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.

Multiplying and Dividing Fractions — Reciprocals Made Easy | Fraction Calculator

Multiplying and Dividing Fractions — Reciprocals Made Easy

Multiplying and dividing fractions follow simple rules — simpler than addition and subtraction since no common denominator is needed!

Multiplying Fractions

Rule: Numerator times numerator, denominator times denominator.

Example:

\frac{2}{3} \cdot \frac{4}{5} = \frac{2 \cdot 4}{3 \cdot 5} = \frac{8}{15}

Tip: You can cross-cancel before multiplying: with 3/4 × 2/9, cancel the 3 and 9 (by 3) and the 2 and 4 (by 2): 1/2 × 1/3 = 1/6.

Multiplying a Fraction by a Whole Number

Write the whole number as a fraction with denominator 1: 3/4 × 5 = 3/4 × 5/1 = 15/4 = 3 3/4.

What Is the Reciprocal?

The reciprocal of a fraction is created by swapping numerator and denominator. The reciprocal of 3/4 is 4/3. The reciprocal of 5 (= 5/1) is 1/5. Important: 0 has no reciprocal!

Dividing Fractions

Rule: Multiply by the reciprocal of the second fraction.

Example:

\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \cdot \frac{5}{4} = \frac{10}{12} = \frac{5}{6}

Why does this work? Division is the inverse operation of multiplication. 'Dividing by 4/5' is the same as 'multiplying by 5/4'.

Common Mistakes

Forgetting to take the reciprocal when dividing.
Flipping both fractions instead of just the second one.
Not simplifying the result.

Multiplying/Dividing Mixed Numbers

Convert mixed numbers to improper fractions first:

1\tfrac{1}{2} \cdot 2\tfrac{1}{3} = \frac{3}{2} \cdot \frac{7}{3} = \frac{21}{6} = \frac{7}{2} = 3\tfrac{1}{2}

Our Fraction Calculator

In the 'Basic Operations' tab, you can calculate multiplication and division instantly. Switch between +, -, × and ÷ with one click!

Multiplying and Dividing Fractions — Reciprocals Made Easy

Multiplying and Dividing Fractions — Reciprocals Made Easy

Multiplying Fractions

Multiplying a Fraction by a Whole Number

What Is the Reciprocal?

Dividing Fractions

Common Mistakes

Multiplying/Dividing Mixed Numbers

Our Fraction Calculator

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