Fraction Calculator
Add, subtract, multiply and divide fractions.
Your fractions
Try an example
Your result
5/6
Simplified fraction
1/2 + 1/3 = 5/6
- Mixed number
- 5/6
- Decimal
- 0.8(3)
- Percent
- 83.33%
- Common denominator
- 6
How it is worked out
- Find a common denominator: the least common multiple of 2 and 3 is 6.
- Rewrite both fractions over 6: 3/6 + 2/6.
- Add the numerators and keep the denominator: 3 + 2 = 5, so 5/6.
- 5/6 is already in simplest form.
Fraction Calculator Math Formula
A fraction a/b means a ÷ b: the numerator a counts the parts you have and the denominator b says how many equal parts make a whole. The denominator can never be zero, because you cannot split something into zero parts. Below are the formulas the calculator uses for each operation, each worked through with real numbers.
Types of fractions
- Proper fraction: the numerator is smaller than the denominator, such as 3/4. Its value is less than 1.
- Improper fraction: the numerator is equal to or bigger than the denominator, such as 7/4. Its value is 1 or more.
- Mixed number: a whole number plus a proper fraction, such as 1 3/4. It is the same value as the improper fraction 7/4.
1. Add fractions
a/b + c/d = (a × (L ÷ b) + c × (L ÷ d)) ÷ L
where L = the least common denominator of b and d
You can only add fractions that share a denominator, so first rewrite both over their least common multiple (LCM). Example: 1/2 + 1/3.
LCM of 2 and 3 = 6
1/2 = 3/6 and 1/3 = 2/6
3 + 2 = 5, so 5/6
So 1/2 + 1/3 = 5/6, which is 0.8(3) as a decimal. Note that you keep the common denominator and only add the numerators.
2. Subtract fractions
a/b − c/d = (a × (L ÷ b) − c × (L ÷ d)) ÷ L
Subtraction uses the same common denominator as addition. Example: 3/4 − 1/6.
LCM of 4 and 6 = 12
3/4 = 9/12 and 1/6 = 2/12
9 − 2 = 7, so 7/12
If the second fraction is bigger, the answer is negative, for example 1/6 − 3/4 = −7/12. The calculator shows the sign and still simplifies the result.
3. Multiply fractions
a/b × c/d = (a × c) ÷ (b × d)
Multiplying needs no common denominator: multiply the tops together and the bottoms together. Example: 2/3 × 3/5.
(2 × 3) ÷ (3 × 5) = 6/15
6 and 15 share the factor 3
6/15 ÷ 3 = 2/5
Multiplying by a fraction smaller than 1 makes a number smaller. That is why "of" in a word problem usually means multiply: half of 3/5 is 1/2 × 3/5 = 3/10.
4. Divide fractions
a/b ÷ c/d = a/b × d/c = (a × d) ÷ (b × c)
To divide, keep the first fraction, flip the second one (swap its numerator and denominator) and multiply. Example: 5/8 ÷ 1/4.
Flip 1/4 to get 4/1
(5 × 4) ÷ (8 × 1) = 20/8
20/8 ÷ 4 = 5/2 = 2 1/2
It works because dividing by 1/4 asks "how many quarters fit in 5/8?", and there are four quarters in every whole. You cannot divide by a fraction whose numerator is 0, because 0/b equals 0 and dividing by zero is undefined.
5. Mixed numbers and improper fractions
Mixed to improper: w n/d = (w × d + n) ÷ d
Improper to mixed: n ÷ d gives the whole part, the remainder is the new numerator
To work with mixed numbers, convert them to improper fractions first. Example: 1 1/2 + 2 3/4.
1 1/2 = (1 × 2 + 1) ÷ 2 = 3/2
2 3/4 = (2 × 4 + 3) ÷ 4 = 11/4
Over 4: 6/4 + 11/4 = 17/4
17 ÷ 4 = 4 remainder 1, so 4 1/4
Do not add or multiply the whole parts and the fractions separately when multiplying or dividing. 1 1/2 × 2 1/2 is not 2 × 1/2 + 1/4: you must convert to 3/2 × 5/2 = 15/4 = 3 3/4.
6. Simplify a fraction (lowest terms)
a/b = (a ÷ G) ÷ (b ÷ G), where G = GCD(a, b)
A fraction is in lowest terms when the top and bottom share no common factor except 1. Find the greatest common divisor (GCD) with the Euclidean algorithm: divide, keep the remainder and repeat until the remainder is 0. Example: simplify 18/24.
