Fraction Calculator
Add, subtract, multiply, or divide two fractions or mixed numbers and see the working, not just the answer. The same card also simplifies fractions, converts decimals to fractions, and turns fractions into decimals — all with exact big-integer math.
How fraction arithmetic works
Adding and subtracting fractions needs a common denominator: rewrite each fraction over the least common denominator (LCD), then combine the numerators. Multiplying is simpler — multiply straight across — and dividing means multiplying by the reciprocal of the second fraction. Mixed numbers are converted to improper fractions first (1 1/2 becomes 3/2), and every answer is reduced by dividing top and bottom by their greatest common factor.
How it’s calculated
a/b + c/d = (aL/b + cL/d)/L where L = LCM(b, d); a/b × c/d = ac/bd; a/b ÷ c/d = ad/bc. Results are reduced by GCD(numerator, denominator) computed with Euclid’s algorithm. All arithmetic uses arbitrary-precision integers, so very large numerators and denominators stay exact.
Results update as you type. Enter whole numbers as a fraction over 1, and enter repeating decimals rounded to the digits you need.
Worked example
2/7 + 3/8: the LCD of 7 and 8 is 56, so 2/7 = 16/56 and 3/8 = 21/56. Adding numerators gives 37/56, which is already in lowest terms and equals about 0.660714. With mixed numbers, 1 1/2 + 2 3/4 = 3/2 + 11/4 = 6/4 + 11/4 = 17/4 = 4 1/4.
Common mistakes
- Adding numerators and denominators (2/7 + 3/8 is not 5/15) — only numerators add, and only after finding a common denominator.
- Forgetting to convert mixed numbers to improper fractions before multiplying or dividing.
- Dividing by a fraction without flipping it — dividing by 1/2 doubles a number, it does not halve it.
- Leaving answers unreduced, which loses marks in class and hides equal results (24/36 vs 2/3).
Where it is used
- Homework checking with visible steps for adding, subtracting, multiplying, and dividing fractions.
- Cooking and recipe scaling (3/4 cup halved is 3/8 cup).
- Woodworking and construction measurements in eighths, sixteenths, and thirty-seconds of an inch.
- Converting measured decimals like 0.375 in back to a tape-measure fraction.
Frequently asked questions
How do I add fractions with different denominators?
Rewrite both fractions over their least common denominator (LCD), then add the numerators. For 2/7 + 3/8 the LCD of 7 and 8 is 56, so 2/7 becomes 16/56 and 3/8 becomes 21/56, giving 37/56. The calculator shows these steps automatically.
How does the calculator simplify a fraction?
It divides the numerator and denominator by their greatest common factor (GCF). For example 24/36 has a GCF of 12, so it reduces to 2/3. Every result is returned in lowest terms, plus a mixed-number form when the fraction is improper.
Can it handle mixed numbers and negative fractions?
Yes. Enter the whole part in the optional whole-number box — 1 1/2 is whole 1, numerator 1, denominator 2 — and it is converted to an improper fraction (3/2) before calculating. A negative whole part or numerator makes the entire value negative, so 1 1/2 + 2 3/4 = 4 1/4.
How do I turn a decimal into a fraction?
Pick the decimal-to-fraction tool. It writes the digits after the decimal point over a power of ten and reduces: 0.375 = 375/1000 = 3/8. Repeating decimals should be entered rounded; the tool converts the exact digits you type.
Does it work with very large numerators and denominators?
Yes. The math runs on arbitrary-precision integers (BigInt), so numerators and denominators with dozens of digits are added, multiplied, and reduced exactly — there is no rounding until you read the decimal line, which is shown to 12 decimal places.