Grades 5-6 Video Solutions 2022-2022_5-6

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Number 10. Which of the following fractions of a whole turn should the Ferris wheel turn to bring a white pod to the top?  The first thing to note is that this Ferris wheel has 12 equally spaced pods, 6 of which are black, 6 of which are white, and they alternate in this fashion shown here.  And then, any rotation of an even numerator of x over 12th of a turn will result in a black pod at the top.  For example, if there's a rotation of 2 twelfths, then we'll go from 1, 2. Similarly, so this is black.  And then similar, if it's 4, then we go 1, 2, 3, 4. So the black pod would go back to the top.  Any rotation of an odd numerator of x over 12th of a turn will result in a white pod at the top.  So if we go 1 twelfth of a turn, then we'll get this white pod. If we go 3 twelfths of a turn, we'll go 1, 2, 3, and again this is going to be another white pod.  Of course, the direction that we turn doesn't really matter because it's symmetrical across this axis. So even if we go 1 this way, we'll still end up with a white pod at the top.  And the same for the previous. So looking at all of our answer choices, we can get them to a common denominator of 12 to see what their numerator will be.  So 1 half is 6 twelfths, 1 third is 4 twelfths, 1 sixth is 2 twelfths, 1 twelfth is just 1 twelfth, and then 5 sixth is 10 twelfths.  So based on this, the only odd number that I see here is 1 twelfth.  And because of that, we'll have a 1 twelfth turn, which will bring a white pod to the top, and the answer must be D.

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