How do you add fractions?

To add fractions, they must have the same denominator. Find the least common multiple (LCM) of the denominators, expand both fractions to that denominator, then add the numerators. Example: 1/4 + 2/3 = 3/12 + 8/12 = 11/12.

How do you multiply fractions?

When multiplying fractions, simply multiply numerator by numerator and denominator by denominator. Example: 2/3 × 3/5 = 6/15 = 2/5 (simplified). A common denominator is not needed.

What does simplifying fractions mean?

Simplifying means dividing numerator and denominator by their greatest common divisor (GCD). The fraction keeps its value but becomes simpler. Example: 12/18 ÷ 6 = 2/3. The GCD of 12 and 18 is 6.

How do you convert fractions to decimals?

Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. Some fractions result in repeating decimals, e.g., 1/3 = 0.333... (repeating 3).

What is a mixed number?

A mixed number consists of a whole number and a proper fraction, e.g., 2 3/4. It arises when the numerator is larger than the denominator (improper fraction): 11/4 = 2 3/4, because 11 ÷ 4 = 2 remainder 3.

How do you divide fractions?

To divide by a fraction, multiply by its reciprocal (numerator and denominator are swapped). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

What is the GCD (greatest common divisor)?

The GCD is the largest number that divides both numerator and denominator without remainder. It's used to simplify fractions. For 24 and 36, the GCD is 12, because 24 = 2×12 and 36 = 3×12.

What is the LCM (least common multiple)?

The LCM of two numbers is the smallest positive number divisible by both. It's used as the common denominator when adding and subtracting fractions. For 4 and 6, the LCM is 12.

How do you compare fractions?

Bring both fractions to the same denominator (LCM) and compare the numerators. The fraction with the larger numerator is greater. Alternatively, convert both to decimals and compare directly.

In which grade do students learn fractions?

In Germany, fraction arithmetic is typically introduced in 5th and 6th grade. Simple fractions and the concept of sharing are covered in elementary school, while formal fraction arithmetic with all operations follows in secondary school.

Fractions Explained — The Complete Guide 2026 | Fraction Calculator

Fractions Explained — Everything You Need to Know

Fraction arithmetic is one of the most important topics in mathematics and appears in daily life — from cooking to splitting a pizza to financial calculations. This guide explains everything from the basics to advanced concepts.

What Is a Fraction?

A fraction consists of two parts: the **numerator** (top) and the **denominator** (bottom), separated by a fraction bar. The numerator tells us how many parts we have, while the denominator tells us how many equal parts the whole was divided into. For example, 3/4 means: we have 3 out of 4 equal parts.

Types of Fractions

1. **Proper fraction:** The numerator is smaller than the denominator (e.g., 2/5). The value is between 0 and 1.

2. **Improper fraction:** The numerator is greater than or equal to the denominator (e.g., 7/3). The value is 1 or greater.

3. **Mixed number:** A whole number combined with a proper fraction (e.g., 2 1/3).

4. **Unit fraction:** A fraction with numerator 1 (e.g., 1/4, 1/7).

Expanding and Simplifying Fractions

When **expanding**, you multiply both numerator and denominator by the same number. The fraction's value doesn't change: 2/3 = 4/6 = 6/9. When **simplifying**, you divide both by the same divisor: 12/18 ÷ 6 = 2/3. The greatest common divisor (GCD) helps simplify completely.

The Four Basic Operations

**Addition and Subtraction:** Bring both fractions to the same denominator (least common multiple), then add or subtract the numerators. Example: 1/4 + 2/3 = 3/12 + 8/12 = 11/12.

**Multiplication:** Numerator times numerator, denominator times denominator. No common denominator needed! Example: 2/3 × 4/5 = 8/15.

**Division:** Multiply by the reciprocal. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

Common Mistakes to Avoid

The most common error: adding numerators and denominators separately (1/2 + 1/3 ≠ 2/5!). Remember: you can only add numerators directly when denominators are the same. Another mistake: forgetting to simplify the result.

Fractions in Everyday Life

Fractions appear everywhere: recipes (1/2 cup flour), discounts (1/4 off), probabilities (1/6 when rolling a die), time (3/4 hour = 45 minutes), and even in music (3/4 time signature).

Conclusion

With our fraction calculator, you can perform all these calculations instantly — including detailed step-by-step solutions. Perfect for learning, checking, and understanding!