Fraction Calculator

Fraction is evaluated from Numerator 1, Denominator 1 and Operation. The calculation reports Result, Result and Mixed Number Form.

Results

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About the Fraction Calculator

Fraction is treated here as a quantitative relation between Numerator 1, Denominator 1, Operation and Numerator 2 and Result, Result and Mixed Number Form.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
Add/Subtract: (a x d ± b x c) / (b x d), then simplify by GCD
Multiply: (a x c) / (b x d), then simplify
Divide: (a x d) / (b x c), then simplify

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

Add/Subtract: (a x d ± b x c) / (b x d), then simplify by GCD
Multiply: (a x c) / (b x d), then simplify
Divide: (a x d) / (b x c), then simplify

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Adding Fractions — Recipe Scaling

Inputs

num1: 2 den1: 3 operation: + num2: 1 den2: 4
Result: 11/12. Result: 0.916667. Mixed Number Form: 11/12

With Numerator 1 = 2, Denominator 1 = 3, Operation = + and Numerator 2 = 1 as the stated inputs, the result is Result = 11/12, Result = 0.916667 and Mixed Number Form = 11/12. Each value corresponds to the declared output fields.

Example 2: Subtracting Fractions — Remaining Material

Inputs

num1: 7 den1: 8 operation: - num2: 1 den2: 3
Result: 13/24. Result: 0.541667. Mixed Number Form: 13/24

With Numerator 1 = 7, Denominator 1 = 8, Operation = - and Numerator 2 = 1 as the stated inputs, the result is Result = 13/24, Result = 0.541667 and Mixed Number Form = 13/24. Each value corresponds to the declared output fields.

Example 3: Multiplying Fractions — Area Calculation

Inputs

num1: 3 den1: 5 operation: * num2: 2 den2: 7
Result: 6/35. Result: 0.171429. Mixed Number Form: 6/35

With Numerator 1 = 3, Denominator 1 = 5, Operation = * and Numerator 2 = 2 as the stated inputs, the result is Result = 6/35, Result = 0.171429 and Mixed Number Form = 6/35. Each value corresponds to the declared output fields.

Example 4: Dividing Fractions — Splitting into Servings

Inputs

num1: 5 den1: 6 operation: / num2: 5 den2: 12
Result: 2/1. Result: 2. Mixed Number Form: 2 0/1

With Numerator 1 = 5, Denominator 1 = 6, Operation = / and Numerator 2 = 5 as the stated inputs, the result is Result = 2/1, Result = 2 and Mixed Number Form = 2 0/1. Each value corresponds to the declared output fields.

Common Use Cases

  • Add two fractions with different denominators
  • Multiply fractions in a recipe scaling problem
  • Divide fractions for rate calculations
  • Simplify an improper fraction to lowest terms