How do you add fractions with different denominators?

Use cross-multiplication: (A×D + C×B) ÷ (B×D), then simplify by GCD.

How do you multiply fractions?

Multiply numerators together and denominators together: (A×C)/(B×D), then simplify.

How do you divide fractions?

Keep, Change, Flip: A/B ÷ C/D = (A×D)/(B×C), then simplify.

What is an improper fraction?

An improper fraction has numerator ≥ denominator (e.g. 7/3). It converts to a mixed number: 7/3 = 2 and 1/3.

What does the pie chart show?

The SVG pie chart shows the fractional part of the result (between 0 and 1). The whole number part is shown separately.

Math

Add, subtract, multiply & divide fractions

Enter two fractions, choose an operation, and get the simplified result, mixed number, decimal equivalent, and step-by-step working — plus an SVG pie chart to visualise the answer.

Add, subtract, multiply, divide Auto-simplify to lowest terms Improper → mixed number Decimal equivalent Step-by-step working SVG pie chart

Fraction Calculator

Add, subtract, multiply & divide

Operation

Fraction 1

Fraction 2

Result

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Decimal —

Mixed —

Fraction Visualised

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Fraction part

Remainder

Step-by-Step Working

Fraction Calculator — Add, Subtract, Multiply & Divide

This free fraction calculator handles all four arithmetic operations on fractions and returns the answer in three forms simultaneously: the simplified fraction in lowest terms, the mixed number (when applicable), and the decimal equivalent. It also shows the step-by-step working so you can follow the method and learn from each calculation.

Enter numerator A, denominator B, choose an operation, enter numerator C and denominator D, then click Calculate. The answer appears instantly — no reloads, no sign-up.

Fraction Operation Rules

Addition

A/B + C/D = (A×D + C×B) / (B×D)

Cross-multiply the numerators, add them, place over the product of both denominators. Then simplify by dividing by the GCD.

−

Subtraction

A/B − C/D = (A×D − C×B) / (B×D)

Same as addition but subtract the cross-multiplied numerators. Result can be negative if A/B < C/D.

Multiplication

A/B × C/D = (A×C) / (B×D)

Multiply numerators together and denominators together. Then simplify. The simplest of all four operations — no common denominator needed.

Division

A/B ÷ C/D = (A×D) / (B×C)

"Keep, Change, Flip" — keep the first fraction, change ÷ to ×, flip (reciprocal) the second fraction. Then multiply and simplify.

How Fractions Are Simplified

Every result is reduced to its lowest terms using the Greatest Common Divisor (GCD). The GCD is found using the Euclidean algorithm:

Euclidean Algorithm (GCD)

gcd(a, b) = gcd(b, a mod b)
gcd(a, 0) = a

Example: gcd(12, 8)
→ gcd(8, 4) → gcd(4, 0) = 4

12/8 ÷ 4/4 = 3/2

Once simplified, if the numerator is larger than the denominator (an improper fraction), the result is also expressed as a mixed number. For example, 3/2 becomes 1½.

Worked Example: 2/3 + 3/4

Cross-multiply 2×4 = 8 3×3 = 9

Add numerators 8 + 9 = 17

Denominator 3 × 4 = 12

Raw result 17/12

GCD(17,12) = 1 — already in lowest terms Simplified: 17/12

Mixed number 17/12 = 1 and 5/12 ≈ 1.4167

Frequently Asked Questions

Cross-multiply: (A×D + C×B) ÷ (B×D). For example, 1/3 + 1/4 = (1×4 + 1×3) ÷ (3×4) = 7/12. Then simplify by dividing numerator and denominator by their GCD. This calculator does all of that automatically.

Same as addition but with subtraction: (A×D − C×B) ÷ (B×D). If the result is negative, the calculator shows a negative fraction. If the fractions are equal, the result is 0.

Multiply numerators together (A×C) and denominators together (B×D), then simplify: (A×C)/(B×D). No common denominator is needed — this is the simplest of the four operations.

Use "Keep, Change, Flip": keep the first fraction, change ÷ to ×, flip the second (reciprocal). So A/B ÷ C/D = (A×D)/(B×C). Then simplify.

An improper fraction has a numerator ≥ denominator (e.g. 7/3). To convert to a mixed number: divide to get the whole part (7÷3 = 2 remainder 1), so 7/3 = 2 and 1/3. The calculator performs this conversion automatically when the result is improper.

The working panel shows each step: the raw calculation (numerator and denominator), the GCD used for simplification, the simplified fraction, the mixed number conversion if applicable, and the decimal equivalent. This is useful for checking homework or learning the method.

Yes. The calculator handles negative values. A fraction like −3/4 can be entered as numerator −3, denominator 4. If both the numerator and denominator are negative, the result will be positive. The calculator normalises the sign to always be on the numerator.

The SVG pie chart shows the fractional part of the result between 0 and 1. If the result is greater than 1, the whole number is shown separately and the chart shows only the fractional remainder. For results of 0 or negative values, the chart displays an empty or full circle accordingly.

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Worked Example: 2/3 + 3/4

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