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Fraction Calculator

Select an operation, enter two fractions, and see the answer with full step-by-step working. Results update as you type.

Fraction 1
+
Fraction 2
Answer: 7/12
Decimal equivalent: 0.58333333
1/3 + 1/4

Find common denominator: LCM(3, 4) = 12

  1/3 = 4/12  (multiply top and bottom by 4)
  1/4 = 3/12  (multiply top and bottom by 3)

  = 4 + 3) / 12
  = 7/12

What Is a Fraction?

A fraction represents a part of a whole. It is written as one integer (the numerator) over another integer (the denominator), separated by a horizontal bar. The denominator tells you how many equal parts the whole is divided into; the numerator tells you how many of those parts you have.

For example, 3/4 means the whole is divided into 4 equal parts and you have 3 of them. Fractions whose numerator is smaller than the denominator are called proper fractions (value between 0 and 1). When the numerator is larger, it is an improper fraction (value greater than 1), which can also be written as a mixed number like 1 3/4.

How to Add Fractions

Addition is only defined when both fractions refer to the same-sized parts. You cannot directly add thirds and fourths without first converting them to a common unit. The process uses the least common multiple (LCM) of the denominators.

Formula:

a/b + c/d = (a × d + c × b) / (b × d)

(Then simplify the result by dividing numerator and denominator by their GCD.)

Worked example: 1/3 + 1/4

Step 1 — Find LCM(3, 4) = 12
Step 2 — Convert: 1/3 = 4/12 and 1/4 = 3/12
Step 3 — Add numerators: 4/12 + 3/12 = 7/12
Step 4 — Check: GCD(7, 12) = 1, already simplified. Answer: 7/12

How to Subtract Fractions

Subtraction follows the same method as addition. Find a common denominator, convert both fractions, then subtract the numerators.

Worked example: 3/4 − 1/6

Step 1 — LCM(4, 6) = 12
Step 2 — Convert: 3/4 = 9/12 and 1/6 = 2/12
Step 3 — Subtract: 9/12 − 2/12 = 7/12
Answer: 7/12

How to Multiply Fractions

Multiplication of fractions is the most straightforward operation: multiply across. There is no need to find a common denominator.

Formula:

a/b × c/d = (a × c) / (b × d)

Worked example: 2/3 × 3/4

Numerators: 2 × 3 = 6
Denominators: 3 × 4 = 12
Result: 6/12
Simplify: GCD(6, 12) = 6, so 6/12 = 1/2

A useful shortcut called cross-cancellation lets you simplify before multiplying: notice that the 3 in the numerator of 3/4 and the 3 in the denominator of 2/3 share a factor of 3. Cancel them first: (2/3) × (3/4) = (2/1) × (1/4) = 2/4 = 1/2. Same answer, less arithmetic.

How to Divide Fractions

Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of a/b is b/a (you flip it). The memory aid is keep, change, flip: keep the first fraction, change division to multiplication, flip the second fraction.

Formula:

a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)

Worked example: 2/3 ÷ 3/4

Flip the second fraction: 3/4 becomes 4/3
Multiply: 2/3 × 4/3 = (2 × 4) / (3 × 3) = 8/9
GCD(8, 9) = 1 — already simplified. Answer: 8/9

How to Simplify Fractions (the GCD Method)

A fraction is in its simplest form (lowest terms) when the numerator and denominator share no common factors other than 1. To simplify, find the greatest common divisor (GCD) of the numerator and denominator using the Euclidean algorithm, then divide both by it.

The Euclidean algorithm works by repeated division. To find GCD(36, 24):

36 = 1 × 24 + 12  →  remainder 12
24 = 2 × 12 + 0  →  remainder 0
When the remainder is 0, the last divisor is the GCD: GCD = 12
Simplified: 36/24 = (36 ÷ 12) / (24 ÷ 12) = 3/2

Frequently Asked Questions

How do you add fractions with different denominators?

To add fractions with different denominators, you must first find a common denominator — usually the least common multiple (LCM) of the two denominators. Then convert each fraction to an equivalent fraction with that common denominator by multiplying numerator and denominator by the same factor. Finally, add the numerators and keep the common denominator. Example: 1/3 + 1/4. LCM(3,4) = 12. Convert: 4/12 + 3/12 = 7/12.

How do you multiply fractions?

Multiplying fractions is the simplest fraction operation: multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. Then simplify. Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. You can also simplify before multiplying by canceling common factors across numerators and denominators.

How do you divide fractions?

To divide fractions, multiply the first fraction by the reciprocal of the second. The reciprocal means you flip the numerator and denominator of the divisor. Example: 2/3 ÷ 3/4 becomes 2/3 × 4/3 = 8/9. The saying "keep, change, flip" describes this: keep the first fraction, change division to multiplication, flip the second fraction.

How do you simplify a fraction?

To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. Example: 12/18. GCD(12, 18) = 6. Divide both: 12÷6 = 2, 18÷6 = 3. Simplified: 2/3. A fraction is fully simplified (in lowest terms) when the GCD of the numerator and denominator is 1.

What is a mixed number and how do you convert to one?

A mixed number combines a whole number and a proper fraction, such as 1 2/3. To convert an improper fraction (where the numerator is larger than the denominator) to a mixed number: divide the numerator by the denominator. The quotient is the whole part and the remainder over the original denominator is the fractional part. Example: 7/3. 7 ÷ 3 = 2 remainder 1, so 7/3 = 2 1/3.

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