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Decimal & Fractions Challenge
Posted:
Aug 23, 1995 3:48 PM


On 8/21/95 we posted a response to Ted Alper regarding the Numbers Challenge Game and a variation of it using a decimal or a fraction in place of one of the whole numbers on each fournumber card. We got so many requests for answers to our sample problems that we decided to post the following. These are possible solutions to reach every target number from 1 to 24. There are other ways of reaching each target number.
An example of Fractions Challenge: use 1,3,6 and 2/3 to reach 1 to 24:
2/3 x 6  3 / 1 = 1 2/3 x 6 + 1  3 = 2 (6+1) / (32/3) = 3 1 x 6  2/3 x 3 = 4 1 + 6  2/3 x 3 = 5 2/3 x 1 x (3+6) = 6 2/3 x 3 + 6  1 = 7 2/3 x 6 + 1 + 3 = 8 2/3 x 3 + 1 + 6 = 9 2/3 x 3 x (61) = 10 2/3 x 6 x 3  1 = 11 (1+3) / 2/3 + 6 = 12 2/3 x 6 x 3 + 1 = 13 2/3 x 3 x (1+6) = 14 ( 1+3+6 ) / 2/3 = 15 2/3 x 6 x (3+1) = 16 (62/3) x 3 + 1 = 17 ( 2/3x3+1 ) x 6 = 18 ( 1+62/3 ) x 3 = 19 1 x 3 x (2/3+6) = 20 (2/3+6) x 3 + 1 = 21 1 x 6 x (3+2/3) = 22 (2/3+3) x 6 + 1 = 23 ( 6/2/31 ) x 3 = 24
An example of Decimal Challenge: use 2,3,6 and .5 to reach 1 to 24:
(.5+3) x 2  6 = 1 2 + 3  .5 x 6 = 2 .5 x 2 + 6 / 3 = 3 .5 x 2 + 6  3 = 4 (.5+2) x 6 / 3 = 5 2 x 6  3 / .5 = 6 (6+2) x .5 + 3 = 7 3 + 6  .5 x 2 = 8 .5 x 2 x 3 + 6 = 9 .5 x 2 + 3 + 6 = 10 .5 x 6 x 3 + 2 = 11 .5 x 3 x (2+6) = 12 3  2 + 6 / .5 = 13 3 x 6  2 / .5 = 14 .5 x 6 x (3+2) = 15 (2+3) / .5 + 6 = 16 3 x 6  2 x .5 = 17 2 x 3 + 6 / .5 = 18 .5 x 2 + 3 x 6 = 19 (6+3) / .5 + 2 = 20 6 x 2 / .5  3 = 21 ( 2+3+6 ) / .5 = 22 (.5+3) x 6 + 2 = 23 (62) x 3 / .5 = 24
Remember, the use of the dice to determine the target number makes it possible to modify the game for four levels of ability: beginners use one die to reach a target number of 1 to 6; two dice reach 1 to 12, 1 to 18, or 1 to 24.
We would appreciate receiving feedback from any of you out there with suggestions about the appropriate grade level for Fractions Challenge and Decimal Challenge. Just email us or post to the list. Thanks!



