Final answer:
The fractions 5/4, 9/10, 2/3, and 1/5 when ordered from largest to smallest are 5/4, 9/10, 2/3, and 1/5. Using our intuition, we determine that 5/4 is larger than 1, making it largest, and 1/5 as the smallest. By simplifying, 2/3 is smaller than 9/10, establishing the middle order.
Step-by-step explanation:
To put the fractions 5/4, 9/10, 1/5, and 2/3 in order from largest to smallest, you need to compare each fraction, which can be helped by converting them to common denominators or by converting them to decimal form for easier comparison. However, by looking at the fractions, we can use our intuition and knowledge of fractions to establish the order without complex calculations.
The fraction 5/4 is greater than 1, so it is immediately the largest. Comparing 9/10 to 2/3, if we convert 2/3 to a denominator of 9 (the same as the second fraction), we get 6/9, which is less than 9/10. Therefore, 9/10 is larger than 2/3. Lastly, we can easily see that 1/5 is the smallest fraction since it is less than 1 and the other fractions are closer to 1 or more than 1. Therefore, the correct order from largest to smallest is 5/4, 9/10, 2/3, 1/5.