Learning Objectives
- Understand the concept of fractions and their representation
- Identify proper, improper, and mixed fractions
- Find equivalent fractions and simplest form
- Compare and order fractions
- Add and subtract fractions
Key Concepts
What Is a Fraction?
A fraction represents a part of a whole. It is written as a/b where a is the numerator (number of parts taken) and b is the denominator (total equal parts). For example, 3/4 means 3 parts out of 4 equal parts. Fractions can also represent a part of a collection.
Types of Fractions
Proper Fraction: The numerator is less than the denominator (e.g., 2/5, 3/7). Its value is always less than 1.
Improper Fraction: The numerator is greater than or equal to the denominator (e.g., 7/3, 5/5). Its value is 1 or more.
Mixed Fraction: A combination of a whole number and a proper fraction (e.g., 2 1/3). Every improper fraction can be written as a mixed fraction and vice versa.
Equivalent Fractions
Equivalent fractions represent the same value. To find an equivalent fraction, multiply or divide both the numerator and denominator by the same non-zero number. For example, 1/2 = 2/4 = 3/6 = 4/8. The simplest form of a fraction is when the numerator and denominator have no common factor other than 1.
Comparing Fractions
Like Fractions (same denominator): Compare the numerators. The fraction with the larger numerator is greater. Example: 5/7 > 3/7.
Unlike Fractions: Convert to like fractions by finding the LCM of the denominators, then compare the numerators.
Addition and Subtraction of Fractions
Like Fractions: Add or subtract the numerators and keep the denominator the same. Example: 3/8 + 2/8 = 5/8.
Unlike Fractions: Find the LCM of the denominators, convert both fractions, then add or subtract. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12.
Summary
Fractions represent parts of a whole or a collection. They come in three types: proper, improper, and mixed. Equivalent fractions have the same value but different numerators and denominators. To compare or add unlike fractions, we first convert them to like fractions using the LCM of the denominators.
Important Terms
- Numerator: The top number in a fraction (parts taken)
- Denominator: The bottom number in a fraction (total equal parts)
- Proper Fraction: Fraction where numerator < denominator
- Improper Fraction: Fraction where numerator ≥ denominator
- Mixed Fraction: A whole number combined with a proper fraction
- Equivalent Fractions: Fractions that represent the same value
- Like Fractions: Fractions with the same denominator
Quick Revision
- Fraction = Numerator / Denominator
- Proper fractions are always less than 1; improper fractions are 1 or greater
- To convert improper to mixed: divide numerator by denominator
- To convert mixed to improper: (whole × denominator + numerator) / denominator
- Equivalent fractions are obtained by multiplying or dividing top and bottom by the same number
- Always reduce fractions to their simplest form
- 1/2 > 1/3 > 1/4 — for unit fractions, larger denominator means smaller fraction