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Number Sense and Numeration

Number Sense and Numeration. Introduction to Fractions. What you will learn during this unit. How to read, represent, compare and order proper and improper fractions, and mixed numbers How to put fractions into lowest terms

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Number Sense and Numeration

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  1. Number Sense and Numeration Introduction to Fractions

  2. What you will learn during this unit • How to read, represent, compare and order proper and improper fractions, and mixed numbers • How to put fractions into lowest terms • How to demonstrate and explain the concept of equivalent fractions using manipulatives (e.g. fraction strips) • How to describe multiplicative relationships between quantities by using simple fractions • How to determine and explain the relationship between fractions and their equivalent decimal forms • How to demonstrate an understanding of simple multiplicative relationships involving whole-number rates

  3. Where we’ll start • In order to do all of the things just mentioned, we have to understand the anatomy of a fraction • A fraction is made up of 2 numbers, the numerator (top number) and the denominator (bottom number) • Each of these numbers has a specific purpose and has to be read correctly to understand the meaning of the fraction as a whole

  4. Parts of a Fraction 3 = the number of parts the fraction is representing (the numerator) 4 = the total number of parts that equal the whole that the fraction is representing (the denominator)

  5. In pictures ¾ looks like… 1/4 1/4 3 4 1/4 1/4

  6. And… 1/4 1/4 3 1/4 4 1/4

  7. And… 1/4 1/4 3 4 1/4 1/4

  8. Now that we know the basics… • There are 3 types of fractions that we have to know: • Proper fractions – fractions where the numerator is a smaller number than its denominator • Improper fractions – fractions where the numerator is a greater number than its denominator (can be converted into a mixed number) • Mixed numbers – a number that is made up of a whole number and a proper fraction (can be converted into an improper fraction)

  9. Proper Fractions

  10. Proper Fractions • These are the most common types of fractions and they cannot be converted to improper fractions or mixed numbers, but they can sometimes be reduced into lowest terms • Lowest terms means that the numerator and thedenominator cannot be divided further by the same number to arrive at a lower valued numerator and denominator

  11. Proper Fractions • Let’s identify and look at some proper fraction examples • If you see that the numerator and denominator can both be divided by the same number (as long as that number is not 1), it is not in lowest terms • If the fraction is not in lowest terms, let’s reduce them to that point

  12. What fraction of the circles are green? 1 4 This fraction is in lowest terms

  13. What fraction of the circles are green? 1 6 This fraction is in lowest terms

  14. What fraction of the circles are green? 4 6 This fraction is not in lowest terms

  15. Let’s put it into lowest terms Image taken from: http://www.gradeamathhelp.com/images/reduce_4_6.gif

  16. What fraction of the rectangle is green? 2 6 This fraction is not in lowest terms

  17. Let’s put it into lowest terms 2 2 ÷ 2 1 ____ ____ ______   3 6 ÷ 2 6

  18. What fraction of the pie is green? 4 4 This fraction is not in lowest terms

  19. Let’s put it into lowest terms 4 4 ÷ 4 1 ____ 1 ______ ____ =   1 4 ÷ 4 4

  20. What fraction of the instruments have strings? 2 5 This fraction is in lowest terms

  21. What fraction of the fish have stripes? 3 5 This fraction is in lowest terms

  22. What fraction of the arrowshit the bull's-eye? 1 3 This fraction is in lowest terms

  23. What fraction of the pins areknocked down? 3 This fraction is in lowest terms 10

  24. Improper Fractions

  25. Improper Fractions • Remember, these are fractions where the numerator is a greater number than the denominator • Improper fractions are looked at as fractions because each of the parts included in the improper fraction is divided into the same fraction (example, halves or quarters) • These can be converted into mixed numbers, but they can also sometimes be reduced into lowest terms

  26. What is the improper fraction? 15 = 4

  27. What is the improper fraction? 19 = 4

  28. What is the improper fraction? 11 = 2

  29. Mixed Numbers

  30. Mixed Numbers • Remember, these are numbers that include both a whole number and a fraction • Just like improper fractions are looked at as fractions because each of the parts included in the improper fraction is divided into the same fraction (example, halves or quarters), so are mixed numbers, but here, we use whole numbers to show each of the pieces where all of the parts are represented • These can be converted into improper fractions, but the fraction portion of a mixed number can also sometimes be reduced into lowest terms

  31. What is the mixed number? 3 = 3 4

  32. What is the mixed number? 3 = 4 4

  33. What is the mixed number? 1 = 5 2

  34. Relationship between Improper Fractions and Mixed Numbers

  35. How is the mixed number below related to the improper fraction? 1 5 = 2 11 = 2

  36. How to change an improper fraction to a mixed number • Divide the numerator by the • denominator. • Put your remainder over the • denominator. 5 = 2

  37. How to change an improper fraction to a mixed number ) numerator 2 5 denominator 5 = 2

  38. How to change an improper fraction to a mixed number 2 r 1 ) numerator 2 5 denominator 5 = 2

  39. How to change an improper fraction to a mixed number 1 2 denominator 2 ) numerator 2 5 Put your remainder over the Denominator. 5 = 2

  40. Change this improper fraction to a mixed number 2 r 1 7 = ) 3 7 3 1 Put your remainder over the denominator. 2 = 3

  41. Change this improper fraction to a mixed number 2 r 2 8 = ) 3 8 3 2 Put your remainder over the denominator. 2 = 3

  42. Change this improper fraction to a mixed number. 4 r 1 9 = ) 2 9 2 1 Put your remainder over the denominator. 4 = 2

  43. Change this improper fraction to a mixed number. 2 r 1 11 = ) 5 11 5 1 Put your remainder over the denominator. 2 = 5

  44. Change this improper fraction to a mixed number. 2 10 = ) 5 10 5 If there is no remainder your answer is a whole number. 2 =

  45. Change this improper fraction to a mixed number. 4 16 = ) 4 16 4 If there is no remainder your answer is a whole number. 4 =

  46. How to change a mixed number to an improper fraction 1 9 + 4 • Multiply the whole number times the denominator. • Add your answer to the numerator. • Put your new number over the denominator. = x 2 2

  47. Change this mixed number to an improper fraction 2 20 + 6 • Multiply the whole number times the denominator. • Add your answer to the numerator. • Put your new number over the denominator. = x 3 3

  48. Change this mixed number to an improper fraction 2 17 + 3 • Multiply the whole number times the denominator. • Add your answer to the numerator. • Put your new number over the denominator. = x 5 5

  49. Change this mixed number to an improper fraction 3 19 + 4 • Multiply the whole number times the denominator. • Add your answer to the numerator. • Put your new number over the denominator. = x 4 4

  50. Change this mixed number to an improper fraction 2 20 + 6 • Multiply the whole number times the denominator. • Add your answer to the numerator. • Put your new number over the denominator. = x 3 3

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