Final answer:
To order the fractions (2/7), (2/9), and (2/3) from greatest to least, find a common denominator, convert each fraction to an equivalent fraction with the denominator, and compare the numerators.
Step-by-step explanation:
We must compare the sizes of the fractions (2/7), (2/9) and (2/3) in order to sort them from greatest to least. Finding a common denominator for each fraction is one method to accomplish this. The common denominator in this instance is 63. Let's now convert each fraction with a denominator of 63 to an equivalent fraction. The equivalent of (2/7) is (18/63), that of (2/9) is (14/63), and that of (2/3) is (42/63).
We can now compare the numerators of the fractions since they all share a common denominator. The fractions (42/63), (18/63), and (14/63) are listed from greatest to least.