Final answer:
To order the fractions from largest to smallest, simplify each fraction, then compare their sizes. The correct order is 5/9, 4/8 (or 1/2), 3/9 (or 1/3), and 1/4.
Step-by-step explanation:
To put the fractions 3/9, 4/8, 1/4, and 5/9 in order from largest to smallest, we need to compare their sizes. If we simplify these fractions where possible, it will be easier to compare them. Here's how we can simplify:
3/9 simplifies to 1/3 since both the numerator and the denominator can be divided by 3.
4/8 simplifies to 1/2 since both parts can be divided by 4.
1/4 is already in its simplest form.
5/9 cannot be simplified any further.
Next, we use our intuition or visualize these fractions as parts of a pie to compare their sizes. A half of a pie (1/2) is larger than a third of a pie (1/3). And since 5/9 is more than 1/2 (because 4/8 is equivalent to 1/2 and 5/9 is one more ninth than 4/8), the largest fraction is 5/9. Lastly, 1/4 is the smallest because it is less than 1/3. Thus, in order from largest to smallest, the fractions are:
5/9
4/8 (which is the same as 1/2)
3/9 (which is the same as 1/3)
1/4