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Compare and order the following fractions from least to greatest 5/4,5/12,5/6

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2 Answers

To answer this question you can find a common denominator for the three fractions and then compare them:

5/4 = 15/12

5/6 = 10/12

5/12 = 5/12    

So, comparing the above, ordered from least to greatest is 5/12, 5/6, 5/4.

You could also glance at the fractions and see that 5/4 is the only improper fraction, so it is greater than 1, while the other two are less than 1. So, 5/4 is the largest of the three fractions.

If you compare the other two fractions, 5/6 with 5/12, you see that the numerators are the same. That means that the fraction with the larger denominator is the smaller of those two fractions.

The answer is 5/12, 5/6, 5/4 This question is being nice to us because the numerator (the number on the top of the fraction) is the same for all three fractions. Let's imagine we have 5 cookies (the numerator) and we want to divide them equally amongst various friends (the denominator). Clearly, trying to divide 5 cookies amongst 12 friends, each friend is going to have less cookie than if we divided the same 5 cookies between 4 friends. So if the Numerator is staying the same (5) and the denominator is decreasing (12, 6, 4) then that means the fraction is increasing (5/12, 5/6, 5/4). The amount of 5 cookies split amongst 6 friends is more than 5 cookies split amongst 12 friends (5/12 < 5/6), and the amount of 5 cookies split amongst 4 friends is more than 5 cookies split amongst 6 friends (5/6 < 5/4). Alternatively we could look at the approximate value of each fraction. We know that 5/4 is more than 4/4 which means that 5/4 is more than 1. Stated again in symbols 1 < 5/4. we know that 5/6 is less that 6/6 and greater than 3/6 which means that 5/6 is between 1/2 and 1 or in symbols 1/2 < 5/6 < 1. Finally 5/12 is a little less than 6/12 which means that 5/12 is less than 1/2 or 5/12 < 1/2. Since 5/6 <1 and 1 < 5/4 we know 5/6 < 5/4 and since 5/12 < 1/2 and 1/2 < 5/6 we know 5/12 < 5/6 so 5/12 < 5/6 < 5/4. Let me know if you have any questions.