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

Inputs

Enter values

Live

CalculateAdd, subtract, multiply or divide two fractions.

Operation

Choose how the two fractions are combined.

Numeratori

The top value of the first fraction (whole number).

Denominatori

The bottom value of the first fraction (not 0).

Numerator 2i

The top value of the second fraction (whole number).

Denominator 2i

The bottom value of the second fraction (not 0).

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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) und 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.

Notes

Common mistakes

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.

Limits

Limitations

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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