August 21, 2007

Some percent basics

The word "percent" means "per hundred", as if dividing by hundred — a hundredth part of something.



We treat some quantity (say 65 or $489 or 1.392 or anything) as "one whole". This "one whole" is then divided to hundred equal parts in our minds, and each such part is one percent of the whole.

If the "one whole" is 650 people, then 1% of it would be 6.5 people (if you have a practical application, you'd need to round such an answer to whole peoples of course).

If the "one whole" is $42, then 1% of it is $0.42. Also, 2% of it would be $0.84.

So to find 1% of something, divide by 100.
To find 24% or 8% or any other percentage, you can technically first find the 1%, then take that times 24 or 8 or whatever is your percentage.





For example:
To find 7% of $41.50, first go $41.50/100 to find 1% or 1/100 of $41.50, then multiply that by 7. But this is the same as (7/100) x $41.50, and 7/100 is 0.07 as a decimal. In most calculations, it is more practical to use decimals instead of this "divide by 100, then multiply" stuff.

So to find 7% of $41.50, I simply calculate 0.07 x $41.50 with a calculator.

To find 10% of something, you could first divide by 100 and then multiply by 10, but it's far quicker to simply divide by 10.

For example:
10% of 90 is 90/10 = 9.
10% of 250.6 is 25.06.

When you can find 10%, it's so easy to find 20%, 30%, 40%, etc., and 5% of anything just by using the 10% as a starting point.

For example:
20% of 52. First find 10% of 52 as 5.2, then double that: it is 10.4.

Example:
A gadget costs $48 and is discounted by 15%. What is the new price?

Imagine the price $48 is divided to 100 equal parts. Then you take a way 15 of those parts. That leaves 85 of those parts - what is the dollar amount that is left? Remember you're not taking away $15 but 15% of the total.

The student needs to realize that $48 is 100% - a "one whole", and 15 of those 100 parts will be taken away.

Solution:
10% of $48 would be $4.80.
5% of $48 would be $2.40 (half of 10%).
So 15% of $48 is $7.20. Subtract that from the orignal price to get the discount price of $40.80.
With a calculator, I'd go 0.85 x $48. (MAKE SURE YOU FIGURE OUT WHERE THE 0.85 COMES FROM!)

How many percent is it?


Of the class of 34 students, 12 are girls. How many percent of the class are girls?

Here, the "one whole" is 34, the whole class. The problem is, if that 34 "one whole" was divided to 100 parts, how many of those parts would we need to make 12 students?

Or, you could compare 34 people side-by-side with 100 "something". Imagine all those 34 people put head-to-toe so they form a long line, and those 12 girls are at the one end of that line. If you'd find 100 equal-size measuring units that would total exactly the same length as your people-line, how many of those measuring units would the 12 girls equal?

This easily leads to a percent proportion:

12/34 = x / 100

Solving x, you'd get
x = (12/34) × 100.

After you do this kind of proportion a few times, you notice that each time we just compare the part to the total using division, such as 12/34 in my example. So it's quite fast then to just write that directly, when solving "what percent" problems.

For example:
A $199 guitar was discounted by $40. How many percent discount was that?

Here, the "one whole" is the original (total) price, $199. It's simply asking how many percent is 40 of 199? Just calculate 40/199, and multiply the given decimal by 100 (which is easy to do mentally).

Hope this helps some. We'll tackle the percent of change next time.
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