Lecture Notes on Fractions

Introduction to Fractions

• Fractions arise when the divisor is larger than the dividend during division.
• A fraction represents a part of a whole.
• Example: Pizza divided into slices.
  • A whole pizza can be divided into 8 slices, each slice is 1/8 of the pizza.
  • If pizza is divided into 4 slices, each slice is 1/4 of the pizza.
  • 2/8 is equivalent to 1/4, showing fraction equivalence by reducing.

Fraction Components

• Numerator: Top part of the fraction.
• Denominator: Bottom part of the fraction.

Comparing Fractions

• Same denominator: Compare numerators directly.
• Different denominators: Convert to common terms or use visual aids.
  • Example: Comparing 3/8 and 3/10, shading circles to compare.
  • 3/8 is greater because it covers more area than 3/10.

Improper Fractions

• Occur when the dividend is greater than the divisor, but results are not whole numbers.
  • Example: 4/3 is an improper fraction.
  • Improper fractions can be written as mixed numbers (e.g., 4/3 as 1 1/3).

Practical Application: Ordering Pizzas

• Calculate needed slices for a group.
  • Example: 10 friends want 3 slices each = 30 slices total.
  • One pizza = 8 slices; 30 slices = 3 6/8 pizzas, which reduces to 3 3/4 pizzas.
  • Need to order 4 pizzas to cover the requirement (32 slices).

Conversion Between Improper Fractions and Mixed Numbers

• Improper fractions can be converted to mixed numbers and vice versa.
  • Example: 4 3/8 pizzas = 35 slices.

Conclusion

• Understanding fractions is crucial for both mathematical calculations and practical applications like ordering food.
• Practice converting between improper fractions and mixed numbers for better comprehension.