📐 Math
Mixed Fraction Calculator
Use this free mixed fraction calculator to get fast, accurate results.
📝 Your Assumptions
This mixed fraction calculator converts any mixed number into an improper fraction and performs addition, subtraction, multiplication, or division with another fraction. It's built for students, cooks, carpenters, and anyone who works with measurements like 2 3/4 cups or 5 1/2 inches. You get the exact result in lowest terms plus a decimal equivalent, so you can double-check your work or move straight to the next step.
How to Use This Calculator
Enter your mixed numbers and pick an operation to get an exact result in seconds.
1
Enter the first mixed number
Type the whole number in the first box, then the numerator and denominator in the next two. For 3 5/8, enter 3, 5, and 8. If you only have a proper fraction like 7/8, leave the whole number as 0.
2
Choose the operation
Select add, subtract, multiply, or divide from the dropdown. For 2 1/2 + 1 3/4, pick addition; for 4 1/3 ÷ 1 1/6, pick division. The calculator uses the same rules you'd apply by hand.
3
Enter the second mixed number
Fill in the whole number, numerator, and denominator for the second value. For 5 2/3, enter 5, 2, and 3. You can mix a mixed number with a simple fraction by setting its whole number to 0.
4
Press Calculate
Click the Calculate button to run the operation. The tool converts both mixed numbers to improper fractions — 2 1/2 becomes 5/2 — then computes the result. It returns the answer as a mixed number, an improper fraction, and a decimal.
5
Read and simplify the result
The answer appears in lowest terms, like 4 1/4 instead of 17/4 or 4.25. Check the improper fraction if you need to show work, or the decimal if you're measuring. Use the reset button to clear the fields for a new problem.
What Your Results Mean
Each part of the output tells you something different about the answer.
Mixed number result
This is the answer written as a whole number and a proper fraction, such as 3 2/5. It's the form most useful for measurements and everyday math. If the result is less than 1, the whole number will be 0.
Improper fraction
The same answer expressed as a single fraction, like 17/5 for 3 2/5. Teachers often require this form because it makes multiplication and division easier. It shows exactly how many equal parts you have.
Decimal equivalent
The fraction converted to a decimal, such as 3.4 for 3 2/5. This is handy when you're using a calculator, scale, or spreadsheet that only accepts decimals. It also helps you compare two results quickly.
Lowest terms
The result is automatically reduced, so 6/8 becomes 3/4 and 10/4 becomes 2 1/2. Reducing makes the answer easier to read and compare. If you need the unreduced form for a specific method, multiply the numerator and denominator back.
Common denominator
For addition and subtraction, the calculator finds a shared denominator. Adding 1/2 + 1/3 uses sixths: 3/6 + 2/6 = 5/6. You don't have to find it yourself, but knowing the step helps you check the answer.
Negative results
If you subtract a larger mixed number from a smaller one, the result is negative, like 1 1/4 − 2 3/4 = −1 1/2. The negative sign applies to the whole value, not just the fraction. This matters when tracking debts, temperature changes, or elevation drops.
Key Terms
Mixed number
A number made of a whole number and a proper fraction, such as 2 3/4. It means 2 plus 3/4.
Improper fraction
A fraction where the numerator is greater than or equal to the denominator, like 11/4. It can be rewritten as a mixed number.
Numerator
The top number in a fraction. In 3/8, the 3 is the numerator and tells you how many parts you have.
Denominator
The bottom number in a fraction. In 3/8, the 8 is the denominator and tells you how many equal parts make one whole.
Lowest terms
A fraction written with the smallest possible numbers, where the numerator and denominator share no common factor other than 1. For example, 4/8 reduces to 1/2.
❓ Frequently Asked Questions
Convert each mixed number to an improper fraction first. 2 3/4 becomes 11/4 (2 × 4 + 3 = 11), and 1 5/6 becomes 11/6 (1 × 6 + 5 = 11). The least common denominator for 4 and 6 is 12, so rewrite both: 11/4 = 33/12 and 11/6 = 22/12. Add the numerators: 33 + 22 = 55, giving 55/12. Convert back to a mixed number: 12 goes into 55 four times with a remainder of 7, so the answer is 4 7/12. The decimal equivalent is about 4.583. If you only need the decimal, a percentage calculator can handle the conversion, but for exact fraction work, keep the mixed number form. Always check that your final fraction is in lowest terms — 55/12 already is, since 55 and 12 share no common factors.
