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approximation fractions

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which math fraction is greater through approximation:
10/21 or 15/28?

  • approximation fractions -

    One way to answer would be to convert to common denominators.
    10/21 = 40/84
    15/28 = 45/84
    so 15/28 is quite a bit larger.

    Here is another way:
    10/21 is 0.5/21 or 1/42 larger than 1/2
    15/28 is 1/28 larger than 1/2.
    Since 1/28 > 1/42, 15/28 is larger

  • approximation fractions -

    increase the first by a factor of 28/21 or 4/3 or 1.3

    10/21 * 1.3/1.3= 13/28

    Which means 15/28 is the larger.

  • approximation fractions -

    here is yet another "very old-fashioned" way:

    write the fractions side by side, and take the product of the "diagonals"

    10/21 vs 15/28

    diagonal leaning left = 10x28 = 280
    diagonal leaning right = 21x15 = 315

    since 280 < 315
    10/21 < 15/28

  • approximation fractions -

    My second method contained an error but got the right answer.
    10/21 is 1/42 LESS than 1/2, not greater.
    15/28 is greater than 1/2.
    I should have seen that right away.

  • approximation fractions -

    http://www.echalk.co.uk/tasters/taster2/taster.html

    A nice Texas estimating fractions exercise (Texas=UK)

  • approximation fractions -

    nice!

    (probably better than some of the "methods" used these days to teach fractions)

  • approximation fractions -

    Cool game !

  • approximation fractions -

    OH,MY Goodness

    went to home page
    http://www.echalk.co.uk/

    The Blob Game is hilarious.
    Catch what happens to the blob when you pick the wrong one.

  • approximation fractions -

    15/56 8/35

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