Fraction Calculator – Free Online Tool for Fraction Arithmetic, Simplification & Conversion

Perform fraction addition, subtraction, multiplication, and division instantly with our free fraction calculator. Simplify fractions, convert decimals to fractions, and switch between mixed numbers and improper fractions — all with detailed step-by-step solutions.

What Is a Fraction?

A fraction represents a part of a whole. It is written as two numbers separated by a line: the numerator (top number) tells you how many parts you have, and the denominator (bottom number) tells you how many equal parts the whole is divided into.

For example, ¾ means you have 3 out of 4 equal parts.

Types of Fractions

• Proper fraction — The numerator is smaller than the denominator (e.g., ⅔, ¾, ⅝). The value is always less than 1.
• Improper fraction — The numerator is greater than or equal to the denominator (e.g., 7/4, 10/3, 5/5). The value is 1 or greater.
• Mixed number — A whole number combined with a proper fraction (e.g., 1 ¾, 3 ⅖). Represents values greater than 1 in a more readable format.
• Unit fraction — A fraction where the numerator is 1 (e.g., ½, ⅓, ¼). These are the building blocks of all fractions.
• Equivalent fractions — Different fractions that represent the same value (e.g., ½ = 2/4 = 3/6 = 50/100).

How to Use the Fraction Calculator

Our fraction calculator offers three powerful modes to handle any fraction problem:

Arithmetic Mode

1. Enter the numerator and denominator of the first fraction
2. Select your operation: add (+), subtract (−), multiply (×), or divide (÷)
3. Enter the numerator and denominator of the second fraction
4. See the result instantly as a simplified fraction, mixed number, and decimal

Simplify Mode

1. Enter any fraction (numerator and denominator)
2. The calculator instantly reduces it to lowest terms
3. View the GCD (Greatest Common Divisor) used and the step-by-step simplification

Convert Mode

• Decimal to Fraction: Enter any decimal number (e.g., 0.75) and get the equivalent fraction (¾)
• Mixed to Improper: Enter a mixed number (e.g., 2 ¾) and convert it to an improper fraction (11/4)

Features

• Instant results — All calculations happen in real-time as you type
• Step-by-step solutions — Every calculation shows the detailed mathematical process
• Multiple formats — Results displayed as fractions, mixed numbers, and decimals
• Visual fraction display — Large, clear fraction notation with numerator over denominator
• Quick examples — Pre-loaded example buttons for common calculations
• Full keyboard support — Navigate and calculate without touching your mouse
• Mobile responsive — Works beautifully on phones, tablets, and desktops
• No sign-up required — Completely free with no registration needed

Fraction Operations Explained

Adding Fractions

To add two fractions, you need a common denominator. Here is the step-by-step process:

1. Find the Least Common Multiple (LCM) of the two denominators — this becomes the common denominator
2. Multiply each numerator by the same factor you used to convert its denominator to the common denominator
3. Add the two new numerators together
4. Keep the common denominator
5. Simplify the result by dividing both numerator and denominator by their GCD

Example: ⅔ + ¼

LCM of 3 and 4 = 12
⅔ = 8/12 (multiply both by 4)
¼ = 3/12 (multiply both by 3)
8/12 + 3/12 = 11/12

Subtracting Fractions

Subtraction follows the same process as addition, except you subtract the numerators instead of adding them:

1. Find the LCM of the denominators
2. Convert both fractions to have the common denominator
3. Subtract the second numerator from the first
4. Simplify the result

Example: ⅝ − ⅓

LCM of 8 and 3 = 24
⅝ = 15/24
⅓ = 8/24
15/24 − 8/24 = 7/24

Multiplying Fractions

Multiplication is the simplest fraction operation — no common denominator needed:

1. Multiply the two numerators together
2. Multiply the two denominators together
3. Simplify the result

Example: ⅔ × 4/5

Numerator: 2 × 4 = 8
Denominator: 3 × 5 = 15
Result: 8/15 (already in simplest form)

Dividing Fractions

Division uses the reciprocal method (also known as "keep, change, flip"):

1. Keep the first fraction as it is
2. Change the division sign to multiplication
3. Flip the second fraction (swap numerator and denominator)
4. Multiply the two fractions
5. Simplify the result

Example: ¾ ÷ ⅖

Flip ⅖ → 5/2
¾ × 5/2 = 15/8
15/8 = 1 ⅞ (mixed number)

How to Simplify Fractions

Simplifying (or reducing) a fraction means finding an equivalent fraction with the smallest possible numerator and denominator. The key is the Greatest Common Divisor (GCD).

