How the four operations work
Multiplying fractions is the easy one: multiply straight across, tops with tops and bottoms with bottoms. Dividing is one step more, flip the second fraction and then multiply. Adding and subtracting need a common denominator first, and the cross-multiplication shortcut builds one automatically:
For 1/2 + 3/4 that is (1 × 4 + 3 × 2) ÷ (2 × 4) = 10/8, which simplifies to 5/4. The shortcut sometimes produces a larger denominator than strictly needed, but since the calculator simplifies every answer anyway, it never matters.
Why the common denominator in the first place? Because you can only add like with like. Halves and quarters are different sized pieces, so 1/2 + 3/4 means nothing until both are expressed in quarters: 2/4 + 3/4 = 5/4. Multiplication skips this step because "a half of three quarters" is a genuine operation on the pieces themselves, not a tally of them. Pick an operation above, type the two fractions, and the working happens live as you type.
Worked examples
Simplifying with the highest common factor
A fraction is fully simplified when the top and bottom share no factor bigger than 1. Divide both by their highest common factor (HCF) and you are done in one step. Take 2/3 × 3/8: multiplying across gives 6/24, the HCF of 6 and 24 is 6, and dividing both by it leaves 1/4. If you cannot spot the HCF at a glance, divide out any common factor you can see and repeat, the fraction lands in the same place.
Simplified answers matter beyond neatness. Recipes, ratios and probabilities are far easier to compare when reduced: 6/24 and 2/8 look unrelated until both collapse to 1/4.
Mixed numbers and improper fractions
The calculator returns improper fractions (top bigger than bottom) alongside their mixed-number form, because each suits a different job. Improper fractions are the ones you calculate with; mixed numbers are the ones you say out loud. Nobody asks for five quarters of an hour, they ask for an hour and a quarter.
To calculate with a mixed number, convert it first: multiply the whole part by the denominator and add the numerator, so 2 1/3 becomes (2 × 3 + 1)/3 = 7/3. Enter that as 7 over 3 and carry on. Going the other way, divide top by bottom for the whole part and keep the remainder as the fraction, which is exactly what the mixed number row does for you. It earns its keep in the kitchen too: doubling a recipe that calls for 3/4 of a pint gives 6/4, which simplifies to 3/2, or 1 1/2 pints. If you need the answer as a percentage instead, our fraction to decimal converter and percentage calculator take it from here.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both over a common denominator, then add the numerators. For 1/2 + 3/4, use quarters: 2/4 + 3/4 = 5/4, which is 1 1/4. Cross-multiplying (each top times the other bottom, over the product of the bottoms) does the same job automatically.
How do I divide one fraction by another?
Flip the second fraction and multiply, sometimes remembered as keep, change, flip. So 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8, which is 1 7/8. Dividing by a fraction smaller than 1 always makes the answer bigger.
How does the calculator simplify results?
It divides the numerator and denominator by their highest common factor (HCF). For example 2/3 × 3/8 = 6/24, and the HCF of 6 and 24 is 6, so the simplified answer is 1/4.
What is the difference between an improper fraction and a mixed number?
An improper fraction has a top number bigger than its bottom, such as 5/4. A mixed number writes the same value as a whole number plus a proper fraction, 1 1/4. The calculator shows both forms whenever they differ.
Can I calculate with negative fractions?
Yes. Put a minus sign in front of either numerator. The calculator keeps the sign on the top of the fraction and handles subtraction that dips below zero, so 1/4 − 1/2 correctly gives −1/4.