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Mastering Fraction Multiplication: Concepts and Practice

This lesson focuses on the principles of multiplying fractions through engaging warm-up problems and practical examples. Students learn to apply strategies for multiplying fractions and simplifying answers into their simplest forms. A problem of the day illustrates real-world application, such as estate division among family members and charity. Additional exercises reinforce concepts and ensure mastery of fraction multiplication. Emphasis is placed on finding the greatest common factor (GCF) for simplification before multiplying to enhance understanding and proficiency.

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Mastering Fraction Multiplication: Concepts and Practice

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  1. 5-7 Multiplying Fractions Course 1 Warm Up Problem of the Day Lesson Presentation

  2. 1 1 1 1 1 __ __ __ __ __ 4 2 4 2 2 Warm Up 1.What is of 12? 2. What is of 100? 3. What is of 120? 4. What is of 100? 5. What is of 480? 6 50 60 25 120

  3. Problem of the Day Your favorite uncle left one-fifth of his estate to each of his three children and the rest to his favorite charity. If his estate was worth $105,000, how much was given to charity? $42,000

  4. Learn to multiply fractions.

  5. 1 1 1 1 1 1 1 1 1 __ __ __ __ __ __ __ __ __ 3 4 4 3 4 3 3 12 4 On average, people spend of their lives asleep. About of the time they sleep, they dream. What fraction of a lifetime does a person typically spend dreaming? One way to find of is to make a model. Find of . = •

  6. 1 1 1 1 __ __ __ __ 12 12 4 3 You can also multiply fractions without making a model. 1 • 1 Multiply the numerators. _____ = • Multiply the denominators. 4 • 3 The answer is in simplest form. = A person typically spends of his or her lifetime dreaming.

  7. 1 1 2 2 1 2 __ __ __ __ __ __ 4 5 5 10 20 4 Additional Example 1A: Multiplying Fractions Multiply. Write each answer in simplest form. • 1 • 2 _____ Multiply numerators. Multiply denominators. = • 4 • 5 The GCF of 2 and 20 is 2. = The answer is in simplest form. =

  8. 5 1 4 4 4 5 4 __ __ __ __ __ __ __ 15 7 21 7 7 3 15 Additional Example 1B: Multiplying Fractions Multiply. Write each answer in simplest form. • Use the GCF to simplify the fractions before multiplying. The greatest common factor of 5 and 15 is 5. 1 = • • 3 1 • 4 _____ Multiply numerators. Multiply denominators. = 7 • 3 The answer is in simplest form. =

  9. 4 4 6 6 4 24 __ __ __ __ __ __ 9 10 10 15 90 9 Additional Example 1C: Multiplying Fractions Multiply. Write each answer in simplest form. • 4 • 6 ______ Multiply numerators. Multiply denominators. = • 9 • 10 The GCF of 24 and 90 is 6. = The answer is in simplest form. =

  10. 1 1 3 3 1 3 __ __ __ __ __ __ 2 6 6 4 12 2 Check It Out: Example 1A Multiply. Write each answer in simplest form. • 1 • 3 _____ Multiply numerators. Multiply denominators. = • 2 • 6 The GCF of 3 and 12 is 3. = The answer is in simplest form. =

  11. 3 1 5 5 5 3 5 __ __ __ __ __ __ __ 9 7 21 7 7 3 9 Check It Out: Example 1B Multiply. Write each answer in simplest form. • Use the GCF to simplify the fractions before multiplying. The greatest common factor of 3 and 9 is 3. 1 = • • 3 1 • 5 _____ Multiply numerators. Multiply denominators. = 7 • 3 The answer is in simplest form. =

  12. 3 5 1 5 3 __ __ __ __ __ 7 15 7 7 15 15 ____ 105 Check It Out: Example 1C Multiply. Write each answer in simplest form. • 3 • 5 ______ Multiply numerators. Multiply denominators. = • 7 • 15 The GCF of 15 and 105 is 15. = The answer is in simplest form. =

  13. 2 2 2 1 1 1 2 __ __ __ __ __ __ __ 5 3 5 5 3 15 3 _____ 1 • 2 3 • 5 Additional Example 2A: Evaluating Fraction Expressions Evaluate the expression b• for each value of b. Write each answer in simplest form. b• b = Substitute for b. • Multiply. The answer is in simplest form.

  14. Helpful Hint You can look for a common factor in a numerator and a denominator to determine whether you can simplify before multiplying.

  15. 3 3 3 3 2 2 3 2 __ __ __ __ __ __ __ __ 8 8 5 5 5 20 8 8 _____ 3 • 1 4 • 5 Additional Example 2B: Evaluating Fraction Expressions b = b• Substitute for b. • 1 Use the GCF to simplify. • 4 Multiply. The answer is in simplest form.

  16. 5 10 5 2 2 2 5 __ __ __ __ __ __ __ 7 35 7 7 5 5 7 _____ 5 • 2 7 • 5 Additional Example 2C: Evaluating Fraction Expressions b = b• Substitute for b. • Multiply. The GCF of 10 and 35 is 5. The answer is in simplest form.

  17. 1 1 1 1 1 1 1 __ __ __ __ __ __ __ 7 7 4 4 4 7 28 _____ 1 • 1 7 • 4 Check It Out: Example 2A Evaluate the expression c• for each value of c. Write each answer in simplest form. c = c• Substitute for c. • Multiply. The answer is in simplest form.

  18. 1 2 2 2 1 1 2 1 __ __ __ __ __ __ __ __ 7 7 4 4 4 14 7 7 _____ 1 • 1 7 • 2 Check It Out: Example 2B c = c• Substitute for c. • 1 Use the GCF to simplify. • 2 Multiply. The answer is in simplest form.

  19. 4 4 4 1 1 1 4 __ __ __ __ __ __ __ 7 28 7 7 4 4 7 _____ 4 • 1 7 • 4 Check It Out: Example 2C c = c• Substitute for c. • Multiply. The GCF of 4 and 28 is 4. The answer is in simplest form.

  20. 1 1 3 1 1 3 5 1 3 3 1 1 2 4 __ __ __ __ __ __ __ __ __ __ __ __ __ __ 20 8 5 5 8 4 10 7 14 10 4 64 5 10 Lesson Quiz Multiply. Write each answer in simplest form. 1.2. Evaluate the expression x• for each value of x. Write the answer in simplest form. 3.x = 4.x = 5. At a particular college of the students take a math class. Of these students, take basic algebra. What fraction of all students take basic algebra? • •

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