Top number of the first fraction.
Bottom number of the first fraction (cannot be 0).
Top number of the second fraction.
Bottom number of the second fraction (cannot be 0).
Choose the arithmetic operation to perform.
Result — Numerator
5
Top of the simplified result fraction.
Result — Denominator
6
Bottom of the simplified result fraction.
Result as Decimal
0.833333
Decimal equivalent of the simplified fraction.
Addition/subtraction: cross-multiply to find a common denominator (b×d), then combine numerators.
Adding 1/2 + 1/3.
First fraction
1/2
Second fraction
1/3
Operation
Addition
Common denominator
2 × 3 = 6
Converted fractions
3/6 + 2/6
Result (simplified)
5/6
Decimal
0.833333
1/2 + 1/3 = 5/6 ≈ 0.8333. The result is already fully simplified since GCD(5,6) = 1.
This tool combines two fractions using any of the four operations — add, subtract, multiply, or divide — and returns the answer reduced to lowest terms along with its decimal value. You enter each numerator and denominator, pick an operation, and get a fully simplified result.
It is built for students learning fraction arithmetic, for anyone scaling a recipe or a measurement, and for quick checks where a calculator that only does decimals would lose the exact fraction. The simplified output means you never have to reduce by hand afterward.
Addition and subtraction need a common denominator. The tool cross-multiplies to put both fractions over the product of the denominators, then adds or subtracts the numerators: a/b ± c/d = (ad ± cb) ÷ (bd).
Multiplication and division are simpler. To multiply, multiply straight across — numerator times numerator, denominator times denominator. To divide, flip the second fraction and multiply, because dividing by a fraction is the same as multiplying by its reciprocal.
After combining the fractions, the calculator finds the greatest common divisor of the numerator and denominator and divides both by it. That reduces the fraction to lowest terms, so 12/16 becomes 3/4 automatically.
The decimal equivalent is provided alongside the fraction for a quick sense of size. If the denominator comes out as 1, the result is a whole number, and the decimal will simply show that integer.
This tool works with simple fractions, so convert mixed numbers before entering them. Multiply the whole part by the denominator, add the numerator, and keep the same denominator: 2¾ becomes (2 × 4 + 3) ÷ 4 = 11/4.
Forgetting this conversion is the most common mistake. Typing the whole number and the fraction separately, or dropping the whole part, will give an answer for the wrong quantity, so always rewrite mixed numbers as improper fractions first.
Subtract 1/6 from 3/4. Cross-multiply over the common denominator 24: 3/4 = 18/24 and 1/6 = 4/24, so 18/24 − 4/24 = 14/24. The greatest common divisor of 14 and 24 is 2, which reduces the answer to 7/12, or about 0.5833.
Multiplication is even quicker: 2/3 × 3/5 multiplies across to 6/15, and dividing both by 3 gives 2/5, or 0.40. Notice you do not need a common denominator to multiply — that step is only for adding and subtracting.
Denominators cannot be zero, since a fraction with a zero bottom is undefined; the calculator substitutes 1 to keep going rather than break. It also combines exactly two fractions at a time, so longer expressions must be done in steps.
Results are shown as improper fractions rather than mixed numbers — 7/4 stays 7/4 instead of displaying as 1¾. The reduction is exact for whole-number inputs, which is the normal case for fraction problems.
Convert to an improper fraction: multiply the whole number by the denominator and add the numerator. E.g., 2¾ = (2×4+3)/4 = 11/4. Enter 11 as numerator, 4 as denominator.
The calculator divides by GCD automatically. If you see 2/4, GCD=2 and it shows 1/2. If it appears unreduced, double-check that both inputs were entered correctly.
The denominator will be 1 (e.g., 3/4 × 4/1 = 12/4 = 3/1). The decimal shows 3.0.
Dividing by a fraction = multiplying by its reciprocal. ½ ÷ ⅓ = ½ × 3 = 3/2 = 1.5.
You can only add parts that are the same size. Thirds and halves are different sizes, so you rewrite both over a shared denominator first. For 1/2 + 1/3, the common denominator is 6, giving 3/6 + 2/6 = 5/6 — now you are adding like-sized pieces.
Divide the numerator by the denominator: the quotient is the whole number and the remainder stays over the denominator. For 7/4, 7 ÷ 4 is 1 with remainder 3, so 7/4 = 1¾. This calculator shows the improper form (7/4) and its decimal, and you can convert by hand from there.
Figures on this page are checked against primary, authoritative sources. Links open in a new tab.
Note
This calculator is an educational tool. For graded coursework, exams, or professional work, double-check the method and rounding against your own requirements.
Built and maintained by Calculator Matters, an independent calculator project. Method checked against published formulas and primary sources · Last reviewed 3 June 2026 · How we calculate · Found an error? corrections@calculatormatters.com