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Understanding Common Denominators for Adding and Subtracting Fractions

This guide explains the process of finding a common denominator when adding and subtracting fractions. Use counting techniques to identify common multiples, which serve as common denominators. The guide illustrates how to make equivalent fractions, add or subtract numerators, and provides practice examples for reinforcement. It's designed for learners looking to improve their fraction skills and understand the importance of a common denominator in arithmetic operations.

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Understanding Common Denominators for Adding and Subtracting Fractions

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  1. & dding ubtracting ractions

  2. We need a common denominator to add these fractions. +

  3. We need a common denominator to add these fractions. + Count by 2's 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Count by 7's 7, 14, 21, 28, 35…

  4. Count by 2's 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Count by 7's 7, 14, 21, 28, 35… The first number IN COMMON that appears on both lists becomes the common denominator

  5. x 7 7 Make equivalent fractions. = X 7 x 2 6 Add the numerators = + 7 + 6 = 13 x 2 13

  6. We need a common denominator to add these fractions. + Count by 7's 7, 14, 21, 28, 35, 42, 49, 56, 63 Count by 5's 5, 10, 15, 20, 25, 30, 35, 40, 45

  7. x 5 15 Make equivalent fractions. = X 5 x 7 7 + Add the numerators = x 7 15 + 7 = 22 22

  8. We need a common denominator to add these fractions. + Count by 7's 7, 14, 21, 28, 35, 42, 49, 56, 63 Count by 8's 8, 16, 24, 32, 40, 48, 56, 64, 72

  9. 32 x 8 Make equivalent fractions. = x 8 21 Add the numerators x 7 + 32 + 21 = 53 = x 7 53

  10. We need a common denominator to add these fractions. + Count by 3's 3, 6, 9, 12, 15, 18, 21, 24, 27 Count by 5's 5, 10, 15, 20, 25, 30, 35, 40, 45

  11. x 3 9 Add the numerators = X 3 9 + 10 = 19 x 5 10 + = x 5 19

  12. We need a common denominator to add these fractions. + Count by 3's 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 Count by 11's 11, 22, 33, 44, 55, 66, 77…

  13. 15 x 3 Make equivalent fractions. = X 3 x 11 Add the numerators 22 + = 15 + 22 = 37 x 11 37

  14. We need a common denominator to add these fractions. + Count by 3's 3, 6, 9, 12, 15, 18, 21, 24, 27 Count by 6's 6, 12, 18, 24,…

  15. 4 x 2 = X 2 Make equivalent fractions. 1 x 1 + Add the numerators = x 1 4 + 1 = 5 5

  16. We need a common denominator to add these fractions. + Count by 11's 11, 22, 33, 44, 55, 66, 77… 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

  17. x 6 18 Make equivalent fractions. = X 6 x 11 11 + Add the numerators. = 18 + 11 = 29 x 11 29

  18. We need a common denominator to add these fractions. +

  19. We need a common denominator to add these fractions. + Count by 5's 5, 10, 15, 20, 25, 30, 35, 40, 45 Count by 9's 9, 18, 27, 36, 45, 54, 63, 72, 81

  20. Count by 5's 5, 10, 15, 20, 25, 30, 35, 40, 45 Count by 9's 9, 18, 27, 36, 45, 54, 63, 72, 81 The first number IN COMMON that appears on both lists becomes the common denominator

  21. x 9 36 Make equivalent fractions. Make equivalent fractions. = x9 x 5 35 Add the numerators. Add the numerators. + = 36 + 35 = 71 36 + 35 = 71 x 5 71

  22. We need a common denominator to add these fractions. + Count by 12's 12, 24, 36, 48, 60, 72, 84, 96 Count by 8's 8, 16, 24, 32, 40, 48, 56, 64, 72, 79, 80, 88, 96

  23. 10 x 2 Make equivalent fractions. = x 2 9 x 3 Add the numerators. + = 10 + 9 = 19 x 3 19

  24. We need a common denominator to subtract a fraction from another. - Count by 5's 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 Count by 11's 11, 22, 33, 44, 55, 66, 77…

  25. 15 x 5 Make equivalent fractions. = x 5 11 x 11 Subtract. = 15 - 11 = 4 - x 11 4

  26. We need a common denominator to subtract one fraction from another. - Count by 2's 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 … Count by 10's 10, 20, 30…

  27. 5 x 5 Make equivalent fractions. = x 5 3 x 1 Subtract. - = 5 – 3 = 2 x 1 2

  28. Try These A D E B F C

  29. Answers On Next Slide • Each click on the next slide reveals an answer. • Check your papers. • If you discover an incorrect answer, be able to explain your mistake.

  30. 17 27 19 20 10 9 41 28 26 21 13 12 Try These A D B E C F

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