The formula this page uses
a/b + c/d = (ad + bc) / bd a/b × c/d = ac / bd a/b ÷ c/d = a/b × d/c = ad / bc
Fraction Calculator
Use the free fraction calculator to work through the number relationship, preserve exact values, and check the result with estimation. Choose a focused operation below to calculate, inspect the method, and connect the result to a visual model.
The visual updates with your calculation.
Result—Choose a mode, enter the known values, and calculate.
Show your work Step-by-step method
- The calculation method and verification will appear here.
Arithmetic
Fraction Calculator explained
The short version
- A fraction is a division that has not happened yet: 3/4 means 3 shared between 4 people.
- Adding and subtracting need the same bottom number first. Multiplying does not need it at all.
- Dividing by a fraction means flipping that fraction over and multiplying instead.
What each part means
SymbolWhat it means
a and c — NumeratorsThe top numbers. They count how many pieces you have.
b and d — DenominatorsThe bottom numbers. They say how many pieces the whole was cut into, so they can never be 0.
bd — A common denominatorAny number both bottoms divide into. The smallest one keeps the arithmetic small.
d/c — The reciprocalThe second fraction turned upside down. Multiplying by it does the same job as dividing.
Show your work: a full example
- Start with the sum3/4 + 5/6
- Find the smallest number 4 and 6 both go into4 × 3 = 12 and 6 × 2 = 12, so use 12
- Rewrite the first fraction over 123/4 = 9/12, because 3 × 3 = 9
- Rewrite the second fraction over 125/6 = 10/12, because 5 × 2 = 10
- Add the tops, leave the bottom alone9/12 + 10/12 = 19/12
- Turn it into a mixed number19 ÷ 12 = 1 remainder 7, so 19/12 = 1 and 7/12
- Check as a decimal19 ÷ 12 = 1.5833, and 0.75 + 0.8333 = 1.5833
A second, different case
- A different case: dividing by a fraction5/6 ÷ 2/9
- Flip the fraction you are dividing by2/9 becomes 9/2
- Multiply straight across instead5/6 × 9/2 = 45/12
- Reduce with the shared factor 345 ÷ 3 = 15 and 12 ÷ 3 = 4, so the answer is 15/4
- Write it as a mixed number15 ÷ 4 = 3 remainder 3, so 15/4 = 3 and 3/4
- Check by multiplying back15/4 × 2/9 = 30/36 = 5/6
Copy-ready example
3/4 + 5/6
Start with the sum
Questions about the Fraction Calculator
Do I have to use the smallest common bottom number?
No. 4 × 6 = 24 works just as well: 3/4 = 18/24 and 5/6 = 20/24, and 18/24 + 20/24 = 38/24, which reduces to 19/12. Using 12 just saves you the reducing step at the end.
Why does flipping the second fraction work for division?
Dividing by 2/9 asks how many lots of 2/9 fit inside 5/6. Because 2/9 is smaller than 1, the answer has to be bigger than 5/6, and multiplying by 9/2 is the only thing that makes it bigger by exactly the right amount.
Can I cancel before I multiply?
Yes, and it keeps the numbers small. For 3/4 × 8/9, the 3 on top cancels with the 9 on the bottom to leave 1 and 3, and the 4 cancels with the 8 to leave 1 and 2. What is left is 1/1 × 2/3 = 2/3, which matches 24/36.
How do I subtract when the first top number is too small, like 5 and 1/4 minus 2 and 3/4?
Borrow one whole from the 5 and turn it into quarters. 5 and 1/4 becomes 4 and 5/4, so the sum reads 4 and 5/4 minus 2 and 3/4 = 2 and 2/4, which tidies up to 2 and 1/2.
Calculate, interpret, verify.
This workspace keeps the formula and the meaning together. Decimal results are rounded for display; retain full precision when you continue a calculation.
Enter known values
Match each input to the quantities in the problem and keep units consistent.
Use the relationship
The result panel identifies the formula or algorithm and shows the main substitutions.
Read the visual
Use the diagram, plot, or data display to check scale, direction, and plausibility.
Practice unaided
Move to targeted questions once you can explain why the method applies.
A calculator gives you the number. If you also want to be able to do this without one, a practical guide to fractions walks through the method step by step, with a worked example and the mistakes that cost marks.
Learn the mathematics
Understand arithmetic behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.