Ratios,+Proportions,+and+Percents

=Ratios, Proportions, and Percents=  =Ratios=

A ratio is simply a comparison between a pair of numbers. A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon.

__Example #1__ Suppose we want to write the ratio of 8 and 12. We can write this as 8:12 or as a fraction 8/12, and we say the ratio is //eight to twelve//.

__Example #2:__ Jeannine has a bag with 3 videocassettes, 4 marbles, 7 books, and 1 orange. This kind of ratio can be written 3 ways 3:15, 3 is to 15, and 3 out of 15. Also these can be reduced to a smaller ratio 1:5 etc.

 =Proportions=

A proportion is two ratios written with an equal sign between them. Proportions are ways to find the percent or if two ratios are equal.

__Example #4__

11 is what percent of 220? Part = __11__ n= Whole = __220__ 100


 * Method#1**- To solve this problem you can write a proportion and cross multiply.

math \frac{11}{220}=\frac{n}{100} math

math 11*100=220*n math

math \frac{11*100}{220}=\frac{220*n}{220} math

n=5%


 * Method #2-** You can also use the Equation Method to solve this problem. But remember...

"Of" in mathematics means "multiplication." "Is" in mathematics means "equals."

__Example #5__ 11 is what percent of 220?

math 11 = n * 220 math

math \frac{11}{220}=\frac{n*220}{220} math

math 0.05=n math

.05*100=5%

 =Percents=

A percent is a ratio that compares a number to 100. Percents, just like fractions, describe how many parts out of a whole.

__Example #6:__

1/4 = 25/100 = 25% = 0.25 5/11 = 0.45 (with a line over it)•100 = 45% 3/8 = 0.375 = 37.5%

__Example #7__
 * Tax**

If you want to find the tax for something you have to multiply the percent into the number. If you want the total price you add the tax ad the price you already have. A coat cost $50.00 and the tax on that jacket is 5% of the price. You would turn the percent into a decimal by moving the decimal to the left two times. Then you multiply 50.00*.05. The tax is $2.50. Then you add the tax to the original price which is $50.00. and you total price would be $52.50.

__Example #8__
 * Commission and Percentage off**__

This process is the same as finding the tax but instead of adding it to the price you subtract it from the original price. Thats how you get the commission. They are having a sale at a store and and a jacket is $40.00 originally. Its 17 % off. How much does it cost? It is the same for finding the tax like I said but you're subtracting. $40.00*.17= $6.80. Then you subtract that out of the original price. You answer for the price of the jacket on sale would be $33.20.