24 = 1 × 18 + 618 = 3 × 6 + 0The last non-zero remainder is 6, so GCD = 6
18/24 = (18 ÷ 6) ÷ (24 ÷ 6) = 3/4
The calculator simplifies every answer automatically, so 18/24 would be shown as 3/4. Both fractions have the same value; the simplified one is just easier to read.
7. Fraction to decimal
Decimal = numerator ÷ denominator
Divide the top by the bottom using long division. Example: 3/8 as a decimal.
3 ÷ 8 = 0, remainder 330 ÷ 8 = 3, remainder 660 ÷ 8 = 7, remainder 440 ÷ 8 = 5, remainder 0Digits in order: 0.375
Some fractions never end. 1/3 = 0.(3), which means the digit 3 repeats forever, and 1/7 = 0.(142857), where the block 142857 repeats. The calculator puts the repeating part in brackets so nothing is hidden by rounding. A fraction ends exactly when its lowest-terms denominator only has the prime factors 2 and 5.
8. Fraction to percentage
Percent = (numerator ÷ denominator) × 100
Multiply the decimal by 100. Example: 3/8 = 0.375, and 0.375 × 100 = 37.5%. The calculator rounds the percentage to two decimal places, so 1/3 is shown as 33.33%.
9. Decimal to fraction
Decimal = digits ÷ 10^(number of decimal places), then simplify
Write the digits over 1 followed by as many zeros as there are decimal places, then simplify. Example: 0.375 has three decimal places.
0.375 = 375/1000
375/1000 simplifies to 3/8
10. Compare two fractions
a/b ? c/d → compare a × d with c × b
To see which fraction is bigger without finding a common denominator, cross multiply. Example: which is bigger, 3/4 or 5/7?
3 × 7 = 21
5 × 4 = 20
21 > 20, so 3/4 is bigger
Check with decimals: 3/4 = 0.750 and 5/7 = 0.714. The calculator shows the decimal and percent of every result, so you can also compare answers that way.
Common mistakes to avoid
- Adding the denominators. 1/2 + 1/3 is not 2/5. Adding tops and bottoms gives 2/5, but the correct answer is 5/6. Always find a common denominator first.
- Flipping the wrong fraction. When dividing, only the second fraction is flipped. The first one stays as it is.
- Forgetting to simplify. 6/15 is correct but not finished. Divide top and bottom by their GCD to reach 2/5.
- Using a zero denominator. A fraction such as 5/0 has no value, so the calculator shows a message instead of an answer.
- Mishandling negative mixed numbers. −1 1/2 means −(1 + 1/2) = −3/2, not −1 + 1/2.
Online Fraction Calculator
Our free online fraction calculator lets you add, subtract, multiply and divide fractions and mixed numbers in seconds. Type a numerator and denominator for each fraction, choose an operation and the answer appears instantly. You get the result as a simplified fraction, a mixed number, a decimal and a percentage, together with the common denominator and every step of the working, so you can learn the method as well as get the answer.
A fraction describes part of a whole. The number on top, the numerator, says how many parts you have. The number underneath, the denominator, says how many equal parts the whole is split into. So 3/4 means three of four equal parts. A proper fraction such as 3/4 is smaller than one, an improper fraction such as 7/4 is bigger than one, and a mixed number such as 1 3/4 shows the whole part and the fractional part side by side. This calculator accepts all three and converts between them for you.
People use fraction calculators for school and college homework, exam revision, cooking and baking when a recipe has to be halved or doubled, woodworking and construction measurements in inches such as 5/8 + 3/16, sewing and craft projects, dividing a bill or a share, and probability and ratio problems. It is also a quick way to check your own working before you hand it in.
The calculator works with exact whole numbers, so nothing is rounded along the way. Large numerators and denominators stay accurate, and repeating decimals are shown properly, for example 1/3 as 0.(3) rather than a rounded 0.333. It is free, needs no sign-up, runs privately in your browser and works on phones, tablets and desktops.
