Do maths with two fractions. The answer is always made as simple as possible, and shown as a decimal and, where useful, a mixed number.
To add or subtract, both fractions are put over a common denominator first.
To multiply, the numerators and denominators are multiplied straight across.
To divide, the second fraction is flipped and then multiplied.
The result is divided by the greatest common divisor to reduce it to lowest terms.
Add / subtract: a/b ± c/d = (a×d ± c×b) ÷ (b×d)
Multiply: a/b × c/d = (a×c) ÷ (b×d)
Divide: a/b ÷ c/d = (a×d) ÷ (b×c)
Adding one half and one third.
First fraction: 1/2
Second fraction: 1/3
Common denominator: 2 × 3 = 6
Convert: 1/2 = 3/6 and 1/3 = 2/6
Add the numerators: 3 + 2 = 5
Result: 5/6, already in lowest terms
Answer: 5/6 (0.8333…)
This fraction calculator handles all four operations on two fractions in one place. You enter a numerator and denominator for each, choose add, subtract, multiply or divide, and it returns the answer in lowest terms along with its decimal value and, where it helps, a mixed number. Every intermediate step is shown, so you can match it line by line with your notebook.
It is built for students from Class 5 to Class 8 who are learning fraction arithmetic, for older students checking algebra that simplifies to fractions, and for anyone scaling a recipe, dividing land shares or splitting a bill in fractional parts. The question it answers is simple: what single fraction results when these two are combined in this way?
1. Write both fractions as a/b and c/d, and check that neither denominator is zero.
2. To add or subtract: (a × d ± c × b) ÷ (b × d).
3. To multiply: (a × c) ÷ (b × d).
4. To divide: flip the second fraction and multiply, giving (a × d) ÷ (b × c). The second fraction must not be zero.
5. Find the HCF of the resulting numerator and denominator and divide both by it.
6. Move any minus sign to the numerator and, if the top is larger than the bottom, rewrite as a mixed number if needed.
A denominator names the size of the pieces. Halves and thirds are different sizes, so 1/2 + 1/3 cannot be done by adding tops and bottoms. Rewriting both over b × d cuts every piece into the same size, after which the counts can be added. Multiplication is different. a/b × c/d means 'take a/b of c/d', a scaling of one quantity by another. Scaling the top by a and the bottom by b, then by c and d, gives (a × c) ÷ (b × d) directly, with no need for matching pieces.
Dividing by c/d asks how many copies of c/d fit into a/b. Since c/d × d/c = 1, multiplying by d/c undoes multiplication by c/d, so dividing by c/d and multiplying by d/c must be the same thing. That gives (a × d) ÷ (b × c). If c is zero, the second fraction is zero and the division is undefined, which the calculator reports. Dividing by a fraction less than 1 always makes the result bigger, because many small pieces fit into the first quantity.
In school you are often taught to use the LCM of the denominators for addition. This calculator uses the product b × d, which is always a common denominator even if not the smallest. The final answer is identical because it reduces the result by the HCF at the end. The product method is easier to automate and shows the idea clearly, while the LCM method keeps the numbers smaller by hand. Either way, the fully reduced fraction is unique.
Meenal's recipe needs 5/6 of a cup of milk, but she has already poured in 1/4 of a cup and wants to know how much more to add.
Starting point: 5/6 − 1/4
Use a common denominator: 6 × 4 = 24
Rewrite both fractions: 20/24 − 6/24
Subtract the numerators: 20 − 6 = 14
Reduce to lowest terms: Divide both by their GCD of 2 → 7/12
Answer: Result 7/12; As a decimal 0.583333
Adding numerators and denominators straight across, such as writing 1/2 + 1/3 as 2/5.
Flipping the first fraction instead of the second when dividing.
Forgetting to reduce the final answer to lowest terms.
Placing a negative sign in the denominator and then losing track of it.
Entering a mixed number such as 2 1/3 as 2/3 instead of converting it to 7/3 first.
Checking fraction homework from NCERT Class 6 to Class 8 exercises.
Scaling recipe quantities given in cups and spoons.
Working out fractional shares of ancestral property or a business partnership.
Combining measurements in inches for carpentry and tailoring.
Simplifying algebraic answers that reduce to a ratio of two integers.
Why do I need a common denominator to add fractions?
Because the bottom number of a fraction shows how big each piece is. You cannot add halves to thirds directly, just like you cannot add metres to feet — both have to be changed to the same size of piece first.
Why does dividing by a fraction make the answer bigger?
Dividing asks how many of the second fraction fit into the first. There are four quarters in one whole, so 1 ÷ 1/4 = 4. Dividing by a number smaller than one always makes the result bigger.
What is a mixed number?
A whole number combined with a fraction, like 2 1/3 instead of 7/3. Both are equal — a mixed number is just easier to picture.