Fraction Calculator - Add, Subtract, Multiply, and Divide Fractions

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Fraction Calculator

Add, subtract, multiply, and divide fractions with step-by-step solutions and visualizations

Fraction Operations
Simplify Fractions
Fraction Conversion
Compare Fractions

Fraction Operations Calculator

Perform operations with fractions. Select an operation and enter the fractions.

Addition
Subtraction
Multiplication
Division

Fraction Calculation Results

1/2
+
1/4
=
3/4
3/4
Formula: (a/b) + (c/d) = (a*d + b*c)/(b*d)

Calculation Steps:

1. Identify the operation: Addition
2. Find common denominator: 2 × 4 = 8
3. Convert fractions: 1/2 = 4/8, 1/4 = 2/8
4. Add numerators: 4 + 2 = 6
5. Result: 6/8 = 3/4

Fraction Properties

Decimal: 0.75

Percentage: 75%

Related Calculations

Reciprocal: 4/3

Mixed Number: 0 3/4

Simplify Fractions Calculator

Simplify fractions to their lowest terms. Enter a fraction to simplify.

Simplification Results

6/8
3/4
3/4
Formula: GCD(6, 8) = 2, 6÷2/8÷2 = 3/4

Calculation Steps:

1. Find the greatest common divisor (GCD) of 6 and 8: 2
2. Divide numerator by GCD: 6 ÷ 2 = 3
3. Divide denominator by GCD: 8 ÷ 2 = 4
4. Simplified fraction: 3/4

Fraction Properties

Decimal: 0.75

Percentage: 75%

GCD Calculation

GCD: 2

Factors: 1, 2, 3, 6 and 1, 2, 4, 8

Fraction Conversion Calculator

Convert between fractions, decimals, percentages, and mixed numbers.

To Decimal
To Percentage
To Mixed Number
From Decimal

Conversion Results

5/4
1.25
1.25
Formula: 5 ÷ 4 = 1.25

Calculation Steps:

1. Divide numerator by denominator: 5 ÷ 4
2. Calculate: 4 goes into 5 one time (1 × 4 = 4)
3. Subtract: 5 - 4 = 1 (remainder)
4. Result: 1.25 or 1 1/4

Conversion Results

Decimal: 1.25

Percentage: 125%

Mixed Number

Mixed: 1 1/4

Reciprocal: 4/5

Compare Fractions Calculator

Compare two fractions to see which is larger or if they are equivalent.

Comparison Results

1/2
>
3/5
1/2 > 3/5
Formula: Cross multiply 1×5=5 and 3×2=6 → 5 < 6 → 1/2 < 3/5

Calculation Steps:

1. Find common denominator: 2 × 5 = 10
2. Convert fractions: 1/2 = 5/10, 3/5 = 6/10
3. Compare numerators: 5 < 6
4. Result: 1/2 < 3/5

Comparison Details

Difference: 1/10

Ratio: 5:6

Decimal Values

1/2 = 0.5

3/5 = 0.6

Understanding Fractions and Fraction Calculations

Fractions represent parts of a whole and are essential in mathematics, engineering, science, and everyday life. Fraction calculators help students, teachers, and professionals quickly solve fraction problems and verify manual calculations.

Key Fraction Concepts

Important concepts in fraction mathematics include:

  • Numerator and Denominator: The top and bottom parts of a fraction
  • Proper and Improper Fractions: Where numerator is less than or greater than denominator
  • Mixed Numbers: Whole numbers combined with fractions
  • Equivalent Fractions: Different fractions that represent the same value
  • Simplification: Reducing fractions to their simplest form

Common Fraction Operations

Some of the most commonly used fraction operations include:

  • Addition: a/b + c/d = (ad + bc)/bd
  • Subtraction: a/b - c/d = (ad - bc)/bd
  • Multiplication: a/b × c/d = ac/bd
  • Division: a/b ÷ c/d = a/b × d/c = ad/bc
  • Simplification: Dividing numerator and denominator by their GCD

Applications of Fractions

Fractions have practical applications in many fields:

  • Cooking and Baking: Measuring ingredients
  • Construction: Measuring lengths and materials
  • Finance: Calculating interest rates and proportions
  • Medicine: Dosage calculations
  • Sports: Statistics and performance metrics

Understanding fractions and having access to reliable calculation tools is essential for professionals and students in these fields.

Frequently Asked Questions About Fractions

What is a fraction?

A fraction represents a part of a whole. It consists of a numerator (top number) and a denominator (bottom number).

How do you add fractions with different denominators?

To add fractions with different denominators, first find a common denominator, convert the fractions, then add the numerators while keeping the common denominator.

What is an improper fraction?

An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as 5/4 or 7/7.

How do you simplify a fraction?

To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number.

What is the difference between a fraction and a decimal?

Fractions and decimals are different ways of representing the same value. A fraction shows a ratio between two numbers, while a decimal expresses the value in base-10 notation.

How do you convert a fraction to a percentage?

To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100.