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Adding Fractions

Adding Fractions. Grade 9 Applied Mathematics Review M. M. Couturier. Adding Fractions. Fractions can only be added when the denominators are identical. Hence the first step in adding fractions is simply to ask: “Are the denominators the same?”. Adding Fractions.

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Adding Fractions

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  1. Adding Fractions Grade 9 AppliedMathematicsReview M. M. Couturier

  2. Adding Fractions • Fractions can only be added when the denominators are identical. Hence the first step in adding fractions is simply to ask: “Are the denominators the same?”

  3. Adding Fractions • Let us take the following example: • 2 + 2 • 3 5 • The denominators are not the same; one is 3 and the other is 5.

  4. Adding Fractions • If they are not the same, we must make them the same WITHOUT changing the number. The second step is therefore to multiply the fractions by 1, such that the denominators become equal.

  5. Adding Fractions • We essentially want to find the lowest common denominator. In this case, 3x5 = 15. • 2 + 2 • 3 5

  6. Adding Fractions • We will therefore multiply (2/3) by (5/5). Recall that (5/5) = 1, hence we are not changing the number. We will also multiply (2/5) by (3/3). Also note that (3/3) = 1 so we are, again, not changing the number.

  7. Adding Fractions • What effect does this have: • (5)(2) + (2)(3) (5)(3) (5)(3) • becomes: • 10 + 6 15 15

  8. Adding Fractions • 10 + 6 15 15 • Now that the denominators are the same we can add the numerators. • 16 15

  9. Adding Fractions • Let’s do another example: • 1 + 2 4 3 • Here, the lowest common is 4x3=12. So we will multiply each fraction by 1.

  10. Adding Fractions • What effect does this have: • (3)(1) + (2)(4) (3)(4) (3)(4) • becomes: • 3 + 8 12 12

  11. Adding Fractions • 3 + 8 12 12 • Hence, • 11 12

  12. Adding Fractions • ... and another • 3 + 1 5 10 • In this case, the lowest common denominator is 10 because 2x5 = 10, so 10 does not need to be modified in any way.

  13. Adding Fractions • What effect does this have: • (2)(3) + 1 (2)(5) 10 • 6 + 1 10 10 • 7 10

  14. THE BLUEPRINT • The following will work for ALL additions of proper fractions.

  15. THE BLUEPRINT • Let us recall our strand in algebra: • a + c b d • The lowest common denominator is therefore bd; hence, • (d)(a) + (c)(b) (d)(b) (d)(b)

  16. THE BLUEPRINT • ad + bc bd bd • ad + bc bd

  17. Interactive Work • Let us visit the world wide web: • http://www.aaamath.com/fra57a-addfractld.html

  18. Interactive Work • Let us visit the world wide web: • http://www.aaamath.com/fra66k-addfracud.html

  19. Interactive Work • Didn’t like my explanations: • http://www.sosmath.com/algebra/fraction/frac3/frac37/frac37.html

  20. Interactive Work • Need more visual explanations: • http://www.visualfractions.com/add.htm

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