Lecture Notes: Fractions

Introduction to Division and Fractions

• Division Components: Dividend, Divisor, and Quotient.
• Whole Number Quotients: When the dividend is larger than the divisor, e.g., 15 divided by 5 equals 3.
• Fractional Quotients: When the divisor is larger than the dividend, resulting in a fraction.
  • Example: Representation of a pizza.
  • Pizza Example:
    • A pizza divided into 8 slices. Each slice = 1/8 of the pizza.
    • Eating 2 slices = 2/8, and so on, up to 8/8 for the whole pizza.

Equivalent Fractions and Simplification

• Equivalent Fractions: Fractions that represent the same value.
  • Example: Pizza cut into fourths - 1/4 slice = 2/8 slice.
  • Reduction: Simplifying 2/8 to 1/4 by dividing both numerator and denominator by 2.

Comparing Fractions

• Same Denominator: Easy to compare numerators.
• Different Denominators:
  • Example: Comparing 3/8 and 3/10.
    • Visualization: 3/8 covers more area than 3/10.
  • Methods of Comparison:
    • Convert to decimal notation.
    • Find the least common denominator.

Improper Fractions

• Definition: Fractions where the dividend is greater than the divisor, not resulting in a whole number.
  • Example: 4 divided by 3 = 4/3 (improper fraction).
  • Conversion: Improper fractions can be converted to mixed numbers, e.g., 4/3 = 1 1/3.

Practical Application: Ordering Pizzas

• Scenario: 10 friends each want 3 slices of pizza.
  • Calculation: 3 slices x 10 friends = 30 slices.
  • Fraction Representation: 30/8.
  • Whole Pizzas Needed:
    • 8/8 = 1 pizza, 16/8 = 2 pizzas, 24/8 = 3 pizzas.
    • Remaining slices = 6/8 = 3/4.
    • Total needed: 3 and 3/4 pizzas -> Order 4 pizzas.

Conversion Practice

• Converting Mixed Numbers to Improper Fractions:
  • Example: 4 and 3/8 pizzas = 35 slices.
    • Calculation: 4 whole pizzas x 8 slices each = 32 + 3 = 35 slices.

Summary

• Understanding how to manipulate, compare, and use fractions in practical situations is crucial.
• Converting between improper fractions and mixed numbers is a key skill.