Fraction Calculator
Add, subtract, multiply, and divide fractions. Automatically simplify results to lowest terms and see the decimal equivalent. Free online fraction calculator.
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What Are Fractions?
A fraction represents a part of a whole. It is written as numerator / denominator, where 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, 3/4 means you have 3 parts out of 4 equal parts. Fractions are a foundational concept in mathematics and appear everywhere from cooking recipes to construction measurements.
Proper fractions have a numerator smaller than the denominator (e.g., 3/4, 7/8) and represent values less than 1. Improper fractions have a numerator greater than or equal to the denominator (e.g., 7/4, 5/3) and represent values of 1 or more. Mixed numbers combine a whole number with a proper fraction (e.g., 1 3/4, 2 1/3). To convert a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, and place over the original denominator. For example, 2 1/3 = (2 × 3 + 1) / 3 = 7/3.
How to Add, Subtract, Multiply, and Divide Fractions
| Operation | Formula | Example | Step-by-Step |
|---|---|---|---|
| Addition | a/b + c/d = (a×d + c×b) / (b×d) | 1/2 + 1/3 = 5/6 | Common denominator 6: 3/6 + 2/6 = 5/6 |
| Subtraction | a/b - c/d = (a×d - c×b) / (b×d) | 3/4 - 1/4 = 1/2 | Same denominator: 3/4 - 1/4 = 2/4 = 1/2 |
| Multiplication | a/b × c/d = (a×c) / (b×d) | 2/3 × 3/4 = 1/2 | Multiply across: (2×3)/(3×4) = 6/12 = 1/2 |
| Division | a/b ÷ c/d = (a×d) / (b×c) | 1/2 ÷ 1/4 = 2 | Flip & multiply: 1/2 × 4/1 = 4/2 = 2 |
For addition and subtraction, you must first find a common denominator – a shared multiple of both denominators. The least common denominator (LCD) is the smallest number divisible by both. For multiplication, simply multiply numerators and denominators across. For division, take the reciprocal of the second fraction (flip it) and multiply.
How to Simplify Fractions Using the GCD Method
To simplify a fraction to its lowest terms, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. For example, to simplify 8/12: the GCD of 8 and 12 is 4. Divide both by 4: 8/4 = 2, 12/4 = 3, so 8/12 = 2/3. A fraction is in simplest form when the numerator and denominator share no common factors other than 1. You can also simplify step by step by dividing by common factors – for instance, 8/12 → divide by 2 = 4/6 → divide by 2 = 2/3.
Common Fraction, Decimal, and Percentage Conversions
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 2/3 | 0.667... | 66.67% |
| 3/4 | 0.75 | 75% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
To convert any fraction to a decimal, divide the numerator by the denominator. To convert a decimal to a percentage, multiply by 100 (or move the decimal point two places to the right). Try our Percentage Calculator for fast percentage conversions. Memorizing these common conversions speeds up mental math in cooking, shopping, and construction.
Real-World Uses of Fractions
- Cooking and Baking: Recipes use fractions for measurements – 1/2 cup flour, 3/4 teaspoon salt, 1/3 cup oil. Scaling recipes up or down requires multiplying and dividing fractions. Doubling a recipe that calls for 2/3 cup means calculating 2 × 2/3 = 4/3 = 1 1/3 cups.
- Construction and Carpentry: Tape measures display fractions of an inch (1/16, 1/8, 1/4, 1/2). Cutting lumber to precise lengths, calculating roof pitches, and measuring drywall all require fraction arithmetic. A 2x4 cut to 57 3/4 inches must be measured with fraction precision.
- Mathematics and Education: Fractions are the gateway to algebra, ratios, proportions, decimals, percentages, and probability. Students must master fraction operations before advancing to more complex math topics like linear equations and geometry.
- Finance and Shopping: Interest rates are often fractional (e.g., 3.5% APR = 7/200). Discounts like "1/3 off" require calculating a fraction of the original price. Stock splits (e.g., a 3-for-2 split) involve fractional share calculations.
FAQ
Find a common denominator – the least common multiple of the two denominators. Convert each fraction to an equivalent fraction with that denominator, then add the numerators. For example, 1/3 + 1/4: LCM of 3 and 4 is 12. 1/3 = 4/12, 1/4 = 3/12, so 4/12 + 3/12 = 7/12. Simplify the result if possible. This method works for any number of fractions.
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number. For example, 8/12 simplifies to 2/3 because the GCD of 8 and 12 is 4. If you are not sure of the GCD, simplify step by step: divide by 2 to get 4/6, then divide by 2 again to get 2/3. A fraction is fully simplified when the numerator and denominator share no common factors other than 1.
A proper fraction has a numerator smaller than the denominator (e.g., 3/4, 7/8) and represents a value less than 1. An improper fraction has a numerator greater than or equal to the denominator (e.g., 7/4, 5/3) and represents a value of 1 or more. Improper fractions are often converted to mixed numbers (e.g., 7/4 = 1 3/4) for easier interpretation, but improper fractions are usually easier to work with in calculations.
Divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75. Some fractions produce repeating decimals (like 1/3 = 0.333...), which are typically rounded to 2-4 decimal places for practical use. To convert a decimal back to a fraction, write the decimal over its place value (e.g., 0.75 = 75/100) and simplify.
To multiply fractions, multiply the numerators together and the denominators together: a/b × c/d = (a×c)/(b×d). Simplify if possible. To divide fractions, flip the second fraction upside down (take its reciprocal) and then multiply: a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). For example, 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. No common denominator is needed for multiplication or division.
You cannot directly add 1/2 and 1/3 because halves and thirds are different-sized pieces. A common denominator converts both fractions to the same-sized parts, making addition valid. Think of it like adding inches and centimeters – you must convert to the same unit first. The common denominator is that shared unit. For 1/2 and 1/3, converting to sixths gives 3/6 + 2/6 = 5/6, which is correct.
Free Online Calculators
Common Fraction Conversions
| Fraction | Decimal | Percent |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333 | 33.3% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 2/3 | 0.667 | 66.7% |
| 3/4 | 0.75 | 75% |
| 1/8 | 0.125 | 12.5% |
Fraction Tips
- Always simplify your final fraction to lowest terms.
- To add or subtract, first find a common denominator.
- Multiply across: multiply the numerators and multiply the denominators.
- To divide, flip the second fraction and multiply (reciprocal).
- Convert mixed numbers to improper fractions before calculating.
