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.

Adding and Subtracting Fractions — Step by Step | Fraction Calculator

Adding and Subtracting Fractions — Step by Step

Adding and subtracting fractions is fundamental to fraction arithmetic. The key to success is the **common denominator**.

The Basic Rule

Fractions can only be added or subtracted when they have the **same denominator**. If they don't, we must first expand the fractions.

Step-by-Step Guide

1. **Find a common denominator:** Calculate the least common multiple (LCM) of the denominators. For 1/4 + 2/3, the LCM of 4 and 3 is 12.

2. **Expand the fractions:** Multiply numerator and denominator of each fraction so the denominator equals the LCM. 1/4 = 3/12 (times 3) and 2/3 = 8/12 (times 4).

3. **Calculate the numerators:** Add (or subtract) the numerators. 3/12 + 8/12 = 11/12.

4. **Simplify:** Check whether the result can be simplified.

Examples

**Addition:** 2/5 + 1/3 → LCM(5,3) = 15 → 6/15 + 5/15 = 11/15

**Subtraction:** 5/6 - 1/4 → LCM(6,4) = 12 → 10/12 - 3/12 = 7/12

**With mixed numbers:** 2 1/3 + 1 2/5 → 7/3 + 7/5 → LCM(3,5) = 15 → 35/15 + 21/15 = 56/15 = 3 11/15

Special Cases

With identical denominators, it's especially simple: 3/7 + 2/7 = 5/7. When one denominator is a multiple of the other, only one fraction needs expanding: 1/4 + 3/8 = 2/8 + 3/8 = 5/8.

Tip

Use our fraction calculator to check your results. The detailed step-by-step solution shows you every single step!