Understanding and Adding Fractions with Unlike Denominators

Explore a lesson on adding fractions with unlike denominators using visual models and concrete materials. Enhance your skills in equivalent fractions and learn to add fractions with different denominators through engaging activities. Work on practical problems and cooperative learning tasks to deepen your understanding of fractions.

• Fractions
• Math
• Education
• Visual Models
• Cooperative Learning

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1. Lesson 17 Add Fractions Unlike Denominators

2. [OBJECTIVE] The student will add fractions with unlike denominators.

3. [MYSKILLS] Equivalent fractions Adding fractions with like denominators

4. [ESSENTIALQUESTIONS] 1. How does it help our understanding of adding fractions to build with concrete materials? 2. How does it help our understanding of adding fractions to build with pictorial models? 3. How can we add fractions with unlike denominators?

5. [LESSON] Dino and Mark are doing a project for art class. It is due on Tuesday. Dino begins by drawing a -inch line, and Mark draws a - - inch line. What is the total length of the lines? 1 __ 2 1 __ 3 S Study the Problem Underline the question. This problem is asking me to find the sum of the lengths of the lines.

6. [Cooperative Pairs] Partner A Partner B

7. Add Fractions Unlike Denominators 3 8 + 1 4 The denominators are different. 1 1 ___ 1 ___ 1 ___ 8 1 ___ 4 The strips are different colors. 8 8 First Addend: RED Second Addend: YELLOW

8. Add Fractions Unlike Denominators Before the fractions can be added, they must be all in one color. Let s legally trade the fractions for fraction strips of all one color.

9. Add Fractions Unlike Denominators 3 8 + 1 4 Legally trade 1 4 for 2 8 1 so that all the strips are the same color. 1 ___ 1 ___ 1 ___ 8 1 ___ 4 8 8 1 ___ 1 ___ 8 8

10. Add Fractions Unlike Denominators 3 8 + 5 8 1 4 = We push the strips together and get the answer: 5 8 1 1 ___ 1 ___ 1 1 ___ 1 ___ 8 ___ 8 8 8 8

11. Add Fractions Unlike Denominators 3 8 + 3 8 + 1 4 2 8 5 8 = What happened to the denominators when the fractions were added? The denominators were not alike, so one had to be changed to make a fraction that was equivalent with a common denominator.

12. Add Fractions Unlike Denominators 3 8 + 3 8 + 1 4 2 8 5 8 = What happened to the numerators when the fractions were added? The numerator of one fraction changed when the denominator was changed. Once the two fractions had a common denominator, the numerators were added together to find the sum.

13. Add Fractions Unlike Denominators 3 8 + 5 8 1 4 = 1 1 ___ 1 ___ 1 1 ___ 1 ___ 8 ___ 8 8 8 8 Can we legally trade the sum for fewer fraction strips in another color? No, the sum is in simplest form.

14. Add Fractions Unlike Denominators 1 3 + 1 2 The denominators are different. 1 1 ___ 3 1 ___ 2 The strips are different colors. First Addend: GREEN Second Addend: BROWN

15. Add Fractions Unlike Denominators Before the fractions can be added, they must be all in one color. Let s legally trade the fractions for fraction strips of all one color.

16. Add Fractions Unlike Denominators 1 3 + 1 2 Legally trade 1 3 for 2 6 1 1 ___ 3 1 ___ 2 1 1 ___ 6 ___ 6

17. Add Fractions Unlike Denominators 1 3 + 1 2 Legally trade 1 2 for 3 6 1 1 ___ 3 1 ___ 2 Now all the strips are the same color. 1 1 1 1 1 ___ 6 ___ 6 ___ 6 ___ 6 ___ 6

18. Add Fractions Unlike Denominators 1 3 + 5 6 1 2 = We push the strips together and get the answer: 5 6 1 1 1 1 1 1 ___ 6 ___ 6 ___ 6 ___ 6 ___ 6

19. Add Fractions Unlike Denominators 1 3 + 2 6 + 1 2 3 6 5 6 = What happened to the denominators when the fractions were added? The denominators were not alike, and they both had to be changed to make fractions that have a common denominator.

20. Add Fractions Unlike Denominators 1 3 + 2 6 + 1 2 3 6 5 6 = What happened to the numerators when the fractions were added? The numerators both changed when the denominators were changed. Once the two fractions had a common denominator, the numerators were added together to find the sum.

21. Add Fractions Unlike Denominators 1 3 + 5 6 1 2 = 1 1 1 1 1 1 ___ 6 ___ 6 ___ 6 ___ 6 ___ 6 Can we legally trade the sum for fewer fraction strips in another color? No, the sum is in simplest form.

