Overview
This lecture introduces fractions, exploring how they relate to division, equivalence, comparison, and conversion between improper fractions and mixed numbers.
Division and Fractions
- Division involves a dividend (number being divided), divisor (number dividing), and quotient (result).
- When the dividend is smaller than the divisor, the result is a fraction between zero and one.
- Fractions represent parts of a whole, often shown with examples like dividing a pizza.
Parts of a Fraction
- The top number (numerator) shows how many parts are considered.
- The bottom number (denominator) indicates how many equal parts make up a whole.
Equivalent Fractions
- Fractions like 2/8 and 1/4 are equivalent because they represent the same portion and can be simplified.
- Equivalent fractions are found by dividing or multiplying both numerator and denominator by the same number.
Comparing Fractions
- With the same denominator, the fraction with the larger numerator is greater.
- With different denominators, compare by visual models, decimal conversion, or finding a common denominator.
Improper Fractions and Mixed Numbers
- Improper fractions have numerators larger than denominators, e.g., 4/3.
- Improper fractions can be converted to mixed numbers, e.g., 4/3 is 1 and 1/3.
- Mixed numbers are useful for real-life situations like dividing pizzas among groups.
Converting Between Forms
- To convert an improper fraction to a mixed number, divide the numerator by the denominator and use the remainder as the new numerator.
- To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and write over the denominator.
Key Terms & Definitions
- Fraction — A number representing part of a whole, formed by dividing.
- Numerator — The top number in a fraction, showing how many parts are considered.
- Denominator — The bottom number, showing total parts of the whole.
- Equivalent fractions — Fractions that have the same value but different forms.
- Improper fraction — A fraction with a numerator greater than or equal to the denominator.
- Mixed number — A number made from a whole number and a fractional part.
Action Items / Next Steps
- Practice converting between improper fractions and mixed numbers.
- Prepare to learn about decimal notation and least common denominators in future lessons.