Features Of ToolVaya Fraction Calculator
Calculate
- Add, subtract, multiply and divide two fractions
- Mixed numbers supported, such as 1 1/2 + 2 3/4
- Whole numbers work too: enter a denominator of 1
- Negative fractions and negative mixed numbers
- Exact whole-number arithmetic with no rounding errors, up to 12 digits per box
- Clear messages instead of errors, for example for a zero denominator or dividing by zero
Understand the answer
- Automatic simplification to lowest terms
- Every answer shown as a fraction, a mixed number, a decimal and a percentage
- Repeating decimals marked correctly, such as 1/3 = 0.(3)
- Common denominator shown for addition and subtraction
- Step-by-step working: improper fractions, common denominator, operation and simplifying
- Bar diagram that compares the first fraction, the second fraction and the result
Easy to use
- A worked example is already filled in, so you see a result straight away
- One-tap examples for each operation and for mixed numbers
- Swap button to exchange the two fractions
- Large touch-friendly inputs and buttons with a numeric keypad on phones
- Free, no sign-up, works on phone, tablet and desktop
- Private: everything is calculated in your browser and nothing is stored
Frequently asked questions
How do I add or subtract fractions with different denominators?
First find a common denominator, usually the least common multiple of the two denominators. Rewrite each fraction over that denominator, then add or subtract the numerators and keep the denominator. For 1/2 + 1/3, the least common multiple of 2 and 3 is 6, so 3/6 + 2/6 = 5/6. For 3/4 − 1/6 the common denominator is 12, giving 9/12 − 2/12 = 7/12. Never add the denominators together.
How do I multiply fractions?
Multiply the numerators together and the denominators together, then simplify. 2/3 × 3/5 = (2 × 3) ÷ (3 × 5) = 6/15, which simplifies to 2/5 after dividing top and bottom by 3. You do not need a common denominator for multiplication. For a mixed number, convert it to an improper fraction first.
How do I divide fractions?
Keep the first fraction, flip the second fraction and multiply. 5/8 ÷ 1/4 becomes 5/8 × 4/1 = 20/8, which simplifies to 5/2, or 2 1/2 as a mixed number. Dividing by a fraction asks how many of that fraction fit into the first one. You cannot divide by a fraction equal to zero.
How do I add, subtract, multiply or divide mixed numbers?
Convert each mixed number to an improper fraction using (whole × denominator + numerator) ÷ denominator, do the operation, then convert back by dividing the numerator by the denominator. For 1 1/2 + 2 3/4, you get 3/2 + 11/4 = 6/4 + 11/4 = 17/4, which is 4 1/4. In this calculator, type the whole number in the Whole box and the fraction part in the Numerator and Denominator boxes.
How do I simplify a fraction to its lowest terms?
Divide the numerator and denominator by their greatest common divisor (GCD). To find the GCD of 18 and 24, use the Euclidean algorithm: 24 = 1 × 18 + 6, 18 = 3 × 6 + 0. The last non-zero remainder, 6, is the GCD, so 18/24 = 3/4. A fraction is in lowest terms when its top and bottom share no common factor other than 1. This calculator simplifies every answer for you.
How do I convert a fraction to a decimal or a percentage?
Divide the numerator by the denominator to get the decimal, then multiply by 100 for the percentage. 3/8 = 3 ÷ 8 = 0.375, which is 37.5%. Some fractions repeat forever: 1/3 = 0.(3) (the 3 repeats) and 1/7 = 0.(142857). The brackets mark the repeating part. To go the other way, write the decimal over a power of ten and simplify, for example 0.375 = 375/1000 = 3/8.
How do I know which of two fractions is bigger?
Cross multiply: multiply the first numerator by the second denominator and the second numerator by the first denominator, and compare the two products. For 3/4 and 5/7, 3 × 7 = 21 and 5 × 4 = 20. Since 21 is bigger, 3/4 is the larger fraction (0.750 against 0.714 as decimals). You can also use the calculator to turn each fraction into a decimal or percent and compare those.
What is the difference between a proper fraction, an improper fraction and a mixed number?
A proper fraction has a numerator smaller than its denominator, such as 3/4, and is worth less than 1. An improper fraction has a numerator equal to or bigger than its denominator, such as 7/4, and is worth 1 or more. A mixed number combines a whole number and a proper fraction, such as 1 3/4, which is the same value as 7/4. Improper fractions are easier to calculate with, while mixed numbers are easier to read, so the calculator shows your answer in both forms.
Can a denominator be zero, and can fractions be negative?
A denominator can never be zero, because splitting something into zero parts has no meaning. A fraction such as 5/0 is undefined, and the calculator shows a message instead of an answer. Likewise you cannot divide by a fraction whose numerator is zero. Fractions can be negative: −3/4, 3/−4 and −(3/4) all mean the same thing. Enter the minus sign in the numerator, and the calculator keeps the sign on the answer and simplifies as normal. For a negative mixed number such as −1 1/2, enter −1 in the Whole box; it equals −3/2.