Hi Shea,
There are two responses on the page you mention, one by Penny and the other by Stephen. I don't know which you are referring to so I will try to explain each of them.
Penny's response:
Penny compares the fractions 2/3, 3/5 and 3/4 using a common denominator. She begins by multiplying the denominators together to get a common denominator. 3 × 5 × 4 = 60. Now consider the fractions one at a time.
2/3: The denominator is 3 and 3 × 20 = 60 so .
Using a similar argument 3/5 = 36/60 and 3/4 = 45/60. Now that the three fractions are expressed with the same denominator you can see that 36/60 < 40/60 < 45/60 so 3/5 < 2/3 < 3/4.
Stephen's response:
Stephen looks at 2/5 and 3/7. He wants to write where the question mark is either < or > but he doesn't know which. Regardless of which sign is correct if you multiply both sides by 7 the expression will remain true. Likewise if you multiply both sides by 5 the expression will remain true. Multiplying both sides by 7 and then by 5 gives 2 × 7 ? 3 × 5 or 14 ? 15. Now it's clear, ? should be <. Hence .
I hope this helps,
Harley
