Rechnerpilot Calculator
Fraction Calculator
Add, subtract, multiply and divide fractions, reduce and expand them – calculated exactly, with a reduced result, mixed number and calculation steps.
Available
Explanation
How Fraction Calculator works
A fraction describes a share made up of a numerator (top) and a denominator (bottom). The fraction calculator works exactly with whole-number numerators and denominators and only rounds for the decimal representation.
When adding and subtracting, the fractions are first brought to a common denominator; when multiplying, the numerators and denominators are each multiplied; when dividing, you multiply by the reciprocal. The result is then fully reduced.
Adding and subtractinga/b ± c/d = (a·d ± c·b) / (b·d)Using the common denominator b·d, the numerators are combined.
Multiplying and dividinga/b · c/d = (a·c)/(b·d) and a/b ÷ c/d = (a·d)/(b·c)When dividing, you multiply by the reciprocal of the second fraction.
Knowledge
Numerator, denominator and value
A fraction describes a share made up of a numerator and a denominator.
The denominator indicates how many equal parts a whole is divided into, the numerator how many of those parts are meant.
- Proper fraction: numerator smaller than denominator (e.g. 3/4).
- Improper fraction: numerator greater than or equal to denominator (e.g. 7/2).
- Equivalent fractions arise through reducing and expanding.
Practice
Practical examples
For illustration only – your own calculation is what counts.
Adding fractions
Half a cake plus a third of a cake: 1/2 + 1/3 together make 5/6.
Result: 1/2 + 1/3 = 5/6 (≈ 0.83).
Reducing a fraction
4/8 can be reduced to 1/2 using the greatest common divisor.
Result: 4/8 reduced is 1/2.
Expanding a fraction
1/2 expanded by the factor 3 gives the equivalent fraction 3/6.
Result: 1/2 expanded by 3 gives 3/6.
- Simply adding the denominators too
For 1/2 + 1/3, numerators and denominators are wrongly added separately (2/5 instead of 5/6).
First give the fractions a common denominator and add only the numerators. The common denominator stays the same.
- Result not reduced
A result like 4/8 is left as is, even though it can be reduced to 1/2.
Always reduce the result by the greatest common divisor. The calculator does this automatically.
- Not multiplying by the reciprocal when dividing
Instead of multiplying by the reciprocal, the numerators and denominators are divided directly.
Dividing by a fraction means multiplying by its reciprocal: a/b ÷ c/d = a/b · d/c.
FAQ
Frequently asked questions
How do I add two fractions?
Fractions are brought to a common denominator and then the numerators are added. The calculator does this automatically: 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6.
What does reducing mean?
Reducing means dividing the numerator and denominator by the same number without changing the value of the fraction. A fraction is fully reduced when the numerator and denominator no longer share a common divisor other than 1.
When do I need to expand a fraction?
Expanding is the opposite of reducing: the numerator and denominator are multiplied by the same number. This is necessary to give fractions a common denominator, for example before adding or subtracting.
Why can't the denominator be 0?
The denominator indicates how many parts the whole is divided into. Division by 0 is undefined, so a fraction with denominator 0 is not a valid value.
What is a mixed number?
If the numerator is larger than the denominator (an improper fraction), the result can be written as a mixed number, for example 7/2 = 3 1/2. The calculator shows both representations.
- Numerator, denominator and expansion factor must be whole numbers. Decimal fractions are not interpreted as a fraction.
- In calculation mode, exactly two fractions are combined. Longer expressions must be calculated step by step.
- The fraction result is exact. The additionally displayed decimal value is rounded and serves only as a guide.
Sources
Sources and references
- Bildungsstandards Mathematik – Sekundarstufe IKultusministerkonferenz (KMK)
The KMK educational standards establish calculating with fractions as a core competency in the numbers and operations strand of lower secondary education.
View sourceRetrieved: 08/24/2026 · Verified on: 08/24/2026 - Bruchrechnung – Grundlagen und RechenregelnSerlo Education e. V.
Freely accessible learning portal with the rules for adding, subtracting, reducing and expanding fractions.
View sourceRetrieved: 08/24/2026 · Verified on: 08/24/2026
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