Lesson 25: Equivalent Fractions

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• Lesson Description
• Learning Objectives
• Topics Covered
• Key Terms
• Lesson Examples
• Practice Problems
• Tips & Common Mistakes
• Summary
• Challenge Problems
• Unit Navigation

Lesson Description

In this lesson, students will learn to recognize fractions that are equivalent, understand how multiplying or dividing numerator and denominator by the same number produces an equivalent fraction, and apply these skills to simplify and compare fractions.

Learning Objectives

• Understand the concept of equivalent fractions.
• Generate equivalent fractions using multiplication and division.
• Compare fractions by creating equivalent fractions with common denominators.

Topics Covered

• Definition of equivalent fractions
• Creating equivalent fractions by multiplying numerator and denominator
• Using equivalent fractions to compare and simplify

Key Terms

• Equivalent Fractions: Fractions that represent the same value or proportion, even if the numerator and denominator are different.
• Multiplying: Using multiplication to scale both numerator and denominator by the same number to create an equivalent fraction.
• Dividing: Using division to reduce both numerator and denominator by the same number to create an equivalent fraction.

Lesson Examples

Example 1: Creating an Equivalent Fraction

1. Start with the fraction 2/3.
2. Multiply both numerator and denominator by 2: 2×2 = 4, 3×2 = 6.
3. The equivalent fraction is 4/6.

Example 2: Reducing to an Equivalent Fraction

1. Start with the fraction 12/16.
2. Find the GCF of 12 and 16, which is 4.
3. Divide numerator and denominator by 4: 12 ÷ 4 = 3, 16 ÷ 4 = 4. The equivalent fraction is 3/4.

Practice Problems

1. Create an equivalent fraction for 3/5 by multiplying numerator and denominator by 3.
2. Reduce 18/24 to its simplest equivalent fraction.
3. Determine which fraction is greater: 2/3 or 4/6 using equivalent fractions.
4. Generate two equivalent fractions for 5/8.

Tips & Common Mistakes

• Always multiply or divide both numerator and denominator by the same number.
• Check that the resulting fraction is indeed equal in value to the original.
• Be careful not to reduce or multiply only the numerator or only the denominator.

Summary

Equivalent fractions are different fractions that represent the same value. Understanding how to create and recognize them is essential for simplifying, comparing, and performing operations with fractions.

Challenge Problems

1. Find three equivalent fractions for 7/9.
2. Reduce 36/48 and 45/60 to their simplest equivalent fractions and determine if they are equivalent to each other.
3. Create a real-world scenario where two different fractions are equivalent.