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Understanding Common and Equivalent Fractions in Mathematics

This resource provides an in-depth exploration of common denominators, equivalent fractions, and the concepts related to adding fractions with different denominators. Students will learn how to model and understand the addition of fractions by finding the lowest common multiple. Through various examples and exercises, learners will discover the rules for adding fractions, recognize patterns in equivalent fractions, and enhance their fraction manipulation skills. Engage with interactive tools to solidify understanding and practice essential math concepts.

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Understanding Common and Equivalent Fractions in Mathematics

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  1. Review Factors – Multiples – Prime Numbers Learn Alberta http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell07.swf

  2. Common Denominators • What is a common denominator?

  3. Common Denominators • What is a common denominator?

  4. Common Denominators • What is a common denominator?

  5. Determine the “Equivalent Fraction” • Which of the models below are examples of common denominators?

  6. Determine the “Equivalent Fraction” • Which of the models below are examples of common denominators?

  7. Equivalent Fractions Equivalent Fractions http://www.learnalberta.ca/content/memg/index.html?term=Division03/Equivalent_Fractions/index.html

  8. Modelling Equivalent Fractions • How can you make the fraction into more equal parts (a larger, but equal fraction) • Multiples: the product of a given number and a natural number like 1,2,3,... • Example: multiples of 2 are 4,6,8,10,...

  9. Make Equivalent Fractions • Make equivalent for the examples below. • 1. • 2. 1 = 3 = 6 = = 12 = 15 • 3 9 12 27 36

  10. Make Equivalent Fractions • Make equivalent for the examples below. • 1. • 2. = = = = =

  11. Make Equivalent Fractions • Make equivalent for the examples below. • 1. 4 = = = = • 5 • 2. 2 = = = = • 3 • Have you notice a pattern (rule) of equivalent fractions? • Hint…denominators and numerators

  12. Make Equivalent Fractions Using Pattern Blocks make equivalent fractions for: 142 2 6 3

  13. Homework • Page 234-235: • #7a, 8a, 10ab, 11, 12cd, 13ab, 16 • Extend #19, 20, 21

  14. Adding Fractions of Different Denominators Multiples http://www.learnalberta.ca/content/memg/index.html?term=Division03/Multiple/index.html Common Multiples http://www.learnalberta.ca/content/memg/index.html?term=Division03/Common_Multiple/index.html

  15. Adding Fractions of Different Denominators • You will be able to model and understand how to add fractions of different denominators • 1 + 1 • 2 3 • How can you add the two fractions together if they are NOT equal • sections (denominators)? Hint…find the lowest common multiple! New Addition Fraction Statement

  16. Adding Fractions of Different Denominators • You will be able to model and understand how to add fractions of different denominators • 1 + 1 • 2 3 • How can you add the two fractions together if they are NOT equal • sections (denominators)? Hint…find the lowest common multiple! New Addition Fraction Statement + 2 6 6

  17. Adding Fractions of Different Denominators • You will be able to model and understand how to add fractions of different denominators • + • How can you add the two fractions together if they are NOT equal • sections (denominators)? Hint…find the lowest common multiple! New Addition Fraction Statement

  18. Adding Fractions of Different Denominators • You will be able to model and understand how to add fractions of different denominators • + • How can you add the two fractions together if they are NOT equal • sections (denominators)? Hint…find the lowest common multiple! New Addition Fraction Statement

  19. What have you NOTICED??? • When adding fractions of different denominators the rules are…

  20. What have you NOTICED??? • When adding fractions of different denominators the rules are… • Both denominators must be the same • Find the lowest common denominator (multiple) • The numerators are multiplied by the same # it’s denominator is multiplied by.

  21. What have you NOTICED??? • When adding fractions of different denominators the rules are… • Both denominators must be the same • Find the lowest common denominator (multiple) • The numerators are multiplied by the same # it’s denominator is multiplied by.

