Answer: Choice B) 2/3, 1/9, 1/15
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Reason:
For choice A, the LCD is 30 since
- 2/3 = 20/30
- 1/6 = 5/30
- 1/5 = 6/30
We get 30 from the fact that 5*6 = 30. Notice 2/3 and 1/6 already have the LCD of 6. We could rewrite the 2/3 into 4/6 to help show this better. Effectively we want to find the LCD of 4/6, 1/6, 1/5
Cross choice A off the list because we want an LCD of 45 instead of 30.
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Choice B is the answer because
- 2/3 = 30/45
- 1/9 = 5/45
- 1/15 = 3/45
What we can do is find the LCD of 2/3 and 1/9 to get 9. The 2/3 turns into 6/9. This means we need to find the LCD of 6/9, 1/9, and 1/15
Multiply the two unique denominators to get 9*15 = 135, then divide by the GCF 3 to get 135/3 = 45.
Recall that LCD(x,y) = (x*y)/GCF(x,y)
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We can stop here since we know choice B is the answer.
But if you wanted to continue, then the LCD of 2/3, 1/5 and 1/3 is 3*5 = 15. This rules out choice C.
Choice D can be ruled out because the LCD is 27*7 = 189.