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Twenty percent more -- than what? How many extra cookies make twenty percent? How many cookies were in the original box before it was "increased?" How many cookies did you really plan to buy? How many people will be eating the cookies? How long do you want them to last?

People often argue that math proficiency is not necessary to the conduct of ordinary business. There is no better way to refute this argument than to look at the way we spend our hard-earned money. Here are a few more examples.

It has become commonplace for commercial products to advertise that they have improved the quality or quantity of their product by a stated a percentage, saying things like this box contains "twenty percent more," or this product is "twenty percent more effective." Such terms are often misleading.

If the original amount in a container is small before the increase, then the percentage of increase is also small. If you increase a box of ten cookies by twenty percent, you've only added two cookies. But to an audience that is mathematically unsophisticated, twenty percent sounds like a lot more than two cookies.

In terms of quality, the percentage of increase has no measurable meaning. To suggest that a washing powder will get your clothes twenty-percent whiter has no meaning unless there is a numerical value assigned to the original word "white."

Another misleading technique is frequently used in automobile advertisements. A typical example relates to "saving" money on the purchase of a new car. It is quite common for a car dealer to advertise that one can "save" on a car if purchased while the "sale" is going on.

The saving is based on an artificial "list" price which may or may not even exist. If a dealer says that a car is worth $10,000, and then agrees to sell it for $7000, the customer did not save $3000. He spent $7,000! Where's the saving?

Another variation is "trade-in value." One ad promises to take a car in trade for "$2000 more than it was worth" and sight unseen. How can anyone offer "more than it's worth" without knowing what it is worth?

The answer, of course, is that the so-called sale price of the car is artificially increased to offset the difference, making it look like the buyer benefits. The dealer gives the buyer a $3000 trade-in figure on a car that's really worth $1,000, then increases the price of the sale car by $2000. Where's the saving?

A scam used frequently to sell mattresses is the fallacy of the long guarantee. It is typical to offer 15- or 20-year guarantees on mattresses. It is also typical for the mattress with the 20-year guarantee to be more expensive than the one with the 15-year guarantee.

If you purchase a mattress with a 20-year guarantee and decide to use the guarantee after 18 years, several factors apply.

1. Is the store that sold the mattress still in business 18 years after purchase?
2. Does the customer still live in the same city? If you now own a mattress that is under a guarantee from a store in another state, what's that guarantee worth?
3. What does the guarantee say? Can you turn in your 18-year old mattress and get a brand new one? Does the same model mattress cost the same as it did 18 years ago?
4. Did you save the receipt? Can you prove that you purchased the mattress 18 years ago? Maybe some people are extremely organized, but many would have difficulty finding receipts for purchases made 18 days ago.

The end result of this particular scam is that these wonderful lengthy guarantees, for which you often paid extra, are usually meaningless and the merchant doesn't have to honor them.

This list would not be complete without mentioning the complexities inherent in the billing procedure. There is no better example than the situation with telephones. Few reading this article can explain every charge shown on a monthly phone bill.

And consider the long list of variables for cellular phones that include: the day of the week and the time of day calls are made, the number of calls made in a given period, zones, roaming charges, long-distance definitions, and extra "services." Try making a logical, economical decision regarding selection of a cell phone plan!

"Sale" prices are yet another example. A price is established for an item when it is put on the market. That price is not only based on the quality of the item, it is based on style, desirability, season, proximity to holidays, and other intangible factors.

Later, when the style or season has changed, or when the gift-giving holiday has passed, the same item is "drastically reduced" by as much as "forty percent." Sometimes it's even sold "below cost." How can merchants sell an item for less than they paid for it, and still make a profit?

This list is only a sampling taken from personal experiences. There are obviously more. What's your favorite? Do you still think math is unimportant?

Here's a math problem for you: Figure out how much money you would save if you didn't fall for these financial "fibs," but rather figured out what things were really worth and whether buying twenty percent more cookies was really a good idea.