How do I find a common denominator for addition or subtraction?

Multiplying the two denominators always gives a valid common denominator, so the calculator uses this simple approach. The least common denominator (LCD) — the smallest common multiple — is more elegant and requires less simplification afterward, but both yield the same correct result.

How do I multiply two fractions?

Multiply the numerators together and the denominators together. No common denominator is needed. For 2/3 × 4/5, the result is (2 × 4) / (3 × 5) = 8/15. Optionally simplify before multiplying if you see a shared factor between any numerator and any denominator.

How do I divide two fractions?

Flip the second fraction (its reciprocal) and multiply. 2/3 ÷ 4/5 becomes 2/3 × 5/4 = 10/12 = 5/6. This works because dividing by a number is mathematically identical to multiplying by its inverse.

What is a mixed number?

A mixed number combines a whole number and a proper fraction, such as 2¾. To convert it to an improper fraction, multiply the whole number by the denominator and add the numerator, keeping the same denominator: 2¾ = (2 × 4 + 3) / 4 = 11/4. The calculator expects improper fractions as input.

Can the denominator be zero?

No. Division by zero is mathematically undefined. The calculator rejects any input where a denominator is zero and asks you to correct it. Zero in the numerator is fine — 0/5 equals 0.

How do I convert a fraction to a decimal?

Divide the numerator by the denominator. 3/8 = 0.375. Some fractions produce repeating decimals (1/3 = 0.333…). This calculator displays both the fractional and decimal forms so you can see the relationship clearly.

What is an improper fraction?

An improper fraction has a numerator equal to or greater than its denominator, such as 7/3 or 5/5. It represents a value ≥ 1. Improper fractions are mathematically fine and are often easier to work with than mixed numbers during calculation; convert to mixed form only for the final answer if preferred.

Fraction Calculator

Math

Add, subtract, multiply, and divide fractions with automatic simplification.

Math

Fraction Calculator

Generated on April 24, 2026

?What is the Fraction Calculator?

A fraction calculator performs the four basic arithmetic operations on fractions — addition, subtraction, multiplication, and division — and returns the result in both fractional and decimal form, automatically reduced to lowest terms. It is useful for students learning fraction arithmetic, parents helping with homework, cooks scaling recipes, carpenters measuring in inches, and anyone working with ratios that do not cleanly divide. This tool handles proper fractions, improper fractions, and can be used repeatedly to chain several operations.

The Formula

a/b + c/d = (ad + cb) / bd. a/b − c/d = (ad − cb) / bd. a/b × c/d = ac / bd. a/b ÷ c/d = ad / bc.

For addition and subtraction, we bring both fractions to a common denominator — using the product of the two denominators works even when it is not the least common denominator. Multiplication is direct: multiply the tops and the bottoms. Division flips the second fraction and multiplies (multiplying by the reciprocal). After any operation, the calculator reduces the result by dividing numerator and denominator by their greatest common divisor (GCD) to present the fraction in lowest terms.

Practical Examples

1/2 + 1/3 = 3/6 + 2/6 = 5/6 — the classic first example of fraction addition requiring a common denominator.

3/4 − 1/8 = 6/8 − 1/8 = 5/8 — subtract after aligning denominators; the result is already in lowest terms.

2/3 × 3/4 = 6/12 = 1/2 — multiplication produces a result that simplifies neatly.

5/6 ÷ 2/3 = 5/6 × 3/2 = 15/12 = 5/4 = 1¼ — division becomes multiplication after flipping the second fraction.

In cooking, halving a recipe that calls for 3/4 cup of milk gives 3/8 cup — fraction multiplication in everyday kitchen use.

Carpentry: cutting a 17/8-inch board into four equal pieces gives 17/32 inch each — precise decimal 0.53125 inches.

Frequently Asked Questions

Simplification presents the fraction in its cleanest form, which is easier to interpret and compare. 5/10 is correct but 1/2 is clearer; most textbooks and exams require the simplified answer. Simplification also makes subsequent operations more efficient.

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Fraction Calculator

Fraction Calculator

?What is the Fraction Calculator?

The Formula

Practical Examples

Frequently Asked Questions

Why should fractions be simplified?

How do I find a common denominator for addition or subtraction?

How do I multiply two fractions?

How do I divide two fractions?

What is a mixed number?

Can the denominator be zero?

How do I convert a fraction to a decimal?

What is an improper fraction?

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