About Add Fractions Calculator
This calculator adds fractions, including fractions with different denominators. Type two fractions, such as 1/2 and 1/3, and it shows the common denominator, the rewritten fractions and the sum in lowest terms. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
You can only add the numerators when the denominators match, so unlike denominators need a common one first. The calculator uses the least common denominator, the smallest number both denominators divide into, which keeps the numbers small. For 1/2 and 1/3 that is 6, so the sum is 3/6 + 2/6 = 5/6.
When the denominators already match, the denominator stays and only the numerators are added: 3/8 + 1/8 = 4/8, which simplifies to 1/2. Mixed numbers and negatives work as well.
How to use Add Fractions Calculator
- Choose a mode: Calculate, Simplify, Compare, Decimal to fraction, Fraction to decimal, Improper to mixed or Fraction to percent.
- In Calculate mode type one expression with +, −, × and ÷ and as many brackets as you need. Mixed numbers are written with a space, such as 2 1/2, and repeating decimals as 0.(3).
- Read the result as a reduced fraction, a mixed number, a decimal and a percent.
- The tool opens on a worked example. Read the steps to see each operation done in the order brackets and precedence require.
- For an improper result, a second panel shows how to convert it to a mixed number.
Features
- Exact rational arithmetic with no floating-point error, using whole-number numerators and denominators of any size.
- Expressions with any number of terms, brackets, mixed numbers, negative fractions, decimals and repeating decimals such as 0.(3) and 0.1(6).
- Results shown as a fraction, a mixed number, a decimal and a percent together.
- Repeating decimals shown exactly with a bar over the repeating block, for example 1/7 = 0.142857 repeating, and accepted as input.
- Step-by-step working in typeset math: converting each number to a fraction, then each operation in order with its least common denominator or reciprocal and the simplification.
- Compare mode that shows both fractions over a common denominator and as decimals.
- Decimal to fraction, fraction to decimal, improper to mixed number and fraction to percent conversions.
- Clear messages for a zero denominator or division by zero.
Adding fractions
Rewrite both over the least common denominator, add the numerators, then simplify.
a/b + c/d = (a × (L ÷ b) + c × (L ÷ d)) / L, where L = lcm(b, d)Worked examples
1/2 + 1/3 gives 5/6
LCD(2, 3) = 6. 1/2 = 3/6 and 1/3 = 2/6. 3/6 + 2/6 = 5/6, and the GCD of 5 and 6 is 1.
3/8 + 1/8 gives 1/2
The denominators match, so 3 + 1 = 4 and the sum is 4/8. The GCD of 4 and 8 is 4, so 4/8 = 1/2.
Privacy: how it works
- The fractions you enter are processed by code running in your browser tab. Nothing is sent to Ulkaa or anyone else, and there is nothing to sign in to.
Tips
- Write a mixed number with a single space between the whole part and the fraction, as in 1 3/4.
- A decimal such as 0.75 is accepted as an input anywhere a fraction is.
- If you want a rounded decimal for a calculation by hand, read it from the repeating form and cut it where you need.
- To check an answer, the Compare mode shows two fractions over one denominator, which is the same test teachers use.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your fractions are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your fractions are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How do I add fractions with different denominators?
Find a common denominator, convert both fractions to it, add the numerators, keep the denominator and simplify.
Do I have to use the least common denominator?
No. Any common denominator gives the right value, such as 6 × 2 = 12 for 1/2 + 1/3. The least one just means less simplifying afterwards.
More Fraction Calculator pages
- Fraction CalculatorAdd, subtract, multiply, divide, simplify, compare and convert fractions, with every step shown.
- Subtract Fractions CalculatorSubtract one fraction from another and get the difference in lowest terms.
- Multiply Fractions CalculatorMultiply two fractions or mixed numbers and simplify the product.
- Divide Fractions CalculatorDivide fractions and mixed numbers, with the reciprocal step shown.
- Simplify Fractions CalculatorReduce a fraction to lowest terms and see the GCD used.
- Mixed Number CalculatorCalculate with mixed numbers such as 2 1/2 and see the answer as a mixed number.
- Decimal to Fraction CalculatorTurn a decimal into an exact, simplified fraction.
- Fraction to Decimal CalculatorDivide a fraction out and see ending and repeating decimals exactly.
- Compare Fractions CalculatorCheck which fraction is bigger and see the proof.
- Improper Fraction to Mixed NumberSplit an improper fraction into a whole number and a proper fraction.
- Fraction to Percentage CalculatorConvert any fraction or mixed number to an exact percentage.