Mixed Number Calculator
Type mixed numbers like 2 1/3 straight in and add, subtract, multiply or divide them, or open “Mixed ↔ improper” to convert between mixed numbers and improper fractions. Every answer shows its working.
- Mixed numbers in, mixed numbers out
- Improper fraction converter
- Step-by-step working
- No sign-up
Enter fractions, mixed numbers or whole numbers
Use / for a fraction bar, a space for mixed numbers (2 1/3), × or * to multiply and ÷ or : to divide. Multiplication and division are done before addition and subtraction.
- Simplified fraction
- 49/12
- Mixed number
- 4 1/12
- Decimal
- 4.083 repeating
- Percentage
- 408.3 repeating%
A bar over digits means they repeat forever. In plain text this is written 4.08(3).
Step-by-step working
Write every number as a fraction
2 and 1 over 3=2 × 3 + 1 over 3=7 over 31 and 3 over 4=1 × 4 + 3 over 4=7 over 4For a mixed number, multiply the whole number by the denominator and add the numerator.
Find the least common denominator (LCD)
3 = 34 = 2²LCD = 2² × 3 = 12The LCD is the smallest number every denominator divides into. Take each prime factor the most times it appears in any one denominator.
Rewrite each fraction with denominator 12
7 over 3=7 × 4 over 3 × 4=28 over 127 over 4=7 × 3 over 4 × 3=21 over 12Multiply the top and the bottom by the same number, so each fraction keeps its value.
Add the numerators
28 over 12+21 over 12=28 + 21 over 12=49 over 12Keep the common denominator and combine only the numerators.
Check the fraction is in simplest form
GCF(49, 12) = 149 over 12 is already in lowest terms.Write it as a mixed number
49 ÷ 12 = 4 remainder 149 over 12=4 and 1 over 12The quotient is the whole number and the remainder becomes the new numerator.
Convert to a decimal
49 ÷ 12=4.083 repeatingThe digits under the bar repeat forever.
Exact arithmetic for numbers of any size, with no rounding errors. Everything runs in your browser, and nothing you type leaves this page.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 2 1/3, which means 2 + 1/3. An improper fraction has a numerator that is as big as or bigger than its denominator, such as 7/3; it is the same value written as one fraction. To calculate with mixed numbers, the reliable method is to turn each one into an improper fraction, do the arithmetic, simplify, and then turn the result back into a mixed number. This calculator does exactly that and shows each conversion. It also accepts plain fractions, whole numbers and decimals in the same problem, and negative mixed numbers such as −1 1/2.
How to use the mixed number calculator
- For each mixed number, type the whole number in the left box and the fraction in the stacked boxes: 2 1/3 is 2, 1 and 3.
- Choose +, −, × or ÷. Add more numbers if you need them, or type the problem as text, for example 3 1/2 − 1 3/4.
- Read the answer as a mixed number, an improper fraction and a decimal.
- Check the working: each mixed number is converted to an improper fraction first, then combined, simplified and converted back.
- To convert a single value, open the “Mixed ↔ improper” tab and enter either a mixed number or an improper fraction.
Mixed number rules
- w n/d = (w × d + n)/d
- 3 2/5 = (3 × 5 + 2)/5 = 17/5.
- n/d = q r/d, where n = q × d + r
- 17/5: 17 = 3 × 5 + 2, so 3 2/5.
- Add or subtract
- Convert to improper fractions, use the LCD, combine the numerators, convert back.
- Multiply or divide
- Always convert to improper fractions first; for ÷, flip the second fraction.
Why use this mixed number calculator
- Every step, freeThe full working is always on the page: common denominator, rewritten fractions, greatest common factor and the final simplification. No account, no premium tier and no daily limit.
- Exact answers at any sizeFractions are stored as exact whole numbers, so a 40-digit numerator stays exact. There is no floating-point rounding of the kind that turns 0.1 + 0.2 into 0.30000000000000004.
- Repeating decimals shown properly1/7 is shown as 0.142857 with a bar over the repeating block, instead of being cut off at 0.1428571429. You also get a rounded value to copy.
- Fast and privateThe answer updates as you type and is worked out on your device. Nothing you enter is sent to a server, and the calculator keeps working if your connection drops.
