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Fraction Calculator

Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.

Fraction Calculator

Please enter valid fractions.

Fraction Result:

Click "Calculate" to see the result

Mixed Numbers Calculator

Please enter valid mixed numbers.

Mixed Numbers Result:

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Simplify Fractions Calculator

Please enter a valid fraction.

Simplified Fraction:

Click "Simplify" to see the result

Decimal to Fraction Calculator

Please enter a valid decimal number.

Decimal to Fraction Result:

Click "Convert" to see the result

Fraction to Decimal Calculator

Please enter a valid fraction.

Fraction to Decimal Result:

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Big Number Fraction Calculator

Use this calculator if the numerators or denominators are very big integers.

Please enter valid fractions.

Big Number Fraction Result:

Click "Calculate" to see the result

What is a Fraction?

A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters.

A common, vulgar, or simple fraction consists of a numerator displayed above a line (or before a slash) and a non-zero denominator displayed below (or after) that line. Numerators and denominators are also used in fractions that are not common, including compound fractions, complex fractions, and mixed numerals.

Numerator / Denominator

The numerator represents a number of equal parts, and the denominator indicates how many of those parts make up a unit or a whole. For example, in the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole.

Fraction Operations

Adding Fractions

To add fractions, the denominators must be the same. If they are not, find a common denominator and convert each fraction to an equivalent fraction with that denominator.

a/b + c/d = (a×d + c×b) / (b×d)
Example: 1/4 + 2/3 = (1×3 + 2×4) / (4×3) = (3 + 8) / 12 = 11/12

Subtracting Fractions

To subtract fractions, the denominators must be the same. If they are not, find a common denominator and convert each fraction to an equivalent fraction with that denominator.

a/b - c/d = (a×d - c×b) / (b×d)
Example: 2/3 - 1/4 = (2×4 - 1×3) / (3×4) = (8 - 3) / 12 = 5/12

Multiplying Fractions

To multiply fractions, multiply the numerators together and multiply the denominators together.

a/b × c/d = (a×c) / (b×d)
Example: 2/3 × 3/4 = (2×3) / (3×4) = 6/12 = 1/2

Dividing Fractions

To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Example: 2/3 ÷ 3/4 = 2/3 × 4/3 = (2×4) / (3×3) = 8/9

Simplifying Fractions

Simplifying (or reducing) fractions means making the fraction as simple as possible. A fraction is considered simplified if there are no common factors (other than 1) between the numerator and the denominator.

To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD).
Example: 8/12 = (8÷4) / (12÷4) = 2/3

The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder. For example, the GCD of 8 and 12 is 4.

Mixed Numbers

A mixed number is a whole number and a proper fraction combined. For example, 2 1/3 is a mixed number. It represents 2 + 1/3.

To convert a mixed number to an improper fraction:

a b/c = (a×c + b) / c
Example: 2 1/3 = (2×3 + 1) / 3 = 7/3

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 numerator of the fraction part.
Example: 7/3 = 2 with remainder 1, so 7/3 = 2 1/3

Converting Decimals to Fractions

To convert a decimal to a fraction, follow these steps:

  1. Write down the decimal divided by 1
  2. Multiply both top and bottom by 10 for every number after the decimal point
  3. Simplify (or reduce) the fraction
Example: Convert 0.75 to a fraction
0.75 = 0.75/1 = 75/100 = 3/4
Example: Convert 0.625 to a fraction
0.625 = 0.625/1 = 625/1000 = 5/8

Converting Fractions to Decimals

To convert a fraction to a decimal, simply divide the numerator by the denominator.

a/b = a ÷ b
Example: 3/4 = 3 ÷ 4 = 0.75
Example: 5/8 = 5 ÷ 8 = 0.625

Some fractions result in repeating decimals:

Example: 1/3 = 1 ÷ 3 = 0.333... (repeating)
Example: 2/7 = 2 ÷ 7 = 0.285714285714... (repeating)

Common Fraction Examples in Real Life

🍕 Pizza Fractions

If you have a pizza cut into 8 slices and you eat 3 slices:

Fraction eaten = 3/8
Fraction remaining = 5/8

📚 Test Scores

If you answered 15 out of 20 questions correctly on a test:

Fraction correct = 15/20 = 3/4
Percentage score = 75%

📏 Measurement

If you need to cut a board that is 3/4 feet long from a 6-foot board:

Fraction of board used = 3/4 ÷ 6 = 3/4 × 1/6 = 3/24 = 1/8

🍰 Recipe Scaling

If a recipe calls for 2/3 cup of flour and you want to make half the recipe:

Amount needed = 2/3 × 1/2 = 2/6 = 1/3 cup

💰 Financial Calculations

If you want to calculate 25% of $80:

25% = 25/100 = 1/4
1/4 of $80 = $80 × 1/4 = $20

Frequently Asked Questions About Fractions

What is the difference between a proper fraction and an improper fraction?

A proper fraction has a numerator that is smaller than the denominator (e.g., 3/4). An improper fraction has a numerator that is equal to or larger than the denominator (e.g., 5/4 or 4/4).

How do I add fractions with different denominators?

To add fractions with different denominators, first find a common denominator (usually the least common multiple of the denominators), convert both fractions to equivalent fractions with that denominator, then add the numerators.

What is a mixed number?

A mixed number combines a whole number and a proper fraction, such as 2 1/3. It represents the sum of the whole number and the fraction (2 + 1/3).

How do I simplify a fraction?

To simplify a fraction, divide both the numerator and denominator by their greatest common divisor (GCD). For example, to simplify 8/12, divide both 8 and 12 by 4 to get 2/3.

What is the reciprocal of a fraction?

The reciprocal of a fraction is created by swapping the numerator and denominator. For example, the reciprocal of 3/4 is 4/3.

How do I convert a fraction to a percentage?

To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. For example, 3/4 = 0.75 × 100 = 75%.

What are equivalent fractions?

Equivalent fractions are different fractions that represent the same value. For example, 1/2, 2/4, and 3/6 are all equivalent fractions.