Ratios,+Proportions,+and+Percents+B-1

= = =**Ratios**=
 * =Ratios, Proportions, and Percents=

Ratios are pairs of numbers and they are used to make comparisons. A ratio compares two numbers by using a fraction. Ratios can be written in three different ways: 1. 2 to 3 2. 2:3 3. 2/3

__Example #1__ The ratio of squares to triangles is 3:4

__Examples #2__ Jenny had 7 Barbie dolls and Jen had 14 Barbie dolls. This ratio would be 7:14 The 7 stands for how many Barbie dolls Jenny has, and the 14 stands for how many Barbie dolls Jen has.

__Example #3__ Kyle has 3 toys and his brother has 5. Compare both results. The ratio will be 3:5. The 3 represents Kyle’s toys and the 5 represent his brother toys. The fraction will be 3/5.

Ratios can be brought to simplest terms by dividing them by the same non zero number. __Example 4:__ math \frac{2}{4}=\frac{2\div2}{4\div2}=\frac{1}{2} math

To compare ratios, create a proportion...

 =Proportions=

A proportion is a name we give to a statement that two ratios are equal. It can be written in two ways:


 * two equal fractions, [[image:http://www.math.com/school/subject1/images/S1U2L2GLa.gif width="89" height="43" align="absmiddle"]]

or,

When two ratios are equal, then the cross products of the ratios are equal. That is, for the proportion, **a:b = c:d, a** x **d = b** x **c**
 * using a colon, **a:b = c:d**

__Example #5__

math 3*35=105 math math 5*21=105 math They are proportional.

Sometimes in proportions, you have to find the unknown number which is x , n, or any other variable.

__Example #6:__ math \frac{3}{x}=\frac{4}{8} math

First you have to cross multiply. So now the solution will be 24=4x because 3*8=24. Now you just have to divide 24/4 and you will get 6 Therefore x will equal 6 and thus we have a proportion.

math \frac{3}{6}=\frac{4}{8} math

__Example #7__ How to find if two shapes are proportional (similar) ? Say if the shape is a right triangle. The height is 3cm and the width is x+6. Okay now there is another right triangle but slightly larger. This triangles height is 4cm and its width is x+7cm.

Now to answer this question, you have to set this up as an equation. It's the distributive property. So the proportions would be: math \frac{3}{x+6}=\frac{4}{x+7} math

Using cross products, the equation will be 3(x+7)=4(x+6) Once you distribute, the equation will now be 3x+21=4x+24 Subtract 24 on both sides gives 3x-3 = 4x Subtract 3x on both sides gives -3=x To find out whether or not this is true you simply plug it in. math \frac{3}{-3+6}=\frac{4}{-3+7} math math \frac{3}{3}=\frac{4}{4} math Obviously both shapes are similar when x = -3.

 =Percents=

A **percent** is a ratio whose second term is 100. The word comes from the Latin //per centum// meaning "out of one hundred," so we can think of 22% as "22 out of 100." __Example #8__

This grid is equal to 96:100 or 96%


A percent is a special ratio that compares a number to 100 using the % sign.

To change a percent back to a decimal you simply divide by 100.

__Example #9__ 16% = 16/100 = .16

To change that back to a fraction you just take that number put it over 100 and simplify.

__Example #10__ math .16=\frac{16}{100}=\frac{4}{25} math

To change a fraction into a percent you could divide the numerator by the denominator and then multiply it by 100.

__Example #11__  math \frac{1}{4} math 1 divided by 4 is .25 and multiply by 100 gives you 25%

__Example #12__ So far we have been learning about how to find the discount, sales tax, and commission. Also, we have been learning about how to make ratios.

An example from our homework to find a discount was "Itamar bought a stereo system for $65, which was 70% of the regular price. How much did the stereo cost originally?" For that problem you had to do $65.00 divided by .70 which was $92.86. The stereo system cost $92.86 before the 70% discount.