Fraction Calculator
Add, subtract, multiply and divide fractions, mixed numbers and whole numbers, with as many terms as you need. You get the simplified fraction, the mixed number and the exact decimal, plus every step of the working.
- Step-by-step working
- Mixed numbers
- Repeating decimals
- Up to 10 numbers
- 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
- 19/12
- Mixed number
- 1 7/12
- Decimal
- 1.583 repeating
- Percentage
- 158.3 repeating%
A bar over digits means they repeat forever. In plain text this is written 1.58(3).
Step-by-step working
Find the least common denominator (LCD)
4 = 2²6 = 2 × 3LCD = 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
3 over 4=3 × 3 over 4 × 3=9 over 125 over 6=5 × 2 over 6 × 2=10 over 12Multiply the top and the bottom by the same number, so each fraction keeps its value.
Add the numerators
9 over 12+10 over 12=9 + 10 over 12=19 over 12Keep the common denominator and combine only the numerators.
Check the fraction is in simplest form
GCF(19, 12) = 119 over 12 is already in lowest terms.Write it as a mixed number
19 ÷ 12 = 1 remainder 719 over 12=1 and 7 over 12The quotient is the whole number and the remainder becomes the new numerator.
Convert to a decimal
19 ÷ 12=1.583 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 fraction calculator?
A fraction calculator does arithmetic with fractions and gives the answer as a fraction instead of a rounded decimal. A fraction has a numerator (the top number, how many parts you have) and a denominator (the bottom number, how many equal parts make a whole). To add or subtract fractions you first give them a common denominator; to multiply you multiply straight across; to divide you flip the second fraction and multiply. This calculator does all four, accepts mixed numbers like 2 1/3, whole numbers and decimals in the same problem, and chains up to 10 numbers using the normal order of operations. Besides the main calculator it can simplify a fraction, convert between mixed numbers and improper fractions, turn fractions into decimals and back, and find the least common denominator of a list of fractions.
How to use the fraction calculator
- Type the top number (numerator) and the bottom number (denominator) of each fraction. For a mixed number such as 2 1/3, put the 2 in the box on the left. For a whole number, use only the left box.
- Choose +, −, × or ÷ between the numbers. Press “Add a number” to chain up to 10 numbers, or type the whole problem, such as 1/2 + 2/3 × 3/4, into the text box.
- Read the answer as a simplified fraction, a mixed number, a decimal and a percentage. It updates as you type.
- Go to “Step-by-step working” to see the common denominator, the rewritten fractions and how the result was simplified. Use “Use answer as first number” to keep going.
Fraction rules at a glance
- a/b + c/d = (ad + cb)/bd
- Using the LCD keeps the numbers small: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.
- a/b − c/d = (ad − cb)/bd
- 3/4 − 1/3 = 9/12 − 4/12 = 5/12.
- a/b × c/d = ac/bd
- Multiply straight across: 2/3 × 3/5 = 6/15 = 2/5.
- a/b ÷ c/d = a/b × d/c
- Flip the second fraction and multiply: 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2.
- w n/d = (w × d + n)/d
- Mixed to improper: 2 1/3 = (2 × 3 + 1)/3 = 7/3.
- Simplify: divide by the GCF
- 18/24: the greatest common factor is 6, so 18/24 = 3/4.
Why use this fraction 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
- Homework and revision. Check an answer and compare your working with the steps, line by line.
- Teaching. Show a class how the common denominator is found, with stacked fractions that look like the textbook.
- Cooking and baking. Scale a recipe: 3/4 cup × 1 1/2, or add 2/3 cup and 1/4 cup.
- Woodworking and DIY. Add inch measurements such as 5/16 + 3/8, or turn 0.3125 inches into a ruler fraction.
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: 3/4 + 5/6
The denominators are 4 and 6. Their least common denominator is 12: 4 = 2 × 2 and 6 = 2 × 3, so the LCD needs 2 × 2 × 3 = 12. Rewrite 3/4 as 9/12 (multiply top and bottom by 3) and 5/6 as 10/12 (multiply by 2). Add the numerators: 9 + 10 = 19, so the sum is 19/12. The greatest common factor of 19 and 12 is 1, so 19/12 is already in lowest terms. As a mixed number it is 1 7/12, and as a decimal it is 1.58333..., written as 1.583 with a bar over the 3.
What to expect from the result
Answers are exact. The calculator handles whole numbers of any size and shows repeating decimals in full up to 1,000 decimal places; anything longer is cut off with a rounded value alongside. Brackets are not supported yet, so work out anything inside brackets first. Multiplication and division are done before addition and subtraction, the same order a scientific calculator uses.
Fraction Calculator questions
How do you add fractions with different denominators?
Find the least common denominator, rewrite each fraction with it, then add the numerators and keep the denominator. For 1/4 + 1/6 the LCD is 12, so 3/12 + 2/12 = 5/12. Simplify the result if the top and bottom share a factor.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. 2/3 × 3/5 = 6/15, and dividing top and bottom by 3 gives 2/5. You do not need a common denominator to multiply.
How do you divide fractions?
Keep the first fraction, change ÷ to ×, and flip the second fraction (use its reciprocal). 3/4 ÷ 1/2 becomes 3/4 × 2/1 = 6/4 = 3/2, which is 1 1/2 as a mixed number.
How do I enter a mixed number or a whole number?
Each number has three boxes. Put the whole number in the left box and the fraction in the stacked boxes, so 2 1/3 is 2, 1 and 3. For a whole number such as 5, fill in only the left box. In the text box, type a space between the whole number and the fraction: 2 1/3.
Can I calculate with more than two fractions?
Yes. Press “Add a number” to chain up to 10 numbers, each with its own operator, or type something like 1/2 + 1/3 − 1/4 × 2. Multiplication and division are worked out first, then addition and subtraction from left to right.
How do I turn the answer into a decimal?
The decimal is shown with every answer. Repeating decimals get a bar over the digits that repeat, so 1/3 appears as 0.3 with a bar. The Fraction → decimal tab shows the long division behind it.