Fractions: the basics

In short: A fraction consists of a numerator (top) and a denominator (bottom) and describes part of a whole. Fractions can be reduced, expanded, added, multiplied and divided.

In more detail: The fraction 3/4 means three of four equal parts.

In detail

• Reducing: Divide numerator and denominator by the same number: 6/8 = 3/4.
• Expanding: Multiply both by the same number: 1/2 = 2/4.
• Adding and subtracting: Make denominators equal, then calculate numerators: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
• Multiplying: Numerator times numerator, denominator times denominator: 2/3 · 3/5 = 6/15 = 2/5.
• Dividing: Multiply by the reciprocal: 2/3 ÷ 4/5 = 2/3 · 5/4 = 5/6.
• Mixed numbers: 1 1/2 = 3/2.
• Decimal and percent: 3/4 = 0.75 = 75 %.
• Tip: Always reduce at the end (potenzen-und-wurzeln-einfach-erklaert).