Fraction Calculator
An all-in-one tool designed to simplify complex fraction operations. Perfect for students, teachers, and professionals needing quick and accurate fraction calculations.
Mixed Numbers Calculator
Result:
-
Simplify Fractions Calculator
Simplified Fraction:
-
Decimal to Fraction Calculator
Fraction Result:
-
Fraction to Decimal Calculator
Decimal Result:
-
Fraction Calculation Guide
Understanding Fractions
Fractions represent parts of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction 3/4, 3 is the numerator and 4 is the denominator.
Fractions can represent values less than 1 (proper fractions), equal to 1 (such as 4/4), or greater than 1 (improper fractions like 5/4).
Mixed Numbers
A mixed number combines a whole number and a proper fraction. For example, 2 1/3 is a mixed number where 2 is the whole number and 1/3 is the fraction.
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 2 1/3: (2 × 3) + 1 = 7, so it becomes 7/3.
Fraction Operations
Addition & Subtraction
To add or subtract fractions, ensure they have a common denominator. Then add or subtract the numerators while keeping the denominator the same. For different denominators, find a common denominator before proceeding.
Multiplication
Multiply the numerators together and the denominators together. Simplify the resulting fraction if possible. For example: (2/3) × (4/5) = (2 × 4) / (3 × 5) = 8/15.
Division
To divide fractions, multiply the first fraction by the reciprocal of the second. Simplify the result. For example: (2/3) ÷ (4/5) = (2/3) × (5/4) = (2 × 5) / (3 × 4) = 10/12 = 5/6.
Simplification
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by this number. For example, 12/18 simplifies to 2/3 because the GCD of 12 and 18 is 6.
Real-World Applications
Fractions are used in various real-life scenarios, including cooking, construction, finance, and science. Understanding how to work with fractions is essential for accurate measurements, calculations, and problem-solving.
- Cooking: Adjusting recipe quantities based on the number of servings.
- Construction: Measuring materials, cutting lengths, and calculating dimensions.
- Finance: Calculating interest rates, proportions, and investment returns.
- Science: Measuring chemical compounds, analyzing data, and understanding ratios.