How it compares with other fraction calculators
| Feature | This calculator | Typical online calculators |
|---|---|---|
| More than two numbers in one problem | Yes, up to 10, with order of operations | Usually two |
| Fractions, mixed numbers, whole numbers and decimals together | Yes | Often separate calculators |
| Full step-by-step working | Always free | Often missing or behind a paywall |
| Repeating decimals | Exact, with a bar over the repeating digits | Rounded to a few places |
| Very large numbers | Exact at any size | Rounded or a separate big number tool |
| Decimal to fraction for repeating decimals | Type 0.1(6) or 0.1666... | Count the repeating digits yourself |
| Privacy | Runs in your browser, nothing sent | Inputs often sent to a server |
Common uses
- Recipes. Double 1 3/4 cups of flour or add 2 1/2 and 1 1/3 cups.
- Measurements. Add lengths like 5 3/8 in + 2 7/16 in without converting to decimals.
- Homework. Check mixed number sums, differences, products and quotients, with the conversions shown.
- Time and distance. Work with 1 1/2 hours or 2 3/4 miles directly.
More math help: the percentage calculator for percent questions, the ratio calculator for simplifying and scaling ratios, and the math editor to type up your working as a neat equation.
Fraction words explained
- Numerator
- The top number. It counts how many parts you have.
- Denominator
- The bottom number. It says how many equal parts make one whole.
- Proper fraction
- The numerator is smaller than the denominator, such as 3/4.
- Improper fraction
- The numerator is as big as or bigger than the denominator, such as 7/4.
- Mixed number
- A whole number and a proper fraction together, such as 1 3/4.
- Equivalent fractions
- Different fractions with the same value, such as 1/2, 2/4 and 50/100.
- Least common denominator
- The smallest number all the denominators divide into.
- Greatest common factor
- The biggest number that divides both the numerator and the denominator.
- Reciprocal
- A fraction turned upside down. The reciprocal of 2/3 is 3/2.
- Repeating decimal
- A decimal whose digits repeat forever, such as 0.333... for 1/3.
For example, in 3 over 4 the numerator is 3 and the denominator is 4.
Worked example: 2 1/3 + 1 3/4
Convert both mixed numbers: 2 1/3 = (2 × 3 + 1)/3 = 7/3, and 1 3/4 = (1 × 4 + 3)/4 = 7/4. The LCD of 3 and 4 is 12, so 7/3 = 28/12 and 7/4 = 21/12. Add the numerators: 28 + 21 = 49, giving 49/12. Divide 49 by 12: 4 remainder 1, so the answer is 4 1/12. As a decimal that is 4.08333..., with the 3 repeating.
What to expect from the result
Results are exact and simplified. A negative sign in front of a mixed number applies to the whole value, so −2 1/2 means −(2 + 1/2) = −5/2. Brackets are not supported, and multiplication and division are done before addition and subtraction.
Mixed Number Calculator questions
How do you add mixed numbers?
Either add the whole numbers and the fractions separately and carry if the fractions add up to more than 1, or turn both into improper fractions, add them over a common denominator and convert back. 1 1/2 + 2 2/3 = 3/2 + 8/3 = 9/6 + 16/6 = 25/6 = 4 1/6.
How do you subtract mixed numbers?
Converting to improper fractions avoids borrowing. 3 1/4 − 1 1/2 = 13/4 − 3/2 = 13/4 − 6/4 = 7/4 = 1 3/4. If you subtract the parts separately, you would have to borrow 1 from the 3 because 1/4 is smaller than 1/2.
How do you multiply mixed numbers?
Turn them into improper fractions first and then multiply across. 1 1/2 × 2 1/3 = 3/2 × 7/3 = 21/6 = 7/2 = 3 1/2. Multiplying the whole numbers and fractions separately gives the wrong answer.
How do you divide mixed numbers?
Convert to improper fractions, flip the second one and multiply. 2 1/2 ÷ 1 1/4 = 5/2 ÷ 5/4 = 5/2 × 4/5 = 20/10 = 2.
How do I change an improper fraction to a mixed number?
Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator over the same denominator. 17/5: 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5.
How do I change a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and put the result over the denominator. 3 2/5 = (3 × 5 + 2)/5 = 17/5.