Percent. It's an ugly word with an uglier place in mathematics. Here are some examples.
Let's say you're working at an office. Normally, the people in the office are okay (except that creepy, rat-like weirdo who chews on your pencils) and your boss is pretty mellow. Now, one day, your boss is feeling a bit hung over from the previous night (his wife left him). So now, feeling pretty crappy and bitter, he decides to take his pent up anger out on you. So, when you don't expect it, he takes the coffee pot and dumps the scalding contents on your head. Realising what he's done, he quickly reacts and decides to increase your pay check as compensation. By 245%.
Now here's the question:
What is 245% of $356.80 (your original paycheck)?
To find this, you merely find 2x (200%) your paycheck, add half the amount of your original pay and subtract 5%.
Doing the first step is easy, just multiply you check x2.
So, 200% of %356.80 is... $713.60!
When we add half of your original amount, which is 178.40, you get $892.
Now, when we subtract 5%... you get $847.4.
You may not be able to build that hi-tech home entertainment system, but at least you can make rent this month. Not too bad.
Here's another example in the form of a word problem.
Let's say you quit your old job and are in need of some money. You only have $129.95 and are pretty desperate. One night at a bar, you make a bet with your friend: You bet the last of your money that you can consume more shots than he can. If you do you get X% of your money. X being the number of shots you drank times 1o.
Twenty minutes later, you and your friend are neck in neck. Your drinking buddy suddenly doesn't feel so good. And a few seconds later, he pukes. You have officially drank him under the table and you have consumed 36 shots. You get 360% of your original $129.95.
How much did you receive?
To find the answer, you have to find your amount of money times 3, then add 3/5 of the original amount to the result.
I'll show you. First to find the 300%. That's simply 3x the $129.95.
129.95 x 3 = $389.85
Now that we have the 300, we need to figure out the 60. The 60 is equal to 3/5 of 129.95.
We can also achieve 60 by subtracting 40%.
So, 129.95 - 40% = $77.97
Now, just add the two together and you get $467.82.
Okay, here's your next question. After your buddy has waken up from his alcohol-induced state you both go home. When you get back to your apartment, you do what you always do: log on to your laptop. Tonight, you decide to play an MMORPG with friends. You are a half-orc barbarian, 18 STR, 16 DEF, 2 CHAR, etc. (To those who can't understand what these mean, LEARN TO PLAY NOOBS.)
Anyway, your walking through a forest, your boots cracking the twigs with every step. You then see something out of the corner of your eye. You turn and find a glowing flower on the side of the path. While going over to inspect it, a fairy suddenly pops out. It's holding a large sword. It offers it to you in exchange for a certain percentage of your gold. You have 730 gold and the fairy demands 68
3/4 % of it. Do you accept the deal?
Okay, first you have to find out what 60% of 730 is, what 8% of it is and what 3/4 of a percent it is.
First, the 60. That's easy, 730 - 40% = 438
Now for the 8. 730 - 92% = 58.4
Finally, the 3/4. To find this, you need to find 1%, divide it by 4, and multiply the product by 3.
730 - 99% = 7.3
7.3 / 4 = 1.825
1.825 x 3 = 5.475
Add your three results together (5.475, 58.4, 438) you get 501.875 gold.
You decide to give him most of your hard earned gold and in return you get a High Quality Long Sword. Now you can kill those annoying goblins.
Now after you completely pwn'd that goblin hoarde and ultimately got beaten out at 2 am by the blue screen of death. You then, reluctantly go to sleep.
1 pm. You are abruptly awakened by the buzzing sound of your alarm. You shut it off and then realize what time it is. Then you realize where you're supposed to be. You quickly burst out of bed, run into the door in your confused state and then get dressed. You then, get yourself to the balcony and slide down the fire escape into your car. You speed your way to the arena. You almost forgot the hockey game you were supposed to go to.
Second period. Half time. You just saw the Toronto Maple Leafs score their third goal against the New Jersey Devils. Now it's time for the half time contest. The announcer goess to the ice and calls out the following position. He says Section A, Row 2, Seat 12. Your seat. You quickly get out and onto the ice. The announcer asks you the following question:
"This arena seats 4900 people. Tonight, only 63% of the arena is filled. How many people are seated in the arena?"
There is an easy way to solve this. There are 4900 people in this arena. Divide the 4900 into 49 100's. Or, 49 wholes. Out of that 100, 63 of the seats are taken. Multiply that 63 by 49 and you get 3087.
After this mental math you quickly answer 3087. The announcer says you are completely right.
Congradulations! You have just won tickets to the Stanley Cup Finals!
On your way home from the game, with your newly claimed prize, you find your friend Miguel. He looks pretty freaked out. He says he just bought a Maxima for $4700. Now, here's the trouble. Miguel completely failed his math when it came to percents. The dealer said he had to pay a down of 19
1/2 percent of the total $4700. Can you help him?This problem can be solved the same way as the last one. Just divide the 4700 into 47 groups of 100. Then subtract 19 1/2 from each group. That is equal to 19 1/2 x 47. 19.5 x 47 = 916.5
Miguel has to pay $916.50 to get his Maxima.
Circumference - The boundary of or distance around a circle.
The angles ABC is called a Central Angle.
Angles ADC and AEC are examples of Subtended Angles.
