Section 22.4 Closing Ideas
As mentioned before, most decimal multiplication is performed by calculators or computers. But computers are usually not able to perform percent calculations without a person correctly identifying the part, the whole, and the percent, and then determining what calculations are required to solve the problem. With the goal of mathematical thinking in mind, the problems in this section were set up so that calculators would not be needed.
But if you were run into a situation where you would need a calculator, as long you have the correct mathematical thinking then all you need to do is replace the mental calculation with a calculator calculation. There is no real loss (from the perspective of logic) in trading that out. Here is the light bulb problem again, but with slightly more realistic numbers:
The last batch of 1500 light bulbs had 37 defects. What is the percent of defective bulbs?
The part: The number of defective bulbs is 37.
The whole: The total number of bulbs in the batch is 1500.
The percent: The percent of defective bulbs is unknown.
Answer: About 2.5% of the bulbs were defective.
Notice that the overall process is unchanged, and it's just a matter of using different numbers. This is very similar to the process of learning to treat variables like numbers in other calculations, such as reducing fractions. In fact, the particular area of mathematical thinking, which is sometimes called algebraic reasoning, is the whole idea that you can generalize the methods and ideas of simple examples so that they can be applied in more complex situations. You got a hint of this type of reasoning in the last few problems where you had to do a mental manipulation before putting the numbers into the parts of a whole framework. And that is the skill that you should be aiming to develop in your college level courses. You want to be more than a calculator.