



 
Kenneth, This is a good question  this sort of thing shouldn't be taken for granted! I don't consider "60% as much as" to be very elegant phrasing, but: "Sixty per cent" is short for "sixty per centum", or "sixty per hundred." This indicates a wholenumber ratio of 60:100 or 3:5, which is represented by the lowestterms fraction 3/5 and the exact decimal 0.6. "As much as" means that quantities are being compared  "much" is an adjective referring to quantity. So "60% as much as" means "for every hundred units of quantity in $\$30,$ the answer has sixty such units." So we could solve this as "$\$30$ is thirty times a hundred cents, so the answer is thirty times sixty cents" or as "$\$30$ has a hundred thirtycent chunks, so the answer has sixty thirtycent chunks" or in many other ways, all giving the answer $\$18.$ We are really dividing and multiplying here: dividing is the same as multiplying by a unitnumerator fraction of the form 1/n, and multiplying by a fraction m/n (or the equivalent decimal) carries out the multiplication and the division in one go. Good Hunting!
 


Math Central is supported by the University of Regina and the Imperial Oil Foundation. 