Starlight Tools

Fraction Calculator With Steps

Add, subtract, multiply, divide, simplify, and convert fractions, mixed numbers, and decimals. Use the visual fraction boxes first, or type formats like -7/4 and 2 3/5 in the advanced fields.

Inputs & Options

Enter two values, then calculate the selected operation.

First value

First value fraction

Second value

Second value fraction
Advanced text input fallback
If a text field is filled, it overrides that value's visual boxes.

Privacy: calculations run locally in your browser. Nothing is uploaded.

Result

Result (fraction):
Results will appear here.
Result (mixed):
—
Result (decimal):
—

Tip: Press Enter in an input field to calculate.

How the Fraction Calculator Works

This tool converts whole numbers, simple fractions, mixed numbers, and finite decimals into exact fractions. It performs the selected operation, reduces the result to lowest terms with the greatest common divisor (GCD), and shows fraction, mixed-number, and decimal forms where they apply.

Operations

  • Add/Subtract: Uses a common denominator (least common multiple of the two denominators) to combine numerators, then simplifies.
  • Multiply: Multiply numerators together and denominators together, then simplify.
  • Divide: Multiply by the reciprocal of the second fraction (i.e., flip it), then simplify.

Example

Compute \( 1 \tfrac{1}{2} + \tfrac{3}{8} \): Convert to improper forms: \( \tfrac{3}{2} + \tfrac{3}{8} \). LCM of 2 and 8 is 8, so \( \tfrac{12}{8} + \tfrac{3}{8} = \tfrac{15}{8} \). Mixed form is \( 1 \tfrac{7}{8} \).

Formula Reference

Add

\( \frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd} \), then reduce.

Subtract

\( \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} \), then reduce.

Multiply

\( \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd} \).

Divide

\( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \).

Simplify

Divide numerator and denominator by \( \gcd(a,b) \).

Mixed to Improper

\( w \frac{a}{b} = \frac{wb + a}{b} \), with the sign applied to the whole value.

Improper to Mixed

Whole \( = a \div b \), remainder \( = a \bmod b \).

Decimal to Fraction

Move the decimal over a power of 10, then reduce by GCD.

Worked Examples

Adding unlike denominators

\( \frac{1}{2} + \frac{3}{4} = \frac{2}{4} + \frac{3}{4} = \frac{5}{4} = 1 \frac{1}{4} \).

Subtracting fractions

\( 2 \frac{1}{3} - \frac{5}{6} = \frac{14}{6} - \frac{5}{6} = \frac{9}{6} = 1 \frac{1}{2} \).

Multiplying mixed numbers

\( 1 \frac{1}{2} \times 2 \frac{2}{3} = \frac{3}{2} \times \frac{8}{3} = 4 \).

Dividing by a fraction

\( \frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2} = \frac{15}{12} = \frac{5}{4} \).

Simplifying a fraction

\( \frac{12}{16} \) reduces by GCD 4, so \( \frac{12}{16} = \frac{3}{4} \).

Decimal to fraction

\( 0.125 = \frac{125}{1000} = \frac{1}{8} \).

Fraction to decimal

\( \frac{7}{8} = 7 \div 8 = 0.875 \).

Method & Transparency

Exact arithmetic

Fraction operations use integer numerator and denominator arithmetic, not floating-point approximations.

Reduced by GCD

Every fraction answer is reduced using the greatest common divisor when possible.

Decimal display only

Decimal places affect only the displayed decimal approximation. They do not change the exact fraction result.

Runs locally

All calculations happen in the browser. Input values are not sent to a server.

Understanding Fractions

A fraction represents a part of a whole. It consists of two numbers:

  • Numerator: the top number, showing how many parts we have.
  • Denominator: the bottom number, showing into how many equal parts the whole is divided.

Types of Fractions

  • Proper fraction: numerator smaller than denominator (e.g., \( \tfrac{3}{4} \)).
  • Improper fraction: numerator larger than or equal to denominator (e.g., \( \tfrac{9}{5} \)).
  • Mixed number: whole number plus a proper fraction (e.g., \( 1 \tfrac{2}{3} \)).

Why Simplify Fractions?

Simplifying means dividing numerator and denominator by their greatest common divisor (GCD). For example:

\( \tfrac{12}{16} = \tfrac{12 \div 4}{16 \div 4} = \tfrac{3}{4} \)

This makes fractions easier to understand and compare.

Fractions in Daily Life

  • Cooking: Recipes often use halves, thirds, or quarters.
  • Construction: Measurements use eighths and sixteenths of an inch.
  • Probability: A fair coin has a probability of \( \tfrac{1}{2} \) for heads or tails.

Quick Conversion Tip

To convert a fraction to a decimal, divide numerator by denominator. For example, \( \tfrac{7}{8} = 0.875 \).

Fraction Calculator FAQ

How do you add fractions with different denominators?

Find the least common denominator, rewrite each fraction with that denominator, add the numerators, and reduce the result by the greatest common divisor.

How do you divide fractions?

Keep the first fraction, flip the second fraction to its reciprocal, multiply across, and simplify the result.

What is a mixed number?

A mixed number combines a whole number and a proper fraction, such as 2 1/3. For calculation, it can be converted to an improper fraction.

How do you simplify a fraction?

Divide the numerator and denominator by their greatest common divisor. For example, 12/16 reduces to 3/4 because the GCD is 4.

Can fractions be negative?

Yes. A negative sign may apply to the numerator or to the whole fraction. The calculator keeps the denominator positive in the final answer.

How do you convert a decimal to a fraction?

Write the decimal over a power of 10 based on its decimal places, then reduce. For example, 0.125 becomes 125/1000, which simplifies to 1/8.

Why can't the denominator be zero?

A denominator shows how many equal parts make one whole. Zero equal parts is undefined, so any fraction with denominator 0 is invalid.

5 Fun Facts about Fractions

Decimal ≠ fraction? Not always

0.1 looks simple, but it’s \(1/10\). Meanwhile 0.1 in binary is repeating—fractions depend on the base you use.

Base-dependent

Egyptians loved unit fractions

Ancient scribes wrote every fraction as sums of distinct unit fractions (like \(1/2 + 1/6\)), never repeated.

History twist

Simplify with primes

Factoring numerator and denominator into primes makes reducing a fraction trivial—just cancel shared factors.

Prime power

Repeating decimals hide fractions

Any repeating decimal is rational. For example, 0.\(\overline{3}\) = 1/3, 0.\(\overline{142857}\) = 1/7.

Pattern clue

Mixed numbers are just improper

\(1\tfrac{3}{4} = \tfrac{7}{4}\). Switching forms is a single multiply-and-add—handy for calculations.

Form swap

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