Overview
This lecture introduces fractions, exploring their parts, visual representations, comparison, ordering, simplification, and the difference between mixed numbers and improper fractions.
Parts of a Fraction
- A fraction represents a part of a whole or a part of a set.
- Each fraction has a numerator (number of parts being considered) and a denominator (total number of equal parts in the whole).
- The horizontal line in a fraction can be read as "out of".
Visualizing Fractions
- If a pie is divided into 12 parts and two people eat 3 pieces each, they eat 6/12 or 1/2 of the pie.
- As the denominator increases, each part of the object gets smaller (e.g., 1/2 > 1/4 for the same whole).
Comparing and Ordering Fractions
- Fraction strips can help compare the sizes of different fractions.
- Two-thirds is greater than one-fourth.
- One-half is equal to two-fourths; these are called equivalent fractions.
- To order fractions: three-tenths < three-eighths < two-fifths < three-fourths.
Simplifying Fractions
- Reduce fractions by finding the greatest common factor (GCF) of the numerator and denominator.
- For 18/24, the GCF is 6; divide both parts by 6 to get 3/4.
Mixed Numbers and Improper Fractions
- A mixed number combines a whole number and a fraction (e.g., 2 3/5).
- An improper fraction has a numerator larger than its denominator (e.g., 3/2).
- Improper fractions can be converted to mixed numbers (3/2 = 1 1/2).
Key Terms & Definitions
- Numerator — the top number in a fraction; number of parts considered.
- Denominator — the bottom number in a fraction; total equal parts in the whole.
- Equivalent Fractions — different fractions that represent the same value.
- Greatest Common Factor (GCF) — the largest number that is a factor of both the numerator and the denominator.
- Mixed Number — a number with a whole number part and a fractional part.
- Improper Fraction — a fraction with a numerator greater than its denominator.
Action Items / Next Steps
- Practice simplifying fractions using the GCF.
- Use fraction strips or drawings to compare and order given fractions.