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Fraction Calculator

Enter two fractions or mixed numbers (e.g. 1 1/2 and 3/4, which add up to 2 1/4) and choose add, subtract, multiply or divide – the calculator works exactly, simplifies the answer and shows every step, whether you are adding or subtracting fractions with different denominators. It also reduces a single fraction and turns decimals, including repeating decimals, into fractions.

Source: Euclid’s Elements, Book VII, Proposition 2 – greatest common measure (Euclidean algorithm), ed. D. E. Joyce, Clark University. Updated: .

e.g. 3/4, mixed number 1 1/2, whole number 5 or decimal 0.5
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Result

Answer (simplest form)
9/4
As a mixed number
2 1/4
As a decimal
2.25
As a percent
225 %
Steps
  • Convert the mixed number to an improper fraction: 1 1/2 = (1 × 2 + 1)/2 = 3/2
  • Least common denominator = LCM(2, 4) = 4
  • Rewrite with the common denominator: 3/2 = 6/4 (× 2), 3/4 = 3/4 (× 1)
  • Add the numerators, keep the denominator: 6/4 + 3/4 = (6 + 3)/4 = 9/4
  • 9/4 is already in simplest form (GCD = 1).
  • As a mixed number: 9 ÷ 4 = 2 remainder 1 → 2 1/4
  • As a decimal: 9 ÷ 4 = 2.25

How it is calculated

How the fraction calculator works

A fraction a/b has a numerator a and a denominator b (b ≠ 0). The calculator only uses whole numbers of any length, so there are no rounding errors: 1/3 + 1/3 + 1/3 is exactly 1.

OperationRuleExample
Adda/b + c/d = (a·d + c·b)/(b·d), simpler with the least common denominator1/6 + 1/10 = 5/30 + 3/30 = 8/30 = 4/15
Subtracta/b − c/d = (a·d − c·b)/(b·d)1/3 − 1/2 = 2/6 − 3/6 = −1/6
Multiplya/b × c/d = (a·c)/(b·d)2/3 × 9/4 = 18/12 = 3/2
Dividea/b ÷ c/d = a/b × d/c (reciprocal)3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8

Example with a mixed number: 1 1/2 + 3/4

  1. Convert the mixed number: 1 1/2 = (1 × 2 + 1)/2 = 3/2.
  2. Least common denominator = LCM(2, 4) = 4.
  3. Rewrite: 3/2 = 6/4; 3/4 stays 3/4.
  4. Add the numerators: 6/4 + 3/4 = 9/4 (GCD(9, 4) = 1, already simplest form).
  5. Mixed number: 9 ÷ 4 = 2 remainder 1 → 2 1/4; as a decimal 2.25.

Everyday fraction problems, calculated

Recipes and workshop measures are where fractions appear most. Scaling a Thanksgiving recipe for 26 November 2026 from 6 to 8 guests means multiplying every amount by 8/6 = 4/3. The results below are exactly what the calculator returns.

ProblemEntryResult
Scale 2 1/4 cups of flour from 6 to 8 servings2 1/4 × 4/33 cups
Scale 3/4 cup of milk the same way3/4 × 4/31 cup
Combine 3/4 cup and 1/3 cup3/4 + 1/313/12 = 1 1/12 cups
Cut 1 3/4 in from a 2 1/2 in board2 1/2 − 1 3/43/4 in
Difference of 7/8 in and 3/16 in drill bits7/8 − 3/1611/16 in
Pieces of 3/8 in that fit into 3 in3 ÷ 3/88 pieces
Two lengths added1 1/2 + 3 3/421/4 = 5 1/4
Fraction of a fraction5/8 × 2/35/12 = 0.41(6)
Area of a 1 1/3 ft by 2 1/4 ft panel1 1/3 × 2 1/43 square feet
Result below zero1/2 − 2/3−1/6

The rules follow standard arithmetic of rational numbers; the greatest common divisor is found with the Euclidean algorithm.

Common mistakes with fractions

Simplifying with the Euclidean algorithm

A fraction is reduced by dividing numerator and denominator by their greatest common divisor (GCD). The calculator finds it with Euclid’s method: divide the larger number by the smaller, keep the remainder and repeat until the remainder is 0. For 12/18: 18 = 1 × 12 + 6, 12 = 2 × 6 + 0 → GCD = 6, so 12/18 = 2/3. The least common denominator is LCM(a, b) = a × b / GCD(a, b).

Decimal to fraction – including repeating decimals

Terminating decimal: count the decimal places, put the digits over the matching power of ten and simplify: 0.75 = 75/100 = 3/4.

Repeating decimal: numerator = all digits up to the end of the first repeating block minus the digits before the block; denominator = one 9 for each repeating digit followed by one 0 for each non-repeating decimal digit. Example 0.1(6) = 0.1666…: (16 − 1)/90 = 15/90 = 1/6. Likewise 0.(3) = 3/9 = 1/3 and 0.(9) = 9/9 = 1. Type the repeating digits in brackets or use the “Repeating digits” field.

Every answer is also shown as a decimal: fractions whose simplified denominator has no prime factors other than 2 and 5 terminate (9/4 = 2.25); all others repeat (1/7 = 0.142857142857…).

Related math tools: solve ratios with the proportion calculator, turn shares into percentages with the percentage calculator, and handle fractional exponents with the exponent calculator.

Several fractions in one expression, and comparing fractions

In “Several fractions” mode you type the whole problem on one line: 1/2 + 3/4 − 1/3 gives 6/12 + 9/12 − 4/12 = 11/12. Multiplication and division come before addition and subtraction, brackets are allowed, and negative fractions take a minus sign in front. The steps list every partial calculation in the order it is done. “Compare fractions” puts up to twelve fractions over a common denominator and orders them: 3/4; 5/6; 2/3 become 9/12, 10/12 and 8/12, so 2/3 < 3/4 < 5/6. Every answer is also shown as a percent – 3/4 is 75%.

Frequently asked questions

How do I enter a mixed number?

Whole number, space, fraction: 1 1/2 for one and a half, -2 3/4 for negative two and three quarters. Whole numbers (5) and decimals (0.5) work too.

How do you add fractions with different denominators?

Rewrite both fractions with the least common denominator (the LCM of the denominators), then add the numerators: 1/6 + 1/10 → LCD 30 → 5/30 + 3/30 = 8/30 = 4/15.

How do you divide fractions?

Multiply by the reciprocal (“keep, change, flip”): 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. You cannot divide by zero.

How do I simplify a fraction to lowest terms?

Divide numerator and denominator by their greatest common divisor. 12/18: GCD = 6, so 2/3. The “Simplify a fraction” mode lists the steps of the Euclidean algorithm.

How do I convert 0.333… to a fraction?

The repeating block 3 has one digit, so the denominator is 9: 0.(3) = 3/9 = 1/3. In “Decimal → fraction” mode type 0.(3), or 0 plus 3 in the repeating digits field.

Can I calculate with three fractions, whole numbers or negative fractions?

Yes. In “Several fractions” mode type one line such as 1/2 + 3/4 − 1/3 = 11/12. Whole numbers work as fractions over 1 (3 ÷ 3/8 = 8) and a minus sign in front makes a fraction negative (−1/2 + 1/3 = −1/6).

How do you multiply fractions?

Multiply the numerators and the denominators, then simplify: 2/3 × 9/4 = 18/12 = 3/2 = 1 1/2. For mixed numbers, convert them to improper fractions first: 1 1/3 × 2 1/4 = 4/3 × 9/4 = 3.

Sources and legal basis

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