Formula used
Addition and subtraction require compatible fractional parts. The calculator finds an exact common denominator automatically. It then combines numerators and reduces the final value.
Multiplication uses numerator times numerator and denominator times denominator. Division changes the second fraction into its reciprocal first. Every answer is normalized to a positive denominator.
| Problem type | General rule | Example result |
|---|---|---|
| Addition | a/b + c/d = (ad + bc)/bd | 1/2 + 1/3 = 5/6 |
| Subtraction | a/b − c/d = (ad − bc)/bd | 3/4 − 1/6 = 7/12 |
| Multiplication | a/b × c/d = ac/bd | 2/3 × 3/5 = 2/5 |
| Division | a/b ÷ c/d = a/b × d/c | 3/4 ÷ 2/5 = 1 7/8 |
| Proportion | a/b = c/d, therefore ad = bc | 3/4 = 9/x gives x = 12 |
How to use this calculator
Select the calculation mode matching your fraction problem. Enter fractions using numerators, denominators, mixed numbers, or decimals. Percentage entries may include the percent symbol directly.
Choose whether detailed solution steps should appear. Press calculate to receive exact and converted answers. Use CSV or print options for saved records.
Understanding fraction solutions
Fractions describe equal parts of a complete quantity. The numerator counts selected parts above the fraction bar. The denominator states how many equal parts form one whole.
Equivalent fractions use different numbers for the same value. Multiplying both parts by one number preserves that value. Simplification reverses this process using a shared factor.
Mixed numbers combine whole units with a proper fraction. Improper fractions store the same quantity in one numerator. Converting between them changes presentation, not mathematical value.
Comparisons should avoid rounded decimals when exactness matters. Cross-products compare fractions without changing their true values. This calculator keeps rational arithmetic exact throughout each operation.
Fraction equations follow ordinary inverse-operation rules. Constants move by subtraction before coefficients divide both sides. Proportions use cross-products to isolate one missing quantity.
Expression mode follows the standard order of operations. Parentheses are completed before multiplication, division, addition, and subtraction. Exact simplification occurs only after each operation finishes.
Common mistakes to avoid
Never add denominators during ordinary fraction addition. Convert both values to a common denominator instead. Also check that no denominator equals zero.
Keep negative signs attached to the entire fraction. When dividing, invert only the second fraction. Reduce answers carefully after completing the required operation.
Frequently asked questions
Can this calculator solve mixed-number problems?
Yes. Enter values like 2 1/3 in supported text fields. Basic mode also provides separate whole-number inputs.
Does it simplify every fraction automatically?
Yes. The fraction class reduces results using the greatest common divisor. Signs and denominators are normalized too.
Can I compare more than two fractions?
Yes. Enter a comma-separated list in comparison mode. The calculator returns ascending or descending exact order.
How are decimals converted into fractions?
Decimal digits create a power-of-ten denominator. The resulting numerator and denominator are then reduced.
Can it solve a missing numerator or denominator?
Yes. Equivalent and proportion modes accept x in one position. Cross multiplication determines the missing value.
Does expression mode support parentheses?
Yes. It follows parentheses and standard operation precedence. Unsupported symbols produce a clear validation message.
What happens when a denominator is zero?
The calculation stops immediately. A friendly error explains that zero cannot serve as a denominator.
Can results be downloaded?
Yes. Download a CSV record or use printing to save a PDF. The result includes formulas and steps.
Are negative fractions supported?
Yes. Negative proper fractions, improper fractions, decimals, and mixed numbers are accepted. Results keep signs in normalized form.
Practice with examples to build reliable fraction-solving confidence today.