You may need to borrow from the whole number. Take 5 1/4 − 2 3/4. The fraction 1/4 is smaller than 3/4, so borrow 1 from the 5 and add it to 1/4: 5 1/4 becomes 4 5/4. Now subtract: 4 − 2 = 2 and 5/4 − 3/4 = 2/4, which reduces to 1/2. The answer is 2 1/2, or 2.5 as a decimal. Alternatively, convert to improper fractions: 5 1/4 = 21/4 and 2 3/4 = 11/4, then 21/4 − 11/4 = 10/4 = 2 1/2. The calculator handles the borrowing automatically. If your result comes out negative, like 1 1/2 − 3 1/4 = −1 3/4, the negative sign applies to the whole answer. For comparing how much a value changed, try the percentage-change-calculator.
For multiplication, convert to improper fractions, multiply straight across, then simplify. Example: 1 1/2 × 2 2/3. First, 1 1/2 = 3/2 and 2 2/3 = 8/3. Multiply: (3 × 8)/(2 × 3) = 24/6 = 4. For division, multiply by the reciprocal of the second fraction. Example: 3 1/3 ÷ 1 1/4. Convert: 3 1/3 = 10/3 and 1 1/4 = 5/4. Then 10/3 ÷ 5/4 = 10/3 × 4/5 = 40/15 = 8/3 = 2 2/3. Notice you never need a common denominator for multiplication or division — that's only for addition and subtraction. The calculator shows both the improper fraction and the mixed number result so you can verify each step. If you're scaling a recipe, multiply the mixed numbers first, then convert the final result to a decimal for measuring cups.
Yes. Enter the whole number with a denominator of 1, or set its whole-number field and leave the fraction portion as 0/1. For example, to compute 4 + 2 1/2, enter 4 as 4 0/1 (or just 4 with numerator 0 and denominator 1) and 2 1/2 as 2, 1, 2. The calculator converts 4 to 4/1 and 2 1/2 to 5/2, finds a common denominator of 2, and adds: 8/2 + 5/2 = 13/2 = 6 1/2. The decimal is 6.5. This works for subtraction, multiplication, and division too. It's especially useful in construction, where you might add a 3 1/2-inch spacer to a 12-inch board. The result, 15 1/2 inches, is easier to read than 15.5 when you're marking a tape measure. For percentage-based adjustments, the percentage-calculator is a better fit.
Divide the numerator by the denominator, then add the whole number. For 3 5/8: 5 ÷ 8 = 0.625, so 3 5/8 = 3.625. For 7 1/3: 1 ÷ 3 = 0.333..., so 7 1/3 ≈ 7.333. Some fractions produce repeating decimals — 1/3, 2/3, 1/6, 1/7 — and the calculator rounds them to a practical number of places. If you need exact precision, keep the fraction form. Common conversions worth memorizing: 1/8 = 0.125, 1/4 = 0.25, 1/3 ≈ 0.333, 3/8 = 0.375, 1/2 = 0.5, 5/8 = 0.625, 2/3 ≈ 0.667, 3/4 = 0.75, 7/8 = 0.875. These cover most tape-measure and recipe measurements. If you're converting a fraction to a percentage instead, multiply the decimal by 100 — 3 5/8 becomes 362.5%. The percentage-calculator can do that step for you.
Lowest terms means the numerator and denominator have no common factor other than 1. For example, 6/8 reduces to 3/4 because both divide by 2, and 10/15 reduces to 2/3 because both divide by 5. An answer like 4 6/8 is mathematically correct but not finished — you'd write 4 3/4. Reducing makes answers easier to compare and use. If you're adding 1/4 + 1/4 and get 2/4, reducing to 1/2 tells you immediately that you have half a cup, not two quarters. In construction, 7/8 is a standard tape-measure mark, while 14/16 is not, even though they're equal. The calculator reduces automatically using the greatest common divisor. To reduce by hand, list the factors of both numbers and divide by the largest shared one. For 18/24, the factors of 18 are 1, 2, 3, 6, 9, 18 and of 24 are 1, 2, 3, 4, 6, 8, 12, 24 — the GCD is 6, so 18/24 = 3/4.
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