  22. Write the Subtraction or Addition Statement • a) _ • b) • + • c) • _

  23. Write the Subtraction or Addition Statement • a) • b) • c)

  24. Write the Subtraction or Addition Statement • a) • b) • c)

  25. Homework • Complete pages… • Page 242-243 • #4ab,5ab, 6ab, 8, 9bc, 10bc, • 11bc, 13, 14, 15, 18a, 19a • Extend #20, 21

  26. Practical Quiz • Solve the following by: • Drawing what it looks like using fractions strips • What are the new fractions (common denominators) • 3 + 1 = 1 - 1 = • 6 6 3

  27. Mixed Numbers Learn Alberta – Mixed Numbers and Improper Fractions http://www.learnalberta.ca/content/mesg/html/math6web/index.html?page=lessons&lesson=m6lessonshell02.swf

  28. Mixed Numbers What is a mixed number? : contains a whole number with a fraction. : is the cousin of the improper fraction. 3 6 1 9 6 = Use pattern blocks to try and prove!!! How did you show this?

  29. Mixed Numbers What is a mixed number? : contains a whole number with a fraction. : is the cousin of the improper fraction. 2 1 2 7 2 2 3 8 3 3 = = Use pattern blocks to try and prove!!! How did you show this?

  30. Mixed Numbers What is a mixed number? : contains a whole number with a fraction. : is the cousin of the improper fraction. 2 1 2 7 2 2 3 8 3 3 = = How could I draw these mixed numbers! How did you show this?

  31. Add Mixed Numbers 1 4 2 4 • 1 + 1 • 1 + 1 + + + = 2 • What steps do you think need to be done in order to find • the answer? 1 4 2 4 3 4

  32. Add Mixed Numbers • 1 + 1 • Steps: • Add the whole #’s • Find Lowest Common Denominators • Add the numerators • Place the fraction into lowest terms 3 8 4 8

  33. Add Mixed Numbers (with uncommon fractions) • 2 + 4 1 3 2 5 • Steps • Add the whole #’s • Find Lowest Common Denominators • Add the numerators • Place the fraction into lowest terms

  34. Improper Fractions Mixed Numbers 23 = 6 18 = 5

  35. Add Mixed Numbers • Steps • Add the whole #’s • Find Lowest Common Denominators • Add the numerators • Place the fraction into lowest terms

  36. Add Mixed Numbers • Steps • Add the whole #’s • Find Lowest Common Denominators • Add the numerators • Place the fraction into lowest terms

  37. Add Mixed Numbers • Xavier got a new job at Perkins. At the start of his shift he • made 2 ½ chocolate pies for morning deserts. In the • afternoon he made another 3 1/3 pies. How many pies did • he make in all...show your work in both an illustration and • in addition statements.

  38. Homework • Complete pages… • Page 249: • # 4ab, 6ac, 8a, 10ef, 11ed, 13, • 18 (Good Luck with this one…)

  39. Subtracting Mixed Numbers 2 4 1 4 • 3 1 • 3 1 + = = 2 • What steps do you think need to be done in order to find • the answer? 2 4 1 4 1 4

  40. Subtracting Mixed Numbers 2 5 1 4 • 5 2 • Steps • Add the whole #’s • Find Lowest Common Denominators • Add the numerators • Place the fraction into lowest terms

  41. Subtracting Mixed Numbers • Steps • Add the whole #’s • Find Lowest Common Denominators • Add the numerators • Place the fraction into lowest terms

  42. Subtracting Mixed Numbers

  43. Subtracting Improper Fractions • Steps • Add the whole #’s • Find Lowest Common Denominators • Add the numerators • Place the fraction into lowest terms

  44. Subtracting Mixed Numbers • In gym class Millz ran 3 3/4 laps. Taylor ran 27/12 • laps. Who ran further and by how much? Show your • work...

  45. Homework • Complete pages… • Page 257-258: • # 3ac, 4c, 5ef, 6cd, 7c, 8b, 9f, 11, 16, 20

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