Numeracy

Basics of Fractions




Fractions are essential in everyday life, whether for dividing a pizza, measuring ingredients, or splitting a bill. Here's everything you need to know about fractions, from basic concepts to advanced operations:

What Are Fractions?

  • Definition: Fractions express parts of a whole and are written as one number over another (e.g., ½).
  • Uses: Measuring time, splitting bills, calculating discounts, and more.

Key Terms and Rules

  1. Numerator: The top number.
  2. Denominator: The bottom number.

Types of Fractions:
- Proper Fractions: Numerator < Denominator (e.g., ¾).
- Improper Fractions: Numerator > Denominator (e.g., 5/4). Convert these into a mixed number (e.g., 5/4 = 1¼).
- Simplified Fractions: Always reduce fractions to their smallest whole numbers (e.g., 2/8 = ¼).

Reduction Rule:
Divide the numerator and denominator by their greatest common factor.

Adding and Subtracting Fractions?

  • Same Denominator: Add or subtract the numerators directly.

  • Example: + =?? = 1.

  • Different Denominators:

  • Find the Lowest Common Denominator (LCD).
  • Adjust numerators accordingly.
  • Example: ¾ + LCD = 20 ¹???? +??? = ²³???.

Multiplying Fractions?

  • Multiply the numerators together and denominators together.
  • Simplify the result.
  • Example: × ¾ = ²???.

Dividing Fractions

  • Flip the second fraction (reciprocal) and multiply.
  • Example: ÷ ¾ ×?? = ¹²???.

Practical Applications

  1. Ratios: A ratio of 1:5 is equivalent to 1/5 or 0.2.
  2. Betting Odds: Odds like 2:1 mean you win $2 for every $1 staked.

Why Learn Fractions?

Fractions are not just math concepts—they’re practical tools for:
- Budgeting: Calculating portions of income.
- Cooking: Scaling recipes.
- Shopping: Understanding discounts.
- Health: Calculating BMI.

Mastering fractions can simplify many daily tasks and help make informed decisions!

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