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Unit 8

Unit 8. Fractions and Ratios. Lesson 8.1. Comparing Fractions. Defining Fractions. Denominator – represents the number of equal sized pieces something is divided into (bottom number) Numerator – indicates the number of those equal pieces being considered (top number) .

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Unit 8

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  1. Unit 8 Fractions and Ratios

  2. Lesson 8.1 Comparing Fractions

  3. Defining Fractions • Denominator – represents the number of equal sized pieces something is divided into (bottom number) • Numerator – indicates the number of those equal pieces being considered (top number)

  4. Warm-Up (use reference page 399 to help) • Are the following fractions closer to 0, ½ , 1, 1 ½ , or 2 • 2/10 • 6/10 • 3/10 • 9/8 • 15/8 • 5/3 • 9/5 • 8/5

  5. Renaming Fractions as Equivalent Fractions • Division Rule: Divide both the numerator and denominator by the same number yields an equivalent fraction.

  6. Image from scimathmn.org Using your fraction sticks

  7. Comparing Fractions • Quick Common Denominator (QCD) – the product of the denominators or two or more fractions. (Quick way to get a common denominator, not the lowest common denominator)

  8. Renaming Fractions as Equivalent Fractions • Equivalent means having the same solution set (They are EQUAL to each other) • Multiplication Rule: Multiply both the numerator and denominator by the same number yields an equivalent fraction.

  9. Lesson 8.2 Adding Mixed Numbers

  10. Improper Fractions • Improper Fraction: when numerator is greater than or equal to the denominator • examples: • 5/3 • 39/31

  11. Warm-Up: Rename as a whole, mixed, or improper fraction • 3/3 • 2 ½ • 3/2 • 13/8 • 4 1/8 • 37/5 • 62/5 • 11 ¼

  12. Adding fractions with the same denominator • When the denominators are the same, add the numerators and keep the common denominator.

  13. What are mixed numbers? • A whole number with a fraction • Written: • Actually:

  14. Adding Mixed Number with the same denominator • Everyday Math Way • 1. Add the whole numbers • 2. Add the fractions • 3. Rename in simplest form

  15. Let’s Practice Together • Problems will be reviewed on the white board

  16. Adding mixed numbers with unlike denominators • 1. find the common denominator for each fraction • 2. use the adding mixed number technique • 3. simplify • Let’s practice finding the common denominator

  17. Let’s Practice Together • Problems will be reviewed on the white board

  18. Lesson 8.3 Subtracting Mixed Numbers

  19. Warm-Up (Find the QCD for the left and CD for the right) QCD CD • 1/2 and 1/3 • answer: 6 • 5/6 and 7/9 • answer: 54 • 4/5 and 7/10 • answer: 50 • 7/10 and 19/20 • answer 200 • 1/2 and 1/3 • answer: 6 • 5/6 and 7/9 • answer: 18 • 4/5 and 7/10 • answer: 10 • 7/10 and 19/20 • answer 20

  20. Warm Up- (rename the fractions to have like denominators) • 1/2 and 1/3 • answer: 3/6 & 2/6 • 5/6 and 7/9 • answer:15/18 & 14/18 • 4/5 and 7/10 • answer: 8/10 & 7/10 • 7/10 and 19/20 • answer:14/20 & 19/20

  21. Subtracting Mixed Numbers with the same denominator • 1. Rename (if necessary) the fraction on the top part of the equation larger than the bottom part. Example: • 2. Subtract the fractions • 3. Subtract the whole numbers • 4. Answer in simplest form : Answer: 1 2/3

  22. Let’s practice renaming fractions to make the fraction part larger • 5 ¼ • answer: 4 5/4 • 6 2/5 • answer: 5 7/5

  23. Let’s Practice Subtracting Mixed Numbers (Complete the following in your binder) • 8 – 3 2/3 • 6 – ¼ • 4 3/5 – 1 4/5 • 6 5/12 – 3 11/12 • answer: 4 1/3 • answer: 5 ¾ • answer: 2 4/5 • answer: 2 ½

  24. Complete Math Journal pg. 254 • Answers: • 1. 2 ½ • 2. 2 4/5 • 3. 5 ½ • 4. 4 • 5. 3 • 6. 23 • 7. 7 • 8. 7 2/3 • 9. 2 2/5 • 10. 3 ½ • 11. ¾ • 12. 1 2/3 • 13. 4 3/5

  25. Subtracting fractions with unlike denominators • 1. Find the common denominator or quick common denominator • 2. Rename (if necessary) the fraction on the top part of the equation larger than the bottom part. • 3. Subtract the fractions • 4. Subtract the whole numbers • 5.Answer in simplest form

  26. LESSON 8.5 – 8.8 Fractions of Fractions

  27. Using paper modeling (What is ½ of ½ ?) • Using a standard sheet of paper fold it in half vertically (the longer dimension)

  28. ½ of ½ is ¼ • Then fold it in half horizontally (the shorter dimension)

  29. Lets try some more using paper modeling • What is 2/3 of 1/2 • 1st fold the paper in half (vertically) (shade 1 of the two) • Then in thirds (horizontally) (shade the 2 of the thirds) • Write and X on the parts shaded twice • Your answer should be 2/6 or 1/3

  30. Continued • What is 3/4 of 2/3 • 1st fold your paper into thirds (vertically) (shade two of the thirds) • Then fold your paper into fourths (horizontally) (shade in three of the fourths) • Write an X in the parts shaded twice • Your answer should be 6/12 or ½ • Practice with pg. 261 in your Math Journal

  31. Multiplication Algorithm • ¾ of ¼ =

  32. Multiplication of Whole Numbers

  33. Multiplication of Mixed Numbers

  34. Multiplication of Mixed Numbers

  35. Partial Products Method • 1. Multiply the whole #’s • 2. Multiply the 1st fraction and the 2nd whole number • 3. Multiply the 1st whole # and the 2nd fraction • 4. Multiply the 1st fraction and the 2nd fraction • 5. Add the products

  36. Lesson 8.9 Finding a Percent of a Number

  37. Percent (%) • Definition – Per hundred, for each hundred, or out of a hundred. 1% = 1/100 = .01 • Examples: • 20% = 20/100 = .20 • 60% = 60/100 = .60 • 33% = 33/100 = .33

  38. Let’s Practice • What is 40% of 320? • 1. Make 40% into a fraction. • 40/100 or 4/10 or 2/5 • 2. Multiple • 2/5 * 320/1 • 3. Simplify for your final answer

  39. Discounts • Definition – The amount by which a price of an item is reduced in sale, usually given as a fraction or percent of the original price or as a percent off. • Example: An item that originally cost $10 at 10% off is now $9.00. • Remember – the discount is the amount to be subtracted from the original whole.

  40. Let’s Practice • Hill’s Sporting Goods was selling all hockey equipment at a 25% discount. How much does each item cost after the discount? • Hockey Stick - $150 • Helmet - $120 • Philadelphia Flyers Jersey - $170 • Goalie Leg Pads - $450

  41. Division (Standard Algorithm) • How many _____ are in _____? • Ex: How many 2’s are in 10? (10 2) • 5 • How many ½ are in 6? (6 1/2 ) • 12 • How many ¾ are in 5? (5 ¾) • 6 2/3

  42. Division (Common Denominators Method) • How many 4/5 are in 4? ( 4 4/5) • 5 • How many 5/6 are in 1/18? ( 1/18 5/6) • 15

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