Misuse of greater than - Math Central

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Question from Kenneth:

Question:

I have an old business mathematics textbook. The authors have indicated that the following expressions indicate multiplication:

$? is 2/3 greater than 90; ? is 2/3 smaller than 90. They also indicated that the following expression would indicate division: 30 is 2/3 greater than ? and 30 is 2/3 smaller than ?.

How can these phrases indicate multiplication and division? How can 60 be 2/3 greater than 90 and also smaller than 90 as indicated above. What were the authors thinking? I have added the page from the book that indicates what I have explained in my message

I thank you for any helpful reply that may be sent to me.

Kenneth

Hi Kenneth,

I have added the page you sent me.

I also find this disturbing. If I asked for ? where "? is a more than 90" and a = 5, then the answer would be ? = 95. But the author seems to be saying that if a is a fraction, for example, a = 2/3 then you multiply 90 by a rather than adding a to 90.

In the explanation the author says that "of", "as much as", "greater than", "less than", "smaller than", etc. all indicate multiplication. I completely disagree. "Of" and "as much as" indicate multiplication but "greater than", "less than", and "smaller than" have completely different meanings.

Harley

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