Fraction Calculator

This fraction calculator performs all four basic operations with fractions and displays results in multiple formats. Whether you need to add, subtract, multiply, or divide fractions, this tool handles all calculations instantly and shows your answer as a simplified fraction, mixed number, decimal, and percentage.

Entering Fractions: Each fraction has two input boxes. Enter the numerator (the top number) in the upper box and the denominator (the bottom number) in the lower box. For example, to enter three-fourths, type 3 in the top box and 4 in the bottom box. The calculator accepts positive and negative whole numbers in both fields.

Selecting an Operation: Click one of the four operation buttons at the top of the calculator. The plus sign adds fractions together. The minus sign subtracts the second fraction from the first. The multiplication symbol finds the product of both fractions. The division symbol divides the first fraction by the second.

Reading Results: After clicking Calculate, view your answer in multiple formats. The large fraction display shows the exact result. Below that, find the simplified version, mixed number form, decimal equivalent, and percentage. The calculator automatically reduces fractions to lowest terms using the greatest common divisor.

Parts of a Fraction: Every fraction consists of two numbers separated by a horizontal line. The numerator sits above the line and represents how many parts you have. The denominator sits below the line and tells you how many equal parts make up one whole. In the fraction 3/4, the numerator 3 indicates three parts, while the denominator 4 means the whole was divided into four equal pieces.

Proper vs. Improper Fractions: A proper fraction has a numerator smaller than its denominator, such as 2/5 or 7/8. These fractions represent values less than one whole. An improper fraction has a numerator equal to or larger than its denominator, like 5/3 or 9/4. Improper fractions represent values of one or greater. Both types are mathematically valid and useful in different situations.

Mixed Numbers: A mixed number combines a whole number with a proper fraction, written like 2 1/2 or 3 3/4. To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the new numerator over the original denominator. For example, 11/4 equals 2 with remainder 3, giving you 2 3/4.

Equivalent Fractions: Different fractions can represent the same value. The fractions 1/2, 2/4, 3/6, and 50/100 all equal one-half. You create equivalent fractions by multiplying or dividing both the numerator and denominator by the same non-zero number. This principle is essential for adding fractions with different denominators.

Simplifying Fractions: A fraction is in simplest form when its numerator and denominator share no common factors other than 1. To simplify, find the greatest common divisor (GCD) of both numbers and divide each by it. The fraction 12/18 simplifies to 2/3 because the GCD of 12 and 18 is 6. Dividing both by 6 yields the reduced fraction.

Recipe Scaling: A cookie recipe calls for 3/4 cup of sugar, but you want to make half the batch. Multiply 3/4 by 1/2: the numerators (3 times 1) give 3, and the denominators (4 times 2) give 8. You need 3/8 cup of sugar. For doubling a recipe that uses 2/3 cup of flour, multiply 2/3 by 2/1 to get 4/3, or 1 1/3 cups.

Measurement Addition: You have two pieces of wood measuring 5/8 inch and 3/4 inch. To find the total length, convert 3/4 to 6/8 so both fractions have the same denominator. Add 5/8 plus 6/8 to get 11/8 inches, which equals 1 3/8 inches. This method works for any measurements needing combination.

Division Problems: If you have 3/4 pound of cheese and want to divide it equally among 3 people, divide 3/4 by 3/1. Flip 3/1 to get 1/3, then multiply: 3/4 times 1/3 equals 3/12, which simplifies to 1/4. Each person receives 1/4 pound of cheese.

Time Calculations: You spent 2/3 of an hour on homework and 1/2 hour on chores. To find total time, convert to sixths: 2/3 equals 4/6 and 1/2 equals 3/6. Adding gives 7/6 hours, or 1 1/6 hours, which is 1 hour and 10 minutes.

Finding Common Denominators Quickly: When adding or subtracting fractions, multiply the two denominators to get a common denominator that always works. For 1/4 plus 1/6, use 24 as the denominator. While this may not give the least common denominator, it guarantees a correct answer that you can simplify afterward. The LCD method produces smaller numbers but requires more thought.

Simplifying Shortcuts: Check if both numbers are even; if so, divide both by 2. If the digits of both numbers add up to multiples of 3, both are divisible by 3. Numbers ending in 0 or 5 are divisible by 5. For large fractions, factor each number into primes and cancel common factors before calculating.

Cooking Measurements: Memorize common cooking fraction equivalents. Two tablespoons equal 1/8 cup. Four tablespoons equal 1/4 cup. One cup equals 16 tablespoons. When halving recipes, 1/4 cup becomes 2 tablespoons (1/8 cup), and 1/3 cup becomes 2 tablespoons plus 2 teaspoons. A kitchen conversion chart saves time.

Mental Math Tricks: To multiply a whole number by a fraction, multiply the whole number by the numerator first, then divide by the denominator. For 12 times 3/4, compute 12 times 3 to get 36, then divide by 4 to get 9. This approach avoids converting the whole number to a fraction.

• Addition: Find a common denominator, convert both fractions, add the numerators, and keep the denominator
• Subtraction: Find a common denominator, convert both fractions, subtract the numerators, and keep the denominator
• Multiplication: Multiply the numerators together and multiply the denominators together
• Division: Flip the second fraction (reciprocal) and multiply

These formulas work for any fractions. For addition and subtraction, the result automatically has a common denominator. For division, multiplying by the reciprocal converts the division into multiplication. Always simplify your final answer by finding the greatest common divisor.

• 1/2 = 0.5 = 50%
• 1/3 = 0.333... = 33.33%
• 2/3 = 0.666... = 66.67%
• 1/4 = 0.25 = 25%
• 3/4 = 0.75 = 75%
• 1/5 = 0.2 = 20%
• 1/8 = 0.125 = 12.5%
• 3/8 = 0.375 = 37.5%