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Common Fractions Reference

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Understanding Fractions

A fraction represents a part of a whole. It consists of two numbers:

• Numerator (top number): How many parts you have
• Denominator (bottom number): How many equal parts the whole is divided into

For example, ¾ means you have 3 parts out of a whole that's divided into 4 equal parts.

Simplifying Fractions

A fraction is simplified (or in lowest terms) when the numerator and denominator have no common factors other than 1. To simplify:

1. Find the Greatest Common Divisor (GCD) of the numerator and denominator
2. Divide both numbers by the GCD

For example, 6/9: The GCD of 6 and 9 is 3. Dividing both by 3 gives us 2/3.

Converting Between Formats

• Fraction to Decimal: Divide the numerator by the denominator (3÷4 = 0.75)
• Fraction to Percentage: Multiply the decimal by 100 (0.75 × 100 = 75%)
• Decimal to Fraction: Write as a fraction over a power of 10, then simplify (0.75 = 75/100 = 3/4)

Real-World Fraction Examples

• Cooking: "Add ¾ cup of flour" — you need 3 out of 4 equal parts of a cup
• Time: "Quarter past the hour" — ¼ or 15 minutes of the 60-minute hour
• Sales: "½ off" — pay only half the original price
• Sports: "⅓ of the game remaining" — one third of total time left
• Construction: "⅝ inch screw" — a screw that's 5 eighths of an inch long