1. Fractions
Nancy Hughes
Olathe District Schools

2. Standards Seventh Grade
N M7.1.4.K2d The student adds, subtracts, multiplies, and divides fractions and expresses answers in simplest form.
Eighth Grade
M8.1.4.A1bThe student models, performs, and explains computation with rational numbers, the irrational number pi, and algebraic expressions in a variety of situations.

3. Vocabulary Addend Common denominators Denominator Dividend Division
Equivalent fraction
Fraction
Improper fraction
Least common denominator
Lowest terms
Minuend
Mixed number
Numerator
Proper fraction
Quotient
Simplify
Subtrahend
Unit fraction

4. Objectives Develop concepts of fractions and mixed numbers
Use models to add, subtract, multiply and divide fractions
Add, subtract, multiply, divide fractions and mixed numbers

5. Adding Fractions – Using Fraction Circles
Pull out your fraction circles and sort them by colors. The clear circle is the number 1 or 1 whole.

6. Do the same with the fraction tiles. Sort them by color.1

7. Adding Fractions – Using Fraction Circles or Fraction Tiles
Let’s add
Which colored circle or tile will you need to add these fractions? Explain.
Because the fraction has a denominator of 4, find the fraction piece that has been divided into fourths.
Take the ¼ piece and add to it the piece. + = + =

8. Adding Fractions – Using Fraction Circles or Tiles
Use either fraction circles or tiles to model
Again, look at the denominator and choose your tiles accordingly. + = + =

9. Adding Fractions – Using Fraction Circles or Tiles
Use either fraction circles or tiles to model
Notice we do not have like denominators. This makes it more of a challenge. Begin by taking the ½ and the 1/3 and find tiles or circles that are exactly the same size.
Did you find like tiles? Explain.
If you found tiles or parts of a circle that have a denominator of 6, you were correct.
Notice the ½ matches up with 3/6 and the 1/3 matches up with 2/6.
Now we can add!

10. Adding Fractions – Using fraction circles or tiles
Use either fraction circles or tiles to model + = = +

11. You Try
Use your fraction circles or fraction tiles to find + = + =

12. Quick Review Quick Review #1 #2 #3 #4 #5 Roll 1st Fraction
Use two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions, and then add.
Roll
1st Fraction
2nd Fraction
Sum #1 #2 #3 #4 #5

13. How to use your calculator to check!
Change to a fraction
Simplify
Mixed Number and Improper Fraction
Change to a decimal
Fraction bar

14. Subtracting Fractions
Visual approach using fraction tiles or fraction circles

15. Subtracting Fractions using fraction circles or fraction tiles
What is ? Again we will have to find like denominators. Which sets of tiles or circles will work? Explain.
If you guessed the 10th’s you were right, 6/10 = 3/5 -

16. Subtracting Fractions using fraction circles or fraction tiles
What is ? If you used fraction circles, your work should be identical to the fraction tiles. = -

17. You Try – Use fraction tiles or fraction circles to show your answer.
What is ? -
or ¼ - =

18. Quick Review Quick Review #1 #2 #3 #4 #5 Roll 1st Fraction
Use two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then subtract.
Roll
1st Fraction
2nd Fraction
Difference #1 #2 #3 #4 #5

19. Multiplying fractions
Multiplying fractions is like finding what one fraction is of another.

20. Multiplying fractions
For example, to find , we begin with an area model.
3/4 1 2 3 7
2/3 4 5 6 8 9 10 11 12

21. Multiplying Fractions
To simplify ,find the prime factorization of 6 and 12.
Composite Prime Composite Prime 3
• = 1
• 2 •

22. Multiplying fractions
What is?

23. Multiplying Fractions
To find the answer to ½ x 3/5, we will use another model.
Show 3 out of 5
Show 1 out of 2
Shade the answer

24. You try! To find the answer to . Model your answer. Show 2 out of 3
Shade the answer

25. Quick Review Quick Review #1 #2 #3 #4 #5 Roll 1st Fraction
Use two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then multiply.
Roll
1st Fraction
2nd Fraction
Product #1 #2 #3 #4 #5

26. Dividing Fractions – Fraction Tiles
Find
Visualize how many ¼’s will go into 5/8. Using fraction tiles, visualize how many ¼’s you can place upon 5/8.

27. Dividing Fractions – Fraction Tiles
Find

28. You try! Use your fraction circles or tiles.
Find

29. Quick Review Quick Review #1 #2 #3 #4 #5 Roll 1st Fraction
Use two double number cubes for this activity. The small number cube will be the numerator and the larger number cube will be the denominator. You will roll both number cubes, record the two fractions from each number cube as fractions and then divide.
Roll
1st Fraction
2nd Fraction
Quotient #1 #2 #3 #4 #5

30. Adding Fractions – Using Arithmetic
Method 2
3 x x = 23
4 x x
Method 1
3 x5 15
4 x
2 x
+5 x4 20 23 20
Method 3

31. You try! Use one of the three methods to find
If you do not know the common denominator, find the LCM.
Composite
Prime 8 4 2
Composite
Prime 3 2 3
LCM = 2x2x2x3=24

32. Subtracting Fractions – Using Arithmetic
Method 2
3 x x = 7
4 x x
Method 1
3 x5 15
4 x
2 x
-5 x4 20 7 20
Method 3

33. You try! Use one of the three methods to find
If you do not know the common denominator, find the LCM.
Composite
Prime 12 6 2 3
Composite
Prime 4 2 2 3
LCM = 2x2x3=12

34. Multiplying Fractions – Using Arithmetic
Method 1
Method 2 1
Composite
Prime 10 2 5
Composite
Prime 40 20 2 5 4

35. You Try!
Use one of the two methods to multiply fractions.

36. Dividing Fractions Using Arithmetic
Divide the following:
Before you begin, change the problem to a multiplication problem by using the reciprocal of the fraction after the division sign.
Multiply the fractions.

37. You try! Divide the following:
Before you begin, change the problem to a multiplication problem by using the reciprocal of the fraction after the division sign.
Multiply the fractions.

38. Journaling Answer two of the following questions in your journal:
Explain how to add fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.
Explain how to subtract fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.
Explain how to multiply fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.
Explain how to divide fractions using either fraction circles or fraction tiles. Give examples. Did the manipulatives help you understand this operation? Explain.

39. Practice Operations with Fractions

40. What is the value of….. ?

41. What is the value of….. ?

42. What is the value of….. ?

43. What is the value of….. ?

44. What is the value of….. ?

45. What is the value of….. ?

46. What is the value of….. ?

47. What is the value of….. ?

48. What is the value of….. ?

49. What is the value of….. ?

50. What is the value of….. ?

51. What is the value of….. ?

52. What is the value of….. ?

53. What is the value of….. ?

54. What is the value of….. ?

55. What is the value of….. ?

56. What is the value of….. ?

57. What is the value of….. ?

58. What is the value of….. ?

59. What is the value of….. ?