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Mastering Fraction Multiplication and Division Techniques

This resource guides learners through efficiently multiplying and dividing fractions and decimals using effective algorithms. It emphasizes the conceptual understanding of multiplication and division relationships. Students will model fraction multiplication through array shading and learn the cancellation technique before multiplying fractions. A self-assessment tool is included to help identify their mastery levels, allowing them to gain confidence in their skills. Engage with practical exercises and visual models to enhance comprehension and teaching capabilities.

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Mastering Fraction Multiplication and Division Techniques

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  1. Multiplying Fractions 6.1.3.1 Multiply and divide decimals and fractions, using efficient and generalizing procedures, including standard algorithms. 6.1.3.2 Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions

  2. Ican… • Model the multiplication of fractions • Multiply fractions Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

  3. MODELING MULITPICATION OF FRATIONS

  4. Draw a model … • Draw a 4 x 2 array • Shade ¾ of the rectangle one color • Shade ½ of the rectangle another color • The part that overlaps is the answer

  5. Your Turn… • Draw a 5 x 2 array • Shade 1/5 of the rectangle one color • Shade 1/2 of the rectangle another color • The part that overlaps is the answer

  6. Your Turn… • Draw a 3 x 5 array • Shade 2/3 of the rectangle one color • Shade 1/5 of the rectangle another color • The part that overlaps is the answer

  7. Fraction Multiplication • Here are some fraction multiplication problems… • Can you tell how to multiply fraction from these examples?

  8. Just Follow These Easy Steps! • Multiply the numerators • Multiply the denominators • Simplify. 5 3 15 x = 32 8 4 There are no common factors for 15 and 32, so this fraction cannot be simplified.

  9. Example 2 3 2 6 1 x = = 9 36 6 4 This fraction can be reduced. Divide the numerator and denominator by 6.

  10. Try SOME…

  11. Try one more…

  12. Canceling • Reducing before multiplying is called canceling. • ICK! Instead think the following in your head.

  13. Canceling on paper • Rule: One factor from any numerator cancels with like factor from the denominator.

  14. Try one • Say “--- goes into ____ this many times.” • As you cross each number out and write what is left after canceling above the number. 1 2

  15. Try another… • Say “--- goes into ____ this many times.” • As you cross each number out and write what is left after canceling above the number. 2 1

  16. And one more… • Say “--- goes into ____ this many times.” • As you cross each number out and write what is left after canceling above the number. 1 1 2 2

  17. Ican… • Model the multiplication of fractions • Multiply fractions Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

  18. 7.2 Notes Multiplying Fractions Example 1 1 Simplify BEFORE Multiplying (if you can) Multiply numerators Multiply denominators Reduce (if necessary) 2 3

  19. Daily Check 7.2 in your math notebook

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