Lesson 28: Adding & Subtracting 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

This lesson guides students through adding and subtracting fractions with like and unlike denominators, including visual aids and practice problems for mastery.

Learning Objectives

• Add fractions with the same denominator.
• Subtract fractions with the same denominator.
• Add and subtract fractions with unlike denominators using least common denominators (LCD).
• Simplify the resulting fractions.

Topics Covered

• Review of fraction parts (numerator & denominator)
• Adding fractions with like denominators
• Subtracting fractions with like denominators
• Finding least common denominators for unlike fractions
• Adding and subtracting fractions with unlike denominators
• Simplifying final results

Key Terms

• Fraction: A number that represents a part of a whole.
• Denominator: The bottom number of a fraction, representing the total number of equal parts.
• Numerator: The top number of a fraction, representing the number of selected parts.
• Least Common Denominator (LCD): The smallest number that is a multiple of both denominators.

Lesson Examples

Example 1: Adding Fractions with Like Denominators

1. Calculate 3/8 + 2/8.
2. Keep the denominator the same: 8.
3. Add the numerators: 3 + 2 = 5.
4. Result: 5/8.

Example 2: Subtracting Fractions with Like Denominators

1. Calculate 7/10 - 3/10.
2. Keep the denominator the same: 10.
3. Subtract the numerators: 7 - 3 = 4.
4. Result: 4/10 (simplify to 2/5).

Example 3: Adding Fractions with Unlike Denominators

1. Calculate 1/3 + 1/4.
2. Find LCD of 3 and 4 → 12.
3. Convert fractions: 1/3 = 4/12, 1/4 = 3/12.
4. Add numerators: 4 + 3 = 7.
5. Result: 7/12.

Example 4: Subtracting Fractions with Unlike Denominators

1. Calculate 5/6 - 1/4.
2. Find LCD of 6 and 4 → 12.
3. Convert fractions: 5/6 = 10/12, 1/4 = 3/12.
4. Subtract numerators: 10 - 3 = 7.
5. Result: 7/12.

Practice Problems

1. 2/5 + 1/5 = ?
2. 7/8 - 3/8 = ?
3. 3/7 + 2/3 = ?
4. 5/9 - 2/6 = ?
5. 1/2 + 3/4 = ?

Tips & Common Mistakes

• Always simplify fractions after adding or subtracting.
• Do not add or subtract denominators; only numerators change.
• When denominators are different, always find the LCD before combining.

Summary

Adding and subtracting fractions requires understanding denominators. Fractions with like denominators are straightforward, while unlike denominators require finding the least common denominator. Always simplify your results.

Challenge Problems

1. Calculate 7/12 + 5/8 and simplify your answer.
2. Subtract 3/10 from 4/5 and simplify.
3. Create a word problem that involves adding and subtracting fractions with unlike denominators.