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Fractions

Fractions. What is a fraction? Equivalent Fractions Making Equivalent Fractions by multiplying Making Equivalent Fractions by dividing Simplest Form Uses of Fractions Fractions Written as a Whole Improper Fraction Mixed Number How to change from Improper Fraction to Mixed Number

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Fractions

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  1. Fractions

  2. What is a fraction? Equivalent Fractions Making Equivalent Fractionsby multiplying Making Equivalent Fractions by dividing Simplest Form Uses of Fractions Fractions Written as a Whole Improper Fraction Mixed Number How to change from Improper Fraction to Mixed Number How to change from Mixed Number to Improper Fraction Comparing Fractions Ordering Fractions Ordering Fractions with Number Line Adding Fractions Index

  3. A fraction is formed by dividing a whole into a number of parts I’m the NUMERATOR. I tell you the number of equal parts you are looking at or have. What is a Fraction? I’m the DENOMINATOR. I tell you the number of equal parts into which the whole is divided.

  4. Uses of Fractions • A fraction may represent division. • Fractions can express probability. • Fractions are used to compare two quantities as a ratio. Student Reference Book p. 57-58

  5. Equivalent Fractions Equivalent fraction: fractions that have the same value 1 WHOLE 1 WHOLE

  6. To Make Equivalent Fractions • Multiply the numerator and denominator by the same number. • You will get a new fraction with the same value as the original fraction. • We are not changing the value of the fraction, because we are simply multiplying by a fraction that is equivalent to ONE.

  7. What do you get when you multiply a fraction by 1? You get AN EQUIVALENT FRACTION that makes adding & subtracting fractions possible.

  8. x = This fraction equals 1. = These fractions represent the same amount.

  9. x = This fraction equals 1. = These fractions represent the same amount.

  10. Make An Equivalent FractionFind the Missing Numerator! Given the new denominator, can you find the missing numerator? x 3 = We multiplied the numerator and denominator by ... x 3 3

  11. Make An Equivalent FractionFind the Missing Numerator! Given the new denominator, can you find the missing numerator? x 4 = We multiplied the numerator and denominator by ... x 4 4

  12. Make An Equivalent FractionIf you have larger numbers, you can make equivalent fractions using division. Divide by a common factor. In this example, we can divide both numbers by 7. 4 ÷ 7 28 = We divided the numerator and denominator by ... 5 35 ÷ 7 7

  13. Fractions in Simplest Form Fractions are in simplest form when the numerator and denominator do not have any common factors besides 1. Examples of fractions that are in simplest form: 4 2 3 8 5 11

  14. Writing Fractions in Simplest Form • Find the greatest common factor (GCF) of the numerator and denominator. • Divide both numbers by the GCF.

  15. Example: 5 20 ÷ 4 = Simplest Form 7 ÷ 4 28 20: 1, 2, 4, 5, 10, 20 20 28 28: 1, 2, 4, 7, 14, 28 1 x 20 2 x 10 4 x 5 1 x 28 2 x 14 4 x 7 Common Factors: 1, 2, 4 GCF: 4 We will divide by 4.

  16. Fractions Written as a Whole

  17. If a hexagon is worth 1, what are 5 trapezoids worth? Trapezoid Trapezoid 1 Whole 1 Whole 2 Trapezoids = 1 Hexagon 1 Whole Trapezoid Trapezoid ½ We can report this as 2 ½ or 5/2 Trapezoid Trapezoid

  18. Improper Fraction fractions that are equal to or greater than 1 5/2 is read as – five halves

  19. Mixed Number a whole number and a fraction written together 2 ½ is read as - two and one half

  20. If a triangle is 1/3,what shape is ONE whole? 1/3 1/3 Trapezoid 1 Whole 1/3 1/3 + 1/3 + 1/3 = 3/3 or 1 Whole What shape can we make? How many more triangles do you need to make a whole? Remember: Numerator is what you have- 1. Denominator is how many pieces your whole is cut into - 3.

  21. If the triangle is 1/3, what is the rhombus? Turn to MJ p. 124 If the rhombus is 1/3, what shape is the WHOLE? If the triangle is ½, what is the trapezoid? If the rhombus is 1/3, what is the triangle? If the triangle is ½, what shape is the WHOLE?

  22. Mixed Number • A mixed number has a part that is a whole number and a part that is a fraction. 3 1 = 4

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

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

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

  26. Improper Fraction • A fraction in which the numerator is greater than the denominator. 8 = 4

  27. What is the improper fraction? 15 = 4

  28. What is the improper fraction? 19 = 4

  29. What is the improper fraction? 11 = 2

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

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

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

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

  34. 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

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

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

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

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

  39. 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 =

  40. 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 =

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

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

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

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

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

  46. Change this mixed number to an improper fraction • Multiply the whole number times the denominator. • Add your answer to the numerator. • Put your new number over the denominator. 3 43 + 8 = x 5 5

  47. Comparing Fractions Cross Multiply or “Butterfly Method” Use >, <, or =. 9 < 10 <

  48. Cross Multiply or “Butterfly Method” Use >, <, or =. 12 10 > >

  49. Ordering Fractions To order fractions you can draw a picture or use the Least Common Denominator (LCD).

  50. One way to compare or order fractions is to express them with the same denominator.

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