Fraction Calculator — Free Online Fraction Calculator

How to Use the Fraction Calculator

1. Choose the operation: Use the dropdown at the top to select from five fraction operations: Add, Subtract, Multiply, Divide, or Simplify. Each mode adjusts the interface to show only the inputs you need. For simplification, the second fraction inputs automatically disappear since only one fraction is required.
2. Enter the first fraction: Type the numerator (top number) and denominator (bottom number) of your first fraction into the labeled fields. You can use whole numbers, negative numbers, or zero. The denominator must be non-zero for a valid fraction. The calculator accepts any integer values and handles the arithmetic precisely.
3. Enter the second fraction: For addition, subtraction, multiplication, or division, enter the second fraction's numerator and denominator. Make sure the denominator is not zero. For division, the second fraction's numerator also cannot be zero since you cannot divide by zero.
4. Read the result: The result panel instantly shows your answer as a fully simplified fraction, the decimal equivalent rounded to four decimal places, and the complete formula that was used. All results are automatically reduced to their lowest terms using the greatest common divisor.

The calculator updates in real time as you type, so there is no need to press a submit button. Switch between operations freely to perform different fraction calculations on the same pair of fractions.

Fraction Formulas and Step-by-Step Examples

Variables Explained

• a: The numerator (top number) of the first fraction. This represents the number of parts you have out of the total number of equal parts.
• b: The denominator (bottom number) of the first fraction. This tells you how many equal parts the whole is divided into and must not be zero.
• c: The numerator of the second fraction. Used in addition, subtraction, multiplication, and division operations as the second operand.
• d: The denominator of the second fraction. Like the first denominator, it must be non-zero. For division, the numerator c must also be non-zero.
• GCD: The Greatest Common Divisor of the numerator and denominator. This is the largest positive integer that divides both numbers evenly and is used to simplify the fraction to its lowest terms.

Step-by-Step Example

Add 3/8 + 5/12:

1. Identify the fractions: a/b = 3/8 and c/d = 5/12
2. Cross-multiply for the numerator: (3 x 12) + (5 x 8) = 36 + 40 = 76
3. Multiply the denominators: 8 x 12 = 96
4. Form the unsimplified fraction: 76/96
5. Find the GCD of 76 and 96: GCD = 4
6. Simplify: 76/4 = 19, 96/4 = 24, so the result is 19/24

The decimal equivalent of 19/24 is approximately 0.7917. This cross-multiplication method works for any two fractions regardless of whether they share a common denominator.

Practical Examples

Example 1: Amanda's Recipe Adjustment

Amanda is baking cookies and her recipe calls for 3/4 cup of sugar and 1/3 cup of brown sugar. She needs to know the total amount of sugar required. Using the fraction calculator in Add mode with 3/4 + 1/3:

• Cross-multiply numerators: (3 x 3) + (1 x 4) = 9 + 4 = 13
• Multiply denominators: 4 x 3 = 12
• Result: 13/12 (or 1 and 1/12 cups total)
• Decimal: approximately 1.0833 cups

Amanda now knows she needs a little more than one full cup of sugar combined. Since 1/12 of a cup is a small amount, she could round to 1 cup plus 1 tablespoon (since 1 tablespoon is roughly 1/16 of a cup, close enough for baking).

Example 2: Kevin's Woodworking Project

Kevin is cutting a board that is 7/8 of an inch thick. He needs to remove 3/16 of an inch to fit it into a groove. He uses the Subtract mode with 7/8 - 3/16:

• Cross-multiply: (7 x 16) - (3 x 8) = 112 - 24 = 88
• Multiply denominators: 8 x 16 = 128
• Unsimplified: 88/128
• GCD of 88 and 128 is 8, so simplified result: 11/16 inch

Kevin now knows the board should be 11/16 of an inch thick after planing. This is a standard measurement on most rulers and tape measures, making it easy to verify with a caliper.

