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Fractions Exploration and Test Preparation

This text provides a review of fractions exploration and test preparation covering sections 4.1, 4.2, 4.3, 5.2, and 5.3. It includes class notes and homework assignments.

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Fractions Exploration and Test Preparation

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  1. April 9, 2009 While we teach, we learn. ~Seneca

  2. April 9, 2009 Test 3  Thursday, 4/16 Covers: • Text sections 4.1, 4.2, 4.3, 5.2, 5.3 • Class Notes (fractions) • Explorations 4.2, 5.8, 5.9, 5.12, 5.13, … *Class Notes (fractions) are due on 4/16*

  3. April 9, 2009 • Go over Explorations 5.12 & 5.13 • Videos of Sean and David • Exploration 5.14 • Exploration 5.10 • Assign Homework

  4. C A B D E 0 1 Exploration 5.12 7/13 + 12/17: since each of these fractions is greater than 1/2, their sum is greater than 1. (E) 7/13 × 12/17: each of these fractions is less than 1, so their product will be less than the smaller fraction (12/17 of 7/13 is less than 7/13 since 12/17 is less than 1). The product will be positive since both fractions are positive. (B)

  5. C A B D E 0 1 Exploration 5.12 7/13 ÷ 12/17: since 12/17 is larger than 7/13, it will go into 7/13 less than one time. Since 12/17 is less than 1, dividing 7/13 by 12/17 will give a result greater than 7/13. This narrows our answers to (C) or (D). If you estimate that 7/13 ~ 6.5/13 = 1/2 and 12/17 ~ 12/18 = 2/3, 1/2 ÷ 2/3 = 3/4 (D) 12/17 ÷ 7/13: Since 12/17 is larger than 7/13, the result of this division will be larger than 1 (E).

  6. 0 2 4 6 8 10 12 Exploration 5.13 1. 12 ounces ÷ 3/4 ounce/dose = 16 doses.

  7. 1/6 3/4 Exploration 5.13 2. 3/4 + 1/6 = 11/12

  8. 0 2 4 6 8 10 12 Exploration 5.13 3. 12 inches ÷ 3/4 inch/piece = 16 pieces.

  9. Exploration 5.13 4. 12 × 3/4 = 9 (Note: this is operator)

  10. Exploration 5.13 5. 12  3/4 = 11 1/4

  11. Exploration 5.13 6. 3/4 × (total distance) = 12 miles so 12 ÷ 3/4 = total distance = 16 miles (see picture from #1 and #3)

  12. Exploration 5.13 7. 3/4 ÷ 12 = 1/16 (The large square is the whole acre. The shaded part is the 3/4 acre.) Each small square is 1/16 of an acre.

  13. Videos Sean: • Written work on pg 27 • Questions on pgs 29 & 33 – 34 David: • Written work on pg 31 (duplicate on pg 35) • Questions on pg 37 (note: transcripts of the videos are on pgs 39 – 45)

  14. Exploration 5.14 An alternative algorithm for dividing fractions. Ex: Lyra is building dog houses. She has 7 1/2 pounds of nails. Each dog house requires 1 1/4 pounds of nails. How many dog houses can she make? Diagram:

  15. Exploration 5.14 7 1/2 ÷ 1 1/4 If we re-draw the diagram as follows, is this question easier to answer?

  16. Exploration 5.14 Why did this new diagram make the question easier to answer? Can you generalize this algorithm?

  17. Exploration 5.10 • Each group will be given 2 fractions to compare on page 111 of your Explorations book. • You must justify your answer. If possible, come up with different ways to justify. • You may not use “find a common denominator and compare”. • You may not use “write the fractions as decimals and compare”.

  18. Exploration 5.10 Ways to compare…

  19. Exploration 5.10 #7 on page 110 (in case you tore it out): • Order each set of fractions without finding the LCM for the set or converting them to decimals. Explain and justify your thinking process. a. 31/80 13/17 2/3 b. 1/3 4/7 2/5 7/8 5/16 c. 3/10 2/3 7/12 4/5 3/7 d. 1/8; 2/5; 5/8; 5/6; 3/49; 3/56

  20. Homework Due Tuesday, 4/14 Link to online homework list: http://math.arizona.edu/~varecka/302AhomeworkS09.htm *Note: approximate grades so far are posted on D2L Exam 3: Thursday, 4/16.

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