How do I add fractions?

Find a common denominator, add the numerators, then simplify. Formula: a/b + c/d = (ad + bc) / bd

How do I subtract fractions?

Find a common denominator, subtract the numerators, then simplify. Formula: a/b - c/d = (ad - bc) / bd

How do I multiply fractions?

Multiply numerators together and denominators together, then simplify. Formula: a/b × c/d = ac / bd

How do I divide fractions?

Multiply by the reciprocal (flip the second fraction). Formula: a/b ÷ c/d = a/b × d/c = ad / bc

What is simplifying a fraction?

Dividing both numerator and denominator by their greatest common divisor (GCD). Example: 6/8 simplifies to 3/4.

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, add the numerator, then place over the original denominator. Example: 2 3/4 = (2×4 + 3)/4 = 11/4

How do I convert a decimal to a fraction?

The calculator uses continued fractions algorithm to find the best fractional representation. Example: 0.75 = 3/4, 0.333... = 1/3

What is a repeating decimal?

A decimal with digits that repeat infinitely. Example: 1/3 = 0.333..., 1/7 = 0.142857... (the pattern 142857 repeats)

How do I compare two fractions?

Find a common denominator (LCD), then compare the scaled numerators. The fraction with the larger numerator is bigger. Example: 3/8 vs 5/12 → LCD=24 → 9/24 vs 10/24 → 5/12 is larger.

How do I solve for X in a fraction equation?

Use cross multiplication. For X/b = c/d, multiply both sides: X = (b × c) / d. For a/X = c/d, then X = (a × d) / c.

Can I add more than two fractions?

Yes — use the "+ Add fraction" button in Operations mode to chain up to 9 fractions together with the same operation.

Fraction Calculator

Fraction calculator: operations on 2-9 fractions, compare, solve for X, mixed numbers, simplify, and decimal conversions with step-by-step solutions.

Calculator Modes

This calculator offers 7 modes for all your fraction needs:

Operations: Add, subtract, multiply, and divide 2-9 fractions
Mixed Numbers: Convert between mixed numbers and improper fractions
Simplify: Reduce fractions to lowest terms
Decimal→Fraction: Convert decimals to fractions
Fraction→Decimal: Convert fractions to decimals with repeating pattern detection
Compare: Determine which of two fractions is larger using LCD
Solve for X: Find the missing value in a fraction equation using cross multiplication

Fraction Operations

Perform basic arithmetic operations on fractions with step-by-step solutions.

Adding Fractions

Formula: a/b + c/d = (ad + bc) / bd

Example: 1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6

Subtracting Fractions

Formula: a/b - c/d = (ad - bc) / bd

Example: 3/4 - 1/2 = (3×2 - 1×4) / (4×2) = 2/8 = 1/4

Multiplying Fractions

Formula: a/b × c/d = ac / bd

Example: 2/3 × 3/4 = 6/12 = 1/2

Dividing Fractions

Formula: a/b ÷ c/d = a/b × d/c = ad / bc

Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2

Understanding Fractions

Parts of a Fraction

Numerator: The top number (how many parts you have)
Denominator: The bottom number (total equal parts)

Types of Fractions

Proper: Numerator < denominator (e.g., 3/4)
Improper: Numerator ≥ denominator (e.g., 5/3)
Mixed: Whole number + fraction (e.g., 1⅔)

Simplifying Fractions

To simplify, find the greatest common divisor (GCD) and divide both parts by it.

Example: 12/18 → GCD is 6 → 12÷6 / 18÷6 = 2/3

Mixed Number Conversions

Mixed to Improper

Formula: Whole × Denominator + Numerator / Denominator

Example: 2 3/4 = (2×4 + 3)/4 = 11/4

Improper to Mixed

Divide numerator by denominator. Quotient becomes whole number, remainder becomes new numerator.

Example: 7/3 = 2 1/3 (7÷3 = 2 remainder 1)

Decimal Conversions

Decimal to Fraction

Uses continued fractions algorithm for accurate conversion. Handles both terminating and repeating decimals.

Examples:

0.75 → 3/4
0.333... → 1/3
0.125 → 1/8

Fraction to Decimal

Divides numerator by denominator and detects repeating patterns.

Examples:

1/4 = 0.25 (terminating)
1/3 = 0.333... (repeating)
1/7 = 0.142857... (repeating pattern: 142857)

Common Fraction-Decimal-Percent Equivalents

1/8 = 0.125 = 12.5%
1/4 = 0.25 = 25%
1/3 = 0.333... = 33.3%
1/2 = 0.5 = 50%
2/3 = 0.666... = 66.7%
3/4 = 0.75 = 75%
7/8 = 0.875 = 87.5%

Comparing Fractions

To compare fractions, find the least common denominator (LCD) and scale both numerators:

3/8 vs 5/12 → LCD = 24 → 9/24 vs 10/24 → 5/12 is larger
2/5 vs 3/7 → LCD = 35 → 14/35 vs 15/35 → 3/7 is larger

Solving for X

When two fractions are equal and one value is unknown, use cross multiplication:

X/12 = 4/16 → X = (12 × 4) / 16 = 3
7/X = 21/9 → X = (7 × 9) / 21 = 3

Multi-Fraction Operations

Chain operations on 3 or more fractions by clicking "+ Add fraction" in Operations mode. The calculator applies each operation left to right, simplifying intermediate results.

Fractions in Real Life

Cooking: Recipes use fractions constantly — 1/2 cup flour, 3/4 tsp salt, 1/3 cup milk. Scaling a recipe requires multiplying fractions
Construction: Tape measures are marked in 1/16-inch increments. Lumber dimensions use fractions (a 2×4 is actually 1 1/2 × 3 1/2 inches)
Music: Note durations are fractions — whole, half, quarter, eighth, sixteenth notes. Time signatures like 3/4 and 6/8 are fractions
Finance: Stock prices historically used fractions (1/8 increments) before switching to decimals in 2001