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what is: 2/3 X 5/6 X 14 = this is so that i can help a 5th grader. and i am horrible at fractions. please show work and or explain how to do it. so that i can show her how to do it as well.

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Lucky for you, fraction multiplication isn't so bad (at least not as bad as addition!). For fraction multiplication, we simply multiply the numerators together and multiply the denominators together. |dw:1359695096128:dw| 14 is the same as 14/1 (this helps so that we have all fractions). We just multiply straight through: the numerators 2*5*14, and the denominators: 3*6*1. Can you see how that works? :)
Does that make sense so far? :) There's just a small detail we should acknowledge after this. If we want it in simplest form, we just have to do one extra step.

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i am with you so far
Alright! :) So, in most cases, we want simplest form. So, we have to find factors in both the numerator and denominator. We can 'cancel' them out because of the property that anything (nonzero) divided by itself is just 1. For example, 3/3 = 1, 120/120 = 1...
Here, we have the factors laid out for us (kind of) and we can see what's going on. I see there is an even number on both the numerator and denominator, so it becomes apparent that there must be a 2 in both the numerator and denominator |dw:1359695697575:dw|
So, what we can do is just cross 'em out: |dw:1359695736644:dw| If it's kind of messy here, we now have this remaining: (5 x 14) / (3 x 3 x 1)
i am with you still.
So, the last step is simply to evaluate what's left. I cannot see any other factors in both the numerator and denominator, so we have the simplest form we can really get. 5 x 14 = 70, 3 x 3 x 1 = 3 x 3 = 9; 70/9 is the remaining fraction. I do not know if it is necessary to put it into a mixed number in this case, but 70/9 is the improper fraction form of our original expressioin.
ok. so if she is just putting it in simplest fraction form 70/9 is the answer?
I am thinking maybe we should put it as a mixed number, just to be safe. I am not particularly familiar with how teachers prefer it in 5th grade, so if it isn't specified I might just try to get it as "simple" as it gets. :) We'd just need to pull the highest number that can be divided by 9 from 70: the highest factor of 9 in 70 is 63 (we could guess and check that out, that might be most understandable), so (63+7)/9 = 63/9 + 7/9 = 7 + 7/9 = 7 7/9.
yeah once i talked her how to get to where we had the 70/9 she was able to help me get it into mixed fractions. thank you so much for your help. i swear this 5th grader is smarter than i am when it comes to math
Heh. :P You are welcome! Good luck to you and the student. :)
thanks. i am most likely about to put up another one. lol

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