Geometry Using Proportions and Ratios

Welcome back to Educator.com.0000

For this next lesson, we are going to talk about ratios and proportions.0002

First, what is a ratio? A ratio is a comparison between two things, most likely two parts or two quantities--two of something.0006

If the first thing is a, and the second thing is b, we have three ways that we can write ratios.0018

The first way is by saying a:b, and it is going to be read with the word "to", "a to b," "x to y."0026

You can write it like this; this is how it is mainly written--ratios are mainly written like this, a:b.0038

It could also be written as a fraction; most likely, instead of writing it like this, you would probably write it like this: a/b.0046

Fractions could be a ratio between a and b.0053

If you have, let's say, boys to girls, you can write it "boys to girls" like that, or you can write boys to girls.0061

You are comparing the number of boys and the number of girls.0080

So, if I say that there is a classroom with 30 students...let's say that 13 are boys and 17 are girls;0085

then you are going to write 0797; and make sure...if I ask for the ratio of boys to girls,0096

you have to give the number of boys before the number of girls.0105

You have to give the numbers in the order of the ratio: boys to girls is 13 to 17.0110

Or if it asks for the ratio of girls to boys, then you would have to say 17 to 13.0117

Then, a proportion would be two equal ratios--if you have a ratio equaling a ratio, then that becomes a proportion.0126

An equation with two equal ratios--we know that an equation is anything with an equals sign,0136

so, since we have a ratio, equals sign, ratio, that becomes an equation, which is a proportion.0141

So, here is one ratio, here: 2:3; if I have an equivalent ratio (equivalent just means anything that is the same, equal to)--0149

an equivalent ratio to that could be, we could say, 4/6; that is equivalent: 2:3 is equal to 4:6.0162