<p>In teaching a lesson on the concept of thirds, Ms. Chu divides disks into three equal groups and sets 1 group aside to illustrate 1/3. She repeats this procedure by taking the disks she had not set aside, dividing them into 3 equal groups, and setting one of these groups aside. If she wants to do this procedure 4 times, which is the minimun number of discs she can start with?
C) 27
E) 81</p>
<p>Why is 81 the answer not 27. Can you explain? My understanding is that if she starts with 81 disks, she has 3 groups of 27, sets one group of 27 aside, and 54 disks (27+27 from the other two groups) remain. How am I misunderstanding this question?</p>
<p>27 splits into 9 three times. So lets say you have 3 groups of 9, take one group out to demonstrate 1/3 (procedure done 1 time, 3 more to come). now you have 18 more disks, so lets make 3 groups with 6 disks each. Take another group out to demonstrate 1/3 ( 2 procedures done, 2 more to go). now you have 12 disks left, so lets make 3 groups of 4. take one group out to demonstrate 1/3 ( 3 procedures one, 1 more to go). now you have 8 disks left, but we cannot split 8 into 3 groups; therefore, with 27 disks we can only demonstrate 1/3 3 times, not 4. </p>
<p>With 81, you can demonstrate 1/3 four times. </p>