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Mastering Integer Rod Operations: Multiplying and Dividing Fractions with Visual Bars

Learn how to represent fractions using integer bars effectively through a six-step approach. This guide explores the concept of part to whole, ensuring the whole adjusts as needed for equivalency. By racing denominators to a tie, you will simplify representations for both multiplication and division. Understand the use of common denominators and the least number of rods for clear visual comprehension. Whether you're working with concrete or semi-abstract methods, this resource will enhance your mathematical representation skills.

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Mastering Integer Rod Operations: Multiplying and Dividing Fractions with Visual Bars

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  1. Integer Rod Operations Multiplying and Dividing

  2. Representing Fractions Using Bars • How do we represent fractions using integer bars? • Part to whole • Whole changes as necessary to make equivalents • A train is two rods put together – ALL trains must have at least one E in them • We will ALWAYS use the least number of bars possible to make a representation • Do NOT draw more lines on representations than necessary

  3. Six Steps Required • Represent the fraction with the smallest and least number of rods possible • Race the denominators to a tie. This will ALWAYS take 3 rows – the new common denominator is at the bottom

  4. Six Steps Required - Continued • Represent the fraction using the “race” as a guide using the common denominator rod and the least number of rods possible for the numerator • Do the operation

  5. Six Steps Required - Continued • Simplify the representation –least number of rods possible • Interpret the representation in #5 as a fraction number answer

  6. Race Representation: Multiplication • Use one common denominator bar • The numerator will represent the SECONDfactoronly • Do NOT represent the first factor

  7. Do the Operation: Multiplication • Use one common denominator bar • Place the numerator of the second factor directly above the common denominator • Look at the first factor in the problem • Treat the numerator of the second factor as the denominator of the first factor • Place a bar above it that represents the numerator for the first factor • Total of 3 rows

  8. Simplify the Representation: Multiplication • Use one original common denominator bar • Place the top bar from the step above directly above the common denominator bar • Represent all with the least number of rods possible • Total of 2 rows

  9. Multiplication – Concrete A. B. C. D. E. F. A. B. C. D. E. F.

  10. Multiplication – Semi-Concrete A. B. C. D. E. F. A. B. C. D. E. F.

  11. Multiplication – Semi-Abstract

  12. Do the Operation: Division • Use one common denominator bar • Place the divisor (the factor) directly above the common denominator • Place the dividend (the product) directly above the divisor (the factor) • Total of 3 rows

  13. Simplify the Representation: Division • Use the divisor (the factor) as the new common denominator • Place the dividend (the product) directly above the divisor (the factor) • Represent all with the least number of rods possible • Total of 2 rows

  14. Division – Concrete A. B. C. D. E. F. A. B. C. D. E. F.

  15. Division – Semi-Concrete A. B. C. D. E. F. A. B. C. D. E. F.

  16. Division – Semi-Abstract

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