Example 3: Sophie's Fabric Division

Sophie has 5/6 of a yard of fabric and needs to divide it equally among 4 projects. She divides 5/6 by 4 (which is 4/1) using the Divide mode:

• Flip the divisor: 4/1 becomes 1/4
• Multiply: (5 x 1) / (6 x 4) = 5/24
• Result: 5/24 of a yard per project
• Decimal: approximately 0.2083 yards (about 7.5 inches)

Each project gets 5/24 of a yard, which equals about 7.5 inches of fabric. Sophie can use a measuring tape marked in fractions to cut each piece accurately.

Example 4: David's Medication Dosage

David takes 2/3 of a tablet in the morning and 1/2 of a tablet at night. He wants to know the total daily dosage. Using Add mode with 2/3 + 1/2:

• Cross-multiply: (2 x 2) + (1 x 3) = 4 + 3 = 7
• Multiply denominators: 3 x 2 = 6
• Result: 7/6 tablets per day (1 and 1/6 tablets)

David takes a total of 7/6 or approximately 1.1667 tablets per day. This information helps him plan how quickly he will go through a prescription and when to request a refill from his pharmacy.

Fraction Equivalents Reference Table

Tips and Complete Guide

Understanding Fraction Types

Fractions come in several forms. A proper fraction has a numerator smaller than its denominator (e.g., 3/7), meaning the value is less than 1. An improper fraction has a numerator equal to or larger than its denominator (e.g., 9/4), meaning the value is 1 or greater. A mixed number combines a whole number with a proper fraction (e.g., 2 and 1/4). All three forms can represent the same value: 9/4 = 2 and 1/4 = 2.25. When performing arithmetic, improper fractions are generally easier to work with than mixed numbers.

Finding the Least Common Denominator

When adding or subtracting fractions by hand, finding the least common denominator (LCD) is often more efficient than cross-multiplication. The LCD is the smallest number that both denominators divide into evenly. For example, to add 5/6 + 3/8, the LCD of 6 and 8 is 24 (not 48, which is what cross-multiplication would give). Convert: 5/6 = 20/24 and 3/8 = 9/24, then add: 20/24 + 9/24 = 29/24. Using the LCD keeps numbers smaller and reduces the need for simplification afterward.

Fractions in Everyday Life

Fractions appear constantly in daily activities. Cooking recipes use fractions for measurements (3/4 cup, 1/2 teaspoon). Construction and woodworking rely on fractional inches (5/16 inch drill bit). Music theory uses fractions for time signatures and note durations (a quarter note is 1/4 of a whole note). Financial splits divide bills and shares into fractions. Even telling time involves fractions: "quarter past" means 1/4 of an hour, and "half past" means 1/2 of an hour. Our percentage calculator can help convert fractions to percentages for additional context.

Cross-Cancellation for Faster Multiplication

When multiplying fractions, you can simplify before multiplying by canceling common factors between any numerator and any denominator. For example, to multiply 4/9 x 3/8: instead of getting 12/72 and then simplifying, notice that 4 and 8 share a factor of 4 (4/4 = 1, 8/4 = 2), and 3 and 9 share a factor of 3 (3/3 = 1, 9/3 = 3). After cross-cancellation: 1/3 x 1/2 = 1/6. This technique keeps numbers small and avoids large intermediate products, making mental math much easier.

Common Mistakes to Avoid

• Adding numerators and denominators separately: 1/4 + 1/3 does not equal 2/7. You must find a common denominator first. The correct answer is 3/12 + 4/12 = 7/12.
• Forgetting to simplify: After performing an operation, always check if the result can be reduced. For example, 6/8 should be simplified to 3/4 by dividing both by the GCD of 2.
• Dividing without flipping: When dividing fractions, you must multiply by the reciprocal of the divisor. 2/3 divided by 4/5 is 2/3 x 5/4, not 2/3 x 4/5.
• Ignoring negative signs: When subtracting, keep track of negative signs carefully. A negative numerator with a negative denominator produces a positive fraction, not a negative one.
• Using zero as a denominator: A fraction with a denominator of zero is undefined. Always check that your denominators are non-zero before computing. Our calculator catches this error automatically.

Frequently Asked Questions