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.

Converting Between Fractions and Decimals | Fraction Calculator

Converting Between Fractions and Decimals

Fractions and decimals are two ways to represent the same values. Converting between them is an important mathematical skill.

Fraction to Decimal

Divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. It's that simple! Some fractions produce **terminating** decimals (like 3/4 = 0.75), while others produce **repeating** decimals (like 1/3 = 0.333...).

When Does the Decimal Terminate?

A decimal terminates when the denominator (after simplifying) only contains the prime factors 2 and 5. Examples: 1/4 = 0.25 (4 = 2²), 3/8 = 0.375 (8 = 2³), 7/20 = 0.35 (20 = 2² × 5).

Repeating Decimals

When the simplified denominator contains prime factors other than 2 and 5, the decimal repeats: 1/3 = 0.333..., 1/7 = 0.142857142857..., 5/6 = 0.8333...

Decimal to Fraction

**Terminating decimal:** Count the decimal places. 0.75 has 2 places → 75/100 → simplify: 3/4.

**Repeating decimal:** 0.333... = x → 10x = 3.333... → 10x - x = 3 → 9x = 3 → x = 3/9 = 1/3.

Common Conversions

1/2 = 0.5 | 1/3 ≈ 0.333 | 1/4 = 0.25 | 1/5 = 0.2 | 1/6 ≈ 0.167 | 1/8 = 0.125 | 3/4 = 0.75 | 2/3 ≈ 0.667

Percentages

Fraction to percent: multiply the decimal by 100. So 3/4 = 0.75 = 75%. Our fraction calculator always shows you all three representations.