Mathematical+Reflections,+p.+25

JaePark Math 7B 1/29/09  Comparing and Scaling Big Idea Many important practical and mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use and how we should use them. __**1)Give an example of a situation in which it makes sense to use percents to make comparisons.**__ When you are dealing with large numbers, and when you might not know how much it could be out of a simpler number, say 100. When you know how much it takes from 100%, you know approximately how big and large it is. __**2)Using your example from part 1, who how to make a comparison using percents.**__ Let's say you don't know what 60 out of 120 is. And you don't know what 100 out of 200 is. Well, let's find out by using percents. 60/120= 6/12= 1/2. Then, you automatically know one half is 50%. The next problem. 100/200= 1/2. Since 1/2 is 50%, you know that 60/120 is equal to 100/200 which are both 50%. __**3)**____**Explain why percents are useful for making comparisons.**__ As you saw from the last question above, it's very useful for making comparisons. When you are dealing with complicated numbers, you might not know which is greater. So you use the steps above (or your own) to find the percentages, and you know which is greater than which. __**4)Give an example of a situation in which you think another form of comparison is better that percents. Explain your reasoning.**__ Sometimes, percentages aren't the bes way to fine out which is greater than which. If the denominators are the same, you can easily tell which is greater than which by just looking at the numerator. Which is a lot easier than just finding the percentage. __**5)Can you find a percent comparison from a ratio comparison? Explain how, or tell what additional information you would need.**__ It is possible for you to find out if a percentage is greater than a ratio. or example: Is 50% greater than 1:2? To do that, you will need to turn the ratio into a fraction, which is 1/2. Then, divide the denominator from 100 which is 50. Then multiply it by the numerator. Then you get 50%. So now you know, 50% is equal to 1:2. __**Summary:**__ Percentages are useful sometimes, but not always. And there is always a way to show what's greater even though the numbers are shown in a different way.