Fraction Calculator

What a Fraction Calculator Does

A fraction calculator helps you work with fractions accurately without losing exactness. Fractions represent a ratio of two integers: the numerator (top) and denominator (bottom). Many real-world quantities are naturally fractional — recipe scaling, measurement conversions, construction cuts, time splits, probability, and classroom math are common examples. A reliable fraction calculator makes these tasks faster, reduces mistakes, and keeps results in simplest form.

This Fraction Calculator supports the four core operations (add, subtract, multiply, divide), plus simplification, conversion between fraction / mixed number / decimal, and comparison. It is designed to be “exact-first”: operations are done as rational numbers, then simplified using the greatest common divisor (GCD). When you input a decimal, it can be converted to a fraction using a rational approximation with a configurable maximum denominator.

Fraction Basics: Numerator and Denominator

A fraction is written as a/b. The numerator a tells you how many parts you have, and the denominator b tells you how many equal parts make a whole. For example, 3/4 means three parts out of four total equal parts. When the numerator is smaller than the denominator, the fraction is a proper fraction. When the numerator is larger, it is an improper fraction, which can also be expressed as a mixed number.

How to Simplify Fractions

Simplifying (reducing) a fraction means writing it in simplest form without changing its value. You do this by dividing both numerator and denominator by their greatest common divisor (GCD). For example, 18/24 simplifies to 3/4 because the GCD of 18 and 24 is 6, and dividing both by 6 gives 3 and 4.

Adding and Subtracting Fractions

To add or subtract fractions, you need a common denominator. If the denominators are already the same, you simply add or subtract the numerators. If they’re different, you can find a common denominator by multiplying the denominators (or by using the least common multiple, LCM). Then convert each fraction into an equivalent fraction with that denominator.

After you compute the new numerator and denominator, simplify the result using the GCD. This calculator also displays the mixed-number form where appropriate.

Multiplying and Dividing Fractions

Multiplying fractions is straightforward: multiply the numerators and multiply the denominators, then reduce. You can often simplify before multiplying by canceling factors across numerator and denominator (cross-reduction), which prevents large intermediate values.

Dividing by a fraction is equivalent to multiplying by its reciprocal. In other words, flip the second fraction and multiply. This is one of the most common fraction “rules” students use, and it’s also how calculators compute exact results.

Mixed Numbers and Improper Fractions

A mixed number combines a whole number and a proper fraction, such as 2 1/3. For calculations, mixed numbers are usually converted to improper fractions:

After the calculation, you can convert an improper fraction back into a mixed number by dividing the numerator by the denominator. The quotient becomes the whole part and the remainder becomes the new numerator.

Converting Fractions to Decimals and Back

Converting a fraction to a decimal is done by division: numerator ÷ denominator. Some fractions become terminating decimals (like 1/4 = 0.25). Others repeat (like 1/3 = 0.333…). When you convert a decimal back to a fraction, there are multiple valid answers unless you specify a rule. This tool uses a practical approach: it finds a close rational approximation with a denominator up to your chosen maximum, then simplifies that result.

This is especially useful when you have a decimal from measurement or a device readout and you want a neat fraction for exact calculations or for sharing in a classroom-friendly form.

Comparing Fractions

To compare two fractions, you can convert them to a common denominator or compare cross-products. For positive denominators, the comparison:

If a·d is greater than c·b, then a/b is greater than c/d. This avoids floating-point rounding issues and keeps the comparison exact. The Compare tab shows the result and the difference between the two values.

Common Fraction Mistakes This Tool Helps Prevent

• Adding denominators directly instead of finding a common denominator
• Forgetting to simplify results after operations
• Dividing fractions without using the reciprocal
• Mixing up mixed-number conversion steps
• Rounding too early when converting to decimals

When to Use a Fraction Calculator

A fraction calculator is useful for schoolwork, quick checks, and real-world tasks where exactness matters. If you are scaling a recipe, splitting time, estimating material lengths, or verifying a worksheet, you typically want the simplest exact fraction rather than a rounded decimal. This tool provides both, so you can use whichever format is best for your situation.