22. Add Fractions Unlike Denominators 1 3 + 4 9 1 1 1 1 1 ___ 9 ___ 9 ___ 9 ___ 9 1 ___ 3

23. Add Fractions Unlike Denominators 1 3 + Addend 4 9 Addend Sum

24. Add Fractions Unlike Denominators 1 3 + 1 3 3 9 9 + 4 9 4 9 3 7 9 = =

25. Add Fractions Unlike Denominators 1 3 + 4 9 7 9 = Can we legally trade the sum for fewer fraction strips in another color? No, the sum is in simplest form.

26. Add Fractions Unlike Denominators Take a look back at what happened when we did our legal trade. 1 3 = 3 9 What happened mathematically? The 3 in the denominator was multiplied by 3 and the 1 in the numerator was also multiplied by 3. 1 3 3 3 3 9 =

27. Add Fractions Unlike Denominators 1 5 + Addend 1 2 Addend Sum

28. Add Fractions Unlike Denominators 1 5 + 1 2 List the multiples of both denominators until you find a common one! 5: 5, 10, 15 2: 2, 4, 6, 8, 10, 12

29. Add Fractions Unlike Denominators 1 5 2 = 10 What happened mathematically? The 5 in the denominator was multiplied by 2 and the 1 in the numerator was also multiplied by 2. 1 2 5 2 2 = 10

30. Add Fractions Unlike Denominators 1 2 5 = 10 What happened mathematically? The 2 in the denominator was multiplied by 5 and the 1 in the numerator was also multiplied by 5. 1 5 2 5 5 = 10

31. Add Fractions Unlike Denominators 1 5 + 2 10 10 1 2 5 7 + = 10

32. Add Fractions Unlike Denominators 1 5 + 2 10 10 1 2 5 7 + = 10 Can we legally trade the sum for fewer fraction strips in another color? No, the sum is in simplest form.

33. Add Fractions Unlike Denominators 1 2 + 2 6

34. Add Fractions Unlike Denominators 1 2 + 2 6 List the multiples of both denominators until you find a common one. 2: 2, 4, 6 6: 6, 12

35. Add Fractions Unlike Denominators 1 2 3 6 =

36. Add Fractions Unlike Denominators 1 2 3 6 = What happened mathematically? The 2 in the denominator was multiplied by 3 and the 1 in the numerator was also multiplied by 3. 1 3 2 3 3 6 =

37. Add Fractions Unlike Denominators 1 2 + 3 6 + 2 6 2 6 5 6 =

38. Add Fractions Unlike Denominators 1 2 + 3 6 + 2 6 2 6 5 6 = Can we legally trade the sum for fewer fraction strips in another color? No, the sum is in simplest form.

39. Add Fractions Unlike Denominators 2 4 + 2 6

40. Add Fractions Unlike Denominators 2 4 + 2 6 List the multiples of both denominators until you find a common one. 4: 4, 8, 12, 16 6: 6, 12, 18

41. Add Fractions Unlike Denominators 2 4 6 = 12

42. Add Fractions Unlike Denominators 2 4 6 = 12 What happened mathematically? The 4 in the denominator was multiplied by 3 and the 2 in the numerator was also multiplied by 3. 2 3 4 3 6 = 12

43. Add Fractions Unlike Denominators 2 6 4 = 12

44. Add Fractions Unlike Denominators 2 6 4 = 12 What happened mathematically? The 6 in the denominator was multiplied by 2 and the 2 in the numerator was also multiplied by 2. 2 2 6 2 4 = 12

45. Add Fractions Unlike Denominators 2 4 + 6 12 12 2 6 4 10 12 + =

46. Add Fractions Unlike Denominators 2 4 + 6 12 12 2 6 4 10 12 + = Can we legally trade the sum for fewer fraction strips in another color? Yes, let s simplify.

47. Add Fractions Unlike Denominators 2 4 + 6 12 12 2 6 4 10 12 5 6 + = =

48. Add Fractions Unlike Denominators 1 6 + 2 3 List the multiples of both denominators until you find a common one. 6: 6, 12, 18 3: 3, 6, 9, 12, 15, 18

49. Add Fractions Unlike Denominators 4 6 2 3 2 = 2

50. Add Fractions Unlike Denominators 1 6 + 1 4 6 6 + Can we legally trade the sum for fewer fraction strips in another color? No, the answer is in the simplest form. 2 3 5 6 =

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