Fraction Calculator
Add, subtract, multiply, and divide two fractions with simplified output
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What this calculator computes
The fraction calculator performs the four arithmetic operations on two fractions — addition, subtraction, multiplication, and division — and returns the result as both a simplified fraction (reduced to lowest terms) and an equivalent decimal. Each fraction is entered as a numerator and a denominator, with optional whole-number parts for mixed numbers like 2 1/3. The calculator handles negative fractions, improper fractions (where the numerator exceeds the denominator), and produces a decimal output rounded to a configurable precision so the result is usable both algebraically and numerically. Behind the scenes it converts mixed numbers to improper fractions, performs the operation using the standard rules (common denominator for addition and subtraction, numerator-times-numerator for multiplication, multiply-by-the-reciprocal for division), and reduces the result by computing the greatest common divisor of the resulting numerator and denominator. Fraction arithmetic is one of the topics primary-school students struggle with most and one that adults reach for again and again in cooking (halving a recipe that calls for 3/4 cup), construction (computing the offset on a 2 1/8 inch trim cut), music (calculating note durations), and statistics (probability ratios). The calculator's main convenience is that it never returns an unsimplified result — 4/8 always reduces to 1/2, 6/4 always reduces to 3/2 (or shows as 1 1/2 in mixed form), and the GCD reduction step is invisible to the user but eliminates the most common source of "right answer, wrong form" frustration.
Calculator
The formula
Formula
a/b + c/d = (ad + bc) / bd a/b × c/d = ac / bd a/b ÷ c/d = ad / bc
Worked example
When to use this calculator
Use this calculator any time you need to add, subtract, multiply, or divide fractions and want a simplified, reduced result rather than computing the GCD by hand. The most common everyday cases are scaling recipes (halving "3/4 cup" to "3/8 cup", doubling "2 1/3 cups" to "4 2/3 cups"), construction layout (computing the offset on a 2 1/8" trim cut from a 16" stud spacing), music theory (combining note durations like 1/4 + 1/8 = 3/8), and probability problems where ratios stay easier to read in fraction form than decimal. The calculator is also useful for checking schoolwork answers, where the textbook expects a simplified result and an unsimplified-but-mathematically-correct answer is marked wrong. For very long fraction chains (more than two operands) chain the calculations: compute a/b + c/d, then add the result to e/f as a second operation. The calculator does not handle algebraic fractions with variables.
Common input mistakes
- Adding numerators and denominators directly. The intuitive "2/3 + 1/4 = 3/7" is wrong — fractions need a common denominator before addition, giving 8/12 + 3/12 = 11/12. The denominators only multiply across in multiplication; in addition and subtraction they must match first.
- Forgetting to reduce the result. 6/8 is mathematically equal to 3/4, but most contexts (textbooks, recipes, blueprints) expect the reduced form. The calculator always reduces automatically by computing the greatest common divisor, but hand calculations frequently leave 4/8, 6/9, or 10/15 unreduced.
Frequently asked questions
How do I add two fractions with different denominators?
Find the least common multiple of the two denominators, convert each fraction to an equivalent fraction with that LCM as the denominator, and then add the numerators while keeping the LCM as the denominator. To add 2/3 + 1/4: LCM(3, 4) = 12, so 2/3 = 8/12 and 1/4 = 3/12, giving 8/12 + 3/12 = 11/12. The denominator stays the same in addition; only the numerators combine.
How do I divide fractions?
Multiply the first fraction by the reciprocal (flipped form) of the second fraction. To compute 2/3 ÷ 4/5: flip 4/5 to 5/4, then multiply 2/3 × 5/4 = 10/12 = 5/6 after simplification. The "keep, change, flip" mnemonic captures this: keep the first fraction, change the operation from divide to multiply, and flip the second fraction.
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For 2 3/5: 2 × 5 + 3 = 13, so 2 3/5 = 13/5. The reverse — converting an improper fraction to a mixed number — uses long division: 13 ÷ 5 = 2 remainder 3, so 13/5 = 2 3/5. The calculator handles both directions automatically.
What does "simplified" mean for a fraction?
A fraction is in simplest form (or lowest terms) when the numerator and denominator share no common factors greater than 1 — that is, when their greatest common divisor is 1. 6/8 is not simplified because GCD(6, 8) = 2; dividing both by 2 gives 3/4, which has GCD(3, 4) = 1 and is in lowest terms. The calculator always reduces results to lowest terms automatically.
Can I enter negative fractions?
Yes — enter a negative sign on the numerator, the whole-number portion, or both. The calculator follows the standard sign rules: negative times negative is positive, negative divided by negative is positive, and so on. A result that simplifies to a negative is rendered with the sign on the whole-number portion (or numerator if there is no whole-number part), matching standard mathematical convention.