Fractions: Equivalent Fractions and Simplification

Objective:

Understand equivalent fractions and learn how to simplify fractions to their lowest terms.

Lesson Plan:

1. Equivalent Fractions

• Definition: Fractions that represent the same quantity but have different numerators and denominators.
• Example: 12=24=36\frac{1}{2} = \frac{2}{4} = \frac{3}{6}21​=42​=63​
• Visual representation with fraction bars or a number line.

1. Finding Equivalent Fractions

• Multiply or divide both the numerator and the denominator by the same number.
• Example: 23×22=46\frac{2}{3} \times \frac{2}{2} = \frac{4}{6}32​×22​=64​

1. Simplifying Fractions

• Definition: Reducing a fraction to its simplest form.
• Example: 1216=34\frac{12}{16} = \frac{3}{4}1612​=43​ (Divide by the greatest common divisor, GCD)
• Step-by-step method to simplify fractions.

1. Why Simplification is Important

• Easier to work with in calculations.
• Commonly used in real-life situations (recipes, measurements).

Practice Exercises:

1. Find three equivalent fractions for 35\frac{3}{5}53​.
2. Simplify the following fractions:

• 812\frac{8}{12}128​
• 1520\frac{15}{20}2015​
• 1824\frac{18}{24}2418​

1. Determine if 46\frac{4}{6}64​ and 23\frac{2}{3}32​ are equivalent fractions.

Conclusion:

Mastering equivalent fractions and simplification makes working with fractions easier and prepares you for operations with different denominators.