Final answer:
To order the fractions, we compare their sizes and convert them to have the same denominator if needed. The order from greatest to least is 3/4, 2/3, 2/5, 1/3, 5/8
Step-by-step explanation:
To order fractions from greatest to least, we need to compare the sizes of the fractions.
- The greatest fraction among the given options is 3/4.
- Next, we compare 2/3 and 5/8. To do this, we can convert them to have the same denominator. We can multiply 2/3 by 8/8 to get 16/24, and we can multiply 5/8 by 3/3 to get 15/24. Now, we can see that 15/24 is less than 16/24, so 2/3 is less than 5/8.
- Next, we compare 2/3 and 1/3. Since the denominators are the same, we can compare the numerator. 2 is greater than 1, so 2/3 is greater than 1/3.
- Finally, we compare 1/3 and 2/5. To compare these fractions, we need to find a common denominator. The least common multiple of 3 and 5 is 15, so we can multiply 1/3 by 5/5 to get 5/15, and we can multiply 2/5 by 3/3 to get 6/15. Now, we can see that 6/15 is greater than 5/15, so 2/5 is greater than 1/3.
Therefore, the order from greatest to least is 3/4, 2/3, 2/5, 1/3, 5/8.