Fraction Calculator
Add, subtract, multiply, and divide fractions in seconds. Every result comes with a simplified fraction, mixed number, decimal equivalent, and full step-by-step working so you can see exactly how it was solved.
All calculations happen in your browser. No data is stored.
Add Fractions
Enter two fractions to add together. Denominators must be non-zero integers.
Subtract Fractions
Enter two fractions to subtract the second from the first.
Multiply Fractions
Multiply two fractions. Numerators multiply together, denominators multiply together.
Divide Fractions
Divide the first fraction by the second using Keep-Change-Flip (KCF).
How Fraction Arithmetic Works
Adding & subtracting fractions
To add or subtract fractions with unlike denominators you must first find a common denominator. The most efficient choice is the Least Common Denominator (LCD) — the smallest number that both denominators divide into evenly. Convert each fraction to that denominator, then add or subtract the numerators, keeping the denominator the same. Finally simplify by dividing numerator and denominator by their GCD.
Example: 1/4 + 1/6 — LCD = 12, so 3/12 + 2/12 = 5/12.
Least Common Denominator (LCD) explained
The LCD of two denominators is the same as their Least Common Multiple (LCM). You can find it by listing multiples of each denominator until you find the first one they share, or use the formula: LCM(a, b) = |a × b| / GCD(a, b).
For denominators 4 and 6: GCD(4,6) = 2, so LCM = (4 × 6) / 2 = 12. This calculator uses the formula automatically.
Mixed numbers
An improper fraction has a numerator larger than its denominator (e.g. 7/4). A mixed number separates it into a whole part and a proper fraction (e.g. 1 3/4). To convert: divide the numerator by the denominator, the quotient is the whole number and the remainder over the original denominator is the fractional part.
7 ÷ 4 = 1 remainder 3, so 7/4 = 1 3/4.
Dividing fractions — Keep-Change-Flip
Dividing by a fraction is the same as multiplying by its reciprocal. The Keep-Change-Flip (KCF) rule makes this easy to remember: Keep the first fraction as-is, Change the ÷ sign to ×, and Flip the second fraction upside down. Then multiply across and simplify.
Example: 2/3 ÷ 4/5 → 2/3 × 5/4 = 10/12 = 5/6.
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How do you add fractions with different denominators?
Find the Least Common Denominator (LCD), convert both fractions to that denominator, then add the numerators and simplify. For example, 1/4 + 1/6: LCD = 12, so 3/12 + 2/12 = 5/12.
What is a mixed number?
A mixed number has a whole-number part and a fractional part, e.g. 1 3/4. It is equivalent to the improper fraction 7/4. Mixed numbers are easier to visualise while improper fractions are easier to compute with. This calculator converts automatically.
How do you simplify a fraction?
Divide the numerator and denominator by their Greatest Common Divisor (GCD). For 8/12, GCD(8,12) = 4, giving 2/3. The result is fully simplified when GCD = 1.
How do you divide fractions?
Use Keep-Change-Flip: keep the first fraction, change ÷ to ×, flip the second fraction. Then multiply across and simplify. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
What is the Least Common Denominator (LCD)?
The LCD is the Least Common Multiple of the two denominators — the smallest number both divide into evenly. It is needed to add or subtract fractions with unlike denominators. LCD of 4 and 6 is 12.