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Question 1150774: A fraction that is bigger than 5/6 but smaller than 6/7
Found 3 solutions by ikleyn, jim_thompson5910, greenestamps:
Answer by ikleyn(52898)   (Show Source):
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website!
The tutor @ikleyn has a great simple approach.
Below is an alternative method.
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Using a calculator,
5/6 = 0.833
6/7 = 0.857
both are approximate
Pick some decimal value between 0.833 and 0.857, say the number 0.840 which is the same as 0.84
Convert that decimal to a fraction. Reduce.
0.84 = 84/100 = (21*4)/(25*4) = 21/25
The fraction 21/25 is between 5/6 and 6/7
We can write  because 
Note: there are infinitely many answers because there are infinitely many values between 0.833 and 0.857 assuming you are allowed to go beyond three decimal places. If you restrict yourself to 3 decimal places, then then there aren't infinitely many answers; however, there are still a lot of answers to choose from.
Answer by greenestamps(13214)  (Show Source):
You can put this solution on YOUR website!
Let me expand a bit on the method shown by tutor @ikleyn, in case you don't see why she did what she did.
First, we will express the two given fractions with a common denominator:
5/6 = (5/6)*(7/7) = 35/42
6/7 = (6/7)*(6/6) = 36/42
With a common denominator, we can get a fraction that is between the two given fractions if we can find another fraction with the same denominator and a numerator between the numerators of the given fractions.
But there is no integer between the numerators of 35 and 36.
So we next express both fractions as equivalent fractions, by multiplying numerator and denominator of both fractions by 2:
35/42 = (35/42)*(2/2) = 70/84
36/42 = (36/42)*(2/2) = 72/84
And now we can find a fraction with denominator 84 that is between the two given fractions: 71/84
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