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).

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.

Converting Mixed Numbers — Improper Fractions and Back | Fraction Calculator

Converting Mixed Numbers — Improper Fractions and Back

Mixed numbers and improper fractions are two ways to represent the same value. In this article, you'll learn to convert in both directions.

What Is a Mixed Number?

A mixed number consists of a whole number and a proper fraction: 2 3/4 means 'two wholes and three quarters'. The fractional part must be a proper fraction (numerator < denominator).

What Is an Improper Fraction?

An improper fraction has a numerator greater than or equal to the denominator: 11/4, 7/3, 5/5. Its value is always ≥ 1.

Mixed Number to Improper Fraction

**Formula:** Numerator = Whole number × Denominator + Numerator of the fractional part.

**Example:** 2 3/4 → Numerator = 2 × 4 + 3 = 11 → Result: 11/4.

**Another example:** 3 2/5 → Numerator = 3 × 5 + 2 = 17 → Result: 17/5.

Improper Fraction to Mixed Number

Divide the numerator by the denominator. The quotient becomes the whole number, the remainder becomes the new numerator.

**Example:** 11/4 → 11 ÷ 4 = 2 remainder 3 → Result: 2 3/4.

**Another example:** 23/6 → 23 ÷ 6 = 3 remainder 5 → Result: 3 5/6.

When to Use Which Form?

Mixed numbers are more intuitive in everyday life (2 1/2 liters of milk). Improper fractions are more practical for calculations since they can be directly used in formulas. Tip: Convert to improper fractions for calculations, then express the result as a mixed number.

Try It Out

In our calculator's 'Convert' tab, you can instantly convert mixed numbers — with a detailed step-by-step solution.