How to Add, Subtract, Multiply and Divide Fractions

Fractions are the point where mental arithmetic quietly stops working. Most people can halve and double all day, and then meet 3/8 + 5/12 and reach for something with buttons.

What the Fraction Calculator does

Adds, subtracts, multiplies and divides two fractions, returning the result in lowest terms.

Reducing the answer is the part that makes it useful. 18/24 and 3/4 are the same number, but only one of them is an answer you would write down or read aloud, and only one lets you compare two results at a glance.

Open the Fraction Calculator and follow the settings and checks below.

The rules being applied

Setting	What it means
Add and subtract	Requires a common denominator first — this is the step people dread
Multiply	Straight across: numerators together, denominators together
Divide	Multiply by the reciprocal — flip the second fraction and multiply
Reducing	Divides both parts by their greatest common divisor
Negatives	Allowed on the numerator; the sign travels with the fraction
Zero denominator	Rejected — the fraction is undefined, not infinite

How to use it

1. Enter the first fraction as a numerator and denominator.
2. Choose the operation.
3. Enter the second fraction.
4. For a mixed number like 2¾, convert first: multiply the whole number by the denominator and add the numerator, so 2 × 4 + 3 = 11, giving 11/4. The same trick runs backwards on the answer: 11/4 is 2 remainder 3, which is 2¾ again.

Practical advice

Dividing by a fraction gives a larger answer, and it feels wrong every time. 1/2 ÷ 1/4 is 2, not 1/8 — because the question is "how many quarters fit into a half", and the answer is two. Whenever a division result looks too big, translate it back into that phrasing and it usually turns out to be right. This is the single most useful sentence about fractions that school tends to skip.

Common questions

Why does dividing by a fraction make the number bigger?

Because you are asking how many of the second fraction fit inside the first. 1/2 ÷ 1/4 asks how many quarters fit into a half, and two do. Dividing only makes numbers smaller when you divide by something greater than one, which is such a common case that the opposite feels like an error.

How do I enter a mixed number like 2¾?

Convert it to an improper fraction first. Multiply the whole number by the denominator and add the numerator: 2 × 4 + 3 = 11, so 2¾ is 11/4. Everything else follows normally, and if the answer comes back improper you can convert it back the same way in reverse.

Why is the answer shown in lowest terms?

Because 18/24 and 3/4 are the same value and only one of them is readable. Reducing divides both parts by their greatest common divisor, which is the conventional way to present a fraction and makes it far easier to compare two results at a glance.

Can I use negative fractions?

Yes — put the minus on the numerator and it carries through the arithmetic correctly. Be careful with subtraction of a negative, which is the classic sign trap: subtracting −1/3 is the same as adding 1/3, and the result gets larger rather than smaller.

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• Discount Calculator — Final sale price and total savings, with stacked coupons and tax.

Vootkit provides a browser calculator and educational guidance. Results depend on the values and units you enter, so verify important financial, academic, safety or professional decisions with an appropriate authoritative source.