The GCD Method

1. Find the GCD of the numerator and denominator
2. Divide both the numerator and denominator by the GCD
3. The result is the fraction in its simplest form

Example: Simplify 18/24

GCD(18, 24) = 6
18 ÷ 6 = 3
24 ÷ 6 = 4
Simplified: ¾

How to Find the GCD

The most efficient method is the Euclidean Algorithm:

1. Divide the larger number by the smaller number
2. Find the remainder
3. Replace the larger number with the smaller number, and the smaller number with the remainder
4. Repeat until the remainder is 0
5. The last non-zero remainder is the GCD

GCD(48, 18):
48 ÷ 18 = 2 remainder 12
18 ÷ 12 = 1 remainder 6
12 ÷ 6 = 2 remainder 0
GCD = 6

Common Fractions Table

Real-World Uses of Fractions

Cooking and Baking

Recipes are full of fractions — ¾ cup of sugar, ½ teaspoon of salt, ⅓ cup of oil. When you need to double a recipe or cut it in half, fraction arithmetic is essential. If a recipe calls for ¾ cup of flour and you are making 1½ batches, you need to multiply: ¾ × 3/2 = 9/8 = 1 ⅛ cups.

Construction and Woodworking

Measurements in construction rely heavily on fractions of an inch: ¼", ½", ¾", ⅜", 5/16". Carpenters constantly add and subtract these measurements. For example, if you cut 3 ¾" from a 7 ½" board, you have 3 ¾" remaining.

Music

Musical time signatures are fractions — 4/4 time, ¾ waltz, 6/8 jig. Note durations are fractional: a half note is ½ of a whole note, a quarter note is ¼, an eighth note is ⅛. Understanding fractions helps musicians read sheet music and understand rhythm.

Finance and Investing

Stock quotes often use fractions for pricing. Interest rates are expressed as fractions of a percent. When calculating returns, fractions help determine exact gains or losses. If your portfolio grows by ⅞ of a percent, knowing the decimal equivalent (0.875%) helps with precise calculations.

Science and Engineering

Chemists use fractions for molar ratios in chemical equations. Physicists use fractions for quantum mechanics calculations. Engineers use fractions for gear ratios, structural calculations, and tolerance specifications.

Health and Fitness

Nutrition labels use fractions for serving sizes. Body fat percentages, dosage calculations, and exercise intervals all involve fractional math. Understanding that ⅔ of your daily calories should come from specific macronutrients helps with meal planning.

Frequently Asked Questions

How do you add fractions with different denominators?

To add fractions with different denominators, find the Least Common Multiple (LCM) of the denominators first. Convert each fraction to an equivalent fraction with the LCM as the denominator, then add the numerators. For example, to add ⅓ + ¼, the LCM of 3 and 4 is 12. Convert ⅓ to 4/12 and ¼ to 3/12. Then add: 4/12 + 3/12 = 7/12.

How do you multiply fractions?

Multiplying fractions is straightforward: multiply the numerators together and multiply the denominators together. No common denominator is needed. For example, ⅔ × ⅘ = (2×4)/(3×5) = 8/15. Always simplify the result if possible by dividing both numbers by their greatest common divisor.

What is a mixed number?

A mixed number combines a whole number with a proper fraction, like 2 ¾ or 5 ⅓. It represents a value greater than 1. To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, 2 ¾ = (2×4+3)/4 = 11/4.

How do you convert a decimal to a fraction?

To convert a decimal to a fraction, count the number of decimal places and use that to determine the denominator (a power of 10). For example, 0.75 has two decimal places, so it becomes 75/100. Then simplify: GCD(75, 100) = 25, so 75/100 = ¾. For repeating decimals like 0.333..., the result is ⅓.

What is an improper fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator. Examples include 7/4, 10/3, and 5/5. Improper fractions are mathematically valid and often easier to work with in calculations. They can always be converted to mixed numbers: 7/4 = 1 ¾.

How do you simplify fractions?

To simplify a fraction, find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by that number. For example, to simplify 12/18: GCD(12, 18) = 6. Divide both by 6: 12÷6 = 2, 18÷6 = 3. The simplified fraction is ⅔. A fraction is in simplest form when the numerator and denominator have no common factors other than 1.

Can fractions be negative?

Yes, fractions can be negative. A fraction is negative when either the numerator or denominator is negative (but not both). For example, −⅔ and 2/−3 both represent negative two-thirds. When both numerator and denominator are negative, the fraction is positive: −2/−3 = ⅔.

What is the difference between a proper and improper fraction?

A proper fraction has a numerator smaller than its denominator (like ⅔ or ¾), and its value is always between 0 and 1. An improper fraction has a numerator greater than or equal to its denominator (like 5/3 or 7/4), and its value is 1 or greater. Both types are valid mathematical expressions, but improper fractions are often converted to mixed numbers for readability.

Why Use Our Fraction Calculator?

• 100% free — No hidden fees, subscriptions, or premium tiers
• Accurate results — Every calculation is mathematically precise
• Educational — Step-by-step explanations help you learn the math, not just get the answer
• Fast and easy — Enter your fractions and get instant results with no page reloads
• No installation needed — Works directly in your browser on any device
• Privacy focused — No data collection or tracking; your calculations stay on your device
• Works offline — Once loaded, the calculator works without an internet connection
• Multiple operations — One tool handles arithmetic, simplification, and conversion
• Mixed number support — Automatically converts improper fractions to mixed numbers
• Decimal equivalents — See the decimal form of every result alongside the fraction