Fraction Calculator

How to Calculate Fractions

A fraction is a number that represents a part of a whole, written as one number over another separated by a line: numerator / denominator. The numerator (top number) tells how many parts you have, and the denominator (bottom number) tells how many equal parts the whole is divided into.

Our calculator above handles addition, subtraction, multiplication, and division of fractions — including proper fractions, improper fractions, and mixed numbers. It shows the complete step-by-step solution so you can follow along and learn the process.

Below you'll find detailed guides for each operation, complete with formulas and worked examples.

How to Add & Subtract Fractions

Adding and subtracting fractions is different from adding whole numbers because the fractions must have the same denominator before you can combine them. You can use the following formula to add two fractions:

a/b + c/d = (a×d + b×c) / (b×d)

This formula works by cross-multiplying to create a common denominator. After applying it, you simplify the result. Here are the three steps in detail:

Step One: Convert to Fractions with a Common Denominator

When adding or subtracting fractions with different denominators, you first need to find the Least Common Denominator (LCD) — the smallest number that both denominators divide into evenly. The LCD is the same as the Least Common Multiple (LCM) of the denominators.

Once you have the LCD, convert each fraction to an equivalent fraction with the LCD as the denominator. To do this, divide the LCD by each fraction's denominator, then multiply both the numerator and denominator by that result.

Example: Add 1/3 + 1/4.

• LCD of 3 and 4 = 12
• 1/3 = (1 × 4) / (3 × 4) = 4/12
• 1/4 = (1 × 3) / (4 × 3) = 3/12

Step Two: Add or Subtract the Numerators

Once both fractions have the same denominator, simply add (or subtract) the numerators and keep the denominator the same.

Continuing the example:

4/12 + 3/12 = (4 + 3) / 12 = 7/12

Step Three: Simplify the Fraction

The final step is to simplify the result. Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it.

In our example, 7/12 is already in its simplest form because GCD(7, 12) = 1. The answer is 7/12 ≈ 0.5833.

How to Multiply Fractions

Multiplying fractions is simpler than adding them — no common denominator needed. Use this formula:

a/b × c/d = (a × c) / (b × d)

Simply multiply the numerators together and multiply the denominators together, then simplify the result.

Step One: Multiply the Numerators and Denominators

Multiply the top numbers together to get the new numerator. Multiply the bottom numbers together to get the new denominator.

Example: Multiply 2/3 × 3/4.

2/3 × 3/4 = (2 × 3) / (3 × 4) = 6/12

Step Two: Simplify the Fraction

Find the GCD of the numerator and denominator, then divide both by it.

GCD(6, 12) = 6. So: 6/12 = (6 ÷ 6) / (12 ÷ 6) = 1/2.

How to Divide Fractions

To divide fractions, use the "keep, change, flip" method — also called multiplying by the reciprocal:

1. Keep the first fraction as it is.
2. Change the division sign (÷) to multiplication (×).
3. Flip the second fraction (swap its numerator and denominator to get the reciprocal).

The formula is: a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)

Step One: Multiply by the Reciprocal

Example: Divide 2/3 ÷ 3/4.

Flip the second fraction: 3/4 → 4/3

Now multiply: 2/3 × 4/3 = (2 × 4) / (3 × 3) = 8/9

Step Two: Simplify the Fraction

GCD(8, 9) = 1, so 8/9 is already in simplest form. The answer is 8/9 ≈ 0.8889.

How to Calculate Mixed Numbers

A mixed number combines a whole number and a proper fraction, like 2 3/5. To perform arithmetic with mixed numbers, the first step is to convert them to improper fractions:

1. Multiply the whole number by the denominator.
2. Add the result to the numerator.
3. Keep the same denominator.

Example: Convert 2 3/5 to an improper fraction.

• 2 × 5 = 10
• 10 + 3 = 13
• 2 3/5 = 13/5

Once you have improper fractions, use any of the formulas above (add, subtract, multiply, or divide) as normal. After calculating, you can convert the result back to a mixed number by dividing the numerator by the denominator — the quotient is the whole number, and the remainder over the denominator is the fraction part.

How to Calculate Negative Fractions

A negative fraction has a minus sign in front. The negative sign can be placed in front of the entire fraction, in front of the numerator, or in front of the denominator — all three are equivalent:

−a/b = (−a)/b = a/(−b)

When both the numerator and denominator are negative, the fraction is actually positive, because a negative divided by a negative is positive.

Key rules for negative fractions:

• Positive × Negative = Negative (e.g., 1/2 × −1/3 = −1/6)
• Negative × Negative = Positive (e.g., −2/3 × −3/4 = 6/12 = 1/2)
• The same rules apply for division — it follows the sign rules of multiplication.
• For addition and subtraction, attach the negative sign to the numerator and follow the standard steps.

Types of Fractions

There are three main types of fractions:

• Proper fractions: The numerator is smaller than the denominator (e.g., 3/4, 2/7). The value is always less than 1.
• Improper fractions: The numerator is equal to or greater than the denominator (e.g., 7/4, 5/3). The value is 1 or greater.
• Mixed numbers: A whole number combined with a proper fraction (e.g., 1 3/4, 2 1/3). Every mixed number can be converted to an improper fraction and vice versa.

Frequently Asked Questions

What are the 3 types of fractions?

The three types are proper fractions (numerator < denominator, like 3/4), improper fractions (numerator ≥ denominator, like 7/4), and mixed numbers (a whole number plus a proper fraction, like 1 3/4). You can convert between improper fractions and mixed numbers: 7/4 = 1 3/4.

What is the golden rule of fractions?

The golden rule is: always find a common denominator before adding or subtracting fractions. This is done by finding the Least Common Multiple (LCM) of the denominators. Without a common denominator, you cannot directly combine fractions — this is the single most important rule in fraction arithmetic.

How do I simplify a fraction?

Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. For example: 18/24 → GCD(18, 24) = 6 → 18/24 = 3/4. If the GCD is 1, the fraction is already in simplest form.

How do I convert a fraction to a decimal?

Divide the numerator by the denominator. For example, 3/8 = 3 ÷ 8 = 0.375. Use our Long Division Calculator to see the full division steps. To convert a fraction to a percentage, multiply the decimal by 100: 3/8 = 0.375 = 37.5%.

Why do we use fractions instead of decimals?

Fractions are exact — they can represent values like 1/3 precisely, while the decimal 0.333... goes on forever. Fractions are essential in cooking (1/2 cup), construction (3/4 inch), music (time signatures like 3/4), probability, and algebra. Many mathematical operations are simpler with fractions than with decimals.