Lesson 30: Signs of 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 teaches how to identify and work with positive and negative fractions, including the rules for multiplying and dividing signed fractions.

Learning Objectives

• Determine whether a fraction is positive or negative.
• Apply rules for multiplying fractions with the same or different signs.
• Apply rules for dividing fractions with the same or different signs.
• Recognize common mistakes with signs in fraction operations.

Topics Covered

• Positive and negative fractions
• Multiplying fractions with signs
• Dividing fractions with signs
• Order of operations with signed fractions

Key Terms

• Positive Fraction: A fraction greater than zero.
• Negative Fraction: A fraction less than zero.
• Sign Rules: Rules determining the sign of a product or quotient:
  • Positive × Positive = Positive
  • Positive × Negative = Negative
  • Negative × Negative = Positive
  • Division follows the same rules as multiplication

Lesson Examples

Example 1: Multiplying Fractions with Signs

1. Multiply -2/3 × 3/4.
2. Multiply numerators: -2 × 3 = -6.
3. Multiply denominators: 3 × 4 = 12.
4. Result: -6/12 = -1/2 after simplification.

Example 2: Dividing Fractions with Signs

1. Divide -5/6 ÷ 2/3.
2. Take reciprocal of divisor: 2/3 → 3/2.
3. Multiply: -5/6 × 3/2 = -15/12.
4. Simplify: -15/12 = -5/4 = -1 1/4.

Example 3: Multiplying Negative Fractions

1. Multiply -3/5 × -2/7.
2. Multiply numerators: -3 × -2 = 6.
3. Multiply denominators: 5 × 7 = 35.
4. Result: 6/35 (positive because negative × negative = positive).

Practice Problems

1. Multiply -2/5 × 3/4 = ?
2. Divide -7/8 ÷ 1/2 = ?
3. Multiply 5/6 × -2/3 = ?
4. Divide -3/4 ÷ -1/2 = ?
5. Multiply -1/3 × -4/5 = ?

Tips & Common Mistakes

• Always track the signs separately from the fraction values.
• Multiplying or dividing two negatives gives a positive.
• Do not confuse subtraction of fractions with multiplying/dividing negatives.

Summary

Understanding positive and negative fractions and applying the correct sign rules is essential for accurate multiplication and division. Remember that signs determine whether the result is positive or negative.

Challenge Problems

1. Multiply -7/9 × 3/5 and explain why the result is negative.
2. Divide -6/7 ÷ -2/3 and simplify.
3. Create a problem combining positive and negative fractions and solve it step by step.