (addition) or borrow (subtraction) occurred — if you don't see that step, none was needed for your specific numbers.
Typical ranges: a fraction part of 0 in the final result means the answer simplified to a whole number, such as 4 1/2 − 1 1/2 = 3.
Manual verification: convert both original mixed numbers to improper fractions and redo the operation using the plain Fraction Calculator — the two tools should always agree.
Where working directly in mixed numbers is more natural than converting first
Practice the whole-and-fraction-parts method for adding and subtracting mixed numbers, with carrying and borrowing shown.
Demonstrate borrowing and carrying with mixed numbers step by step, before introducing the improper-fraction shortcut.
Combine or scale ingredient quantities written as mixed numbers, like 1 1/2 cups plus 2/3 cup.
Add or subtract tape-measure readings given directly as mixed numbers, like 5 3/8 inches.
Combine mixed-number yardages of fabric or trim without manually converting to improper fractions first.
Work with mixed-number pipe and fitting lengths directly as written on the gauge.
Add up mixed-number serving sizes or workout set counts logged throughout the day.
Convert a mixed-number model dimension into an exact improper fraction before scaling.
Practice mixed-number word problems that appear in pre-algebra and elementary math assessments.
Add board lengths or cut measurements expressed as mixed numbers of inches.
Combine partial-unit stock counts recorded as mixed numbers.
Verify a mixed-number answer from a textbook, worksheet, or online quiz instantly.
What this mixed fraction calculator does well, and where manual judgment is still needed
Two valid ways to solve the same problem
| Method | How It Works | Best For |
|---|---|---|
| Mixed-Number Method (this calculator's Operations tool) | Combine whole parts and fraction parts separately, carrying or borrowing as needed | Addition and subtraction; intuitive, measurement-friendly working |
| Improper-Fraction Method (the Fraction Calculator) | Convert everything to a single a/b fraction first, then apply one formula | Multiplication and division; fewer special cases to track |
Summary: This mixed fraction calculator gives you an instant, free way to convert between mixed numbers and improper fractions, and to add, subtract, multiply, and divide mixed numbers directly — with carrying, borrowing, and every step shown. Pair it with the Fraction Calculator for plain a/b arithmetic, and the Ratio Calculator for a fuller picture of proportional math.
Common questions about mixed number conversion and arithmetic
Trusted educational references to go deeper on mixed-number arithmetic
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