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Understanding Multiplying and Dividing Fractions in Rational Numbers

This lesson focuses on the multiplication and division of fractions, essential concepts within rational numbers. Students will explore models to visualize how fractions interact, including the use of reciprocals in division. Key examples demonstrate the process of multiplying fractions by multiplying numerators and denominators, as well as simplifying results. Exercises are included to practice these skills, emphasizing different methods of simplification. Communication prompts encourage students to reflect on their preferred methods of fraction manipulation, enhancing their understanding and problem-solving techniques.

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Understanding Multiplying and Dividing Fractions in Rational Numbers

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  1. Monday 9/8 • Block 1 Rational Numbers & Equations In Class p.15 Lesson 1.4 Multiplying & Dividing Fractions Examples 1-4 Homework p.17 Exercises 1-32

  2. Warm-Up

  3. Lesson 1.4 Multiplying and Dividing Fractions Multiply and divide fractions.

  4. Good to Know! In math, the word “of” often means multiply. Example: What is ? According to the model above, . The yellow-shaded part represents . The green shaded part represents .

  5. Multiplying Fractions For any numbers a, b, c and d:

  6. Example 1 Find the value of using models. Draw a model and shade of a rectangle. Draw horizontal lines to cut the model into thirds. Shade 2 of the three horizontal rectangles to represent . The final model has 6 out of 15 regions which are double shaded. Write in simplest form.

  7. Example 2 Multiply the numerators. Find the value of . Multiply. Simplify. Multiply the denominators.

  8. Vocabulary Reciprocal Two numbers are reciprocals if their product is 1. To find a reciprocal, “flip” the fraction so the numerator becomes the denominator and the denominator becomes the numerator. Reciprocal Reciprocal Good to Know!  Reciprocals are used when dividing fractions.

  9. Dividing Fractions For any numbers a, b, c and d :

  10. Example 3 Multiply the first fraction by the reciprocal of the second fraction. Find the value of . Divide. Simplify.

  11. Example 4 Find the value of . Divide. Simplify. Change to a mixed number.

  12. Monday 9/8 • Block 1 Rational Numbers & Equations In Class p.15 Lesson 1.4 Multiplying & Dividing Fractions Examples 1-4 Homework p.17 Exercises 1-32

  13. Communication Prompt Fractions can be simplified before or after multiplying. Which method do you prefer and why?

  14. Exit Problems Find each product or quotient. Write answers in simplest form. 1. 2. 3. 4.

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