Can some describe to me an application for the use of ratios ?

Answer 1

Sure!
Scales on aerial photographs and maps. Sometimes called the representative fraction, they allow you to esitmate the distances/sizes of features. Also, finding the scale of an aerial photo involves finding the numerator (the focal length of the camera in the airplane) and the denominator (the altitude at which the plane is flying)... that last part can get a bit tricky.

Answer 2

There are many. One practical one is cooking. (hopefully we are talking about the same kinds of ratios here). For example, I eat white rice. When I prepare my generic white rice I usually do a 2/3 ratio. 2 cups of rice and 3 cups of water. That is 3 cups of water per every two of rice. Now, my wife bought this other instant rice which says that the ratio is a 2 to 2. 2 cups of water for every 2 cups of rice. Cooking always use ratios to make the recipe come out right.

The thing is that ocationally you may have to make a different amount of X food than usual. For example you may decide to cook more rice than the normal 3 of water and 2 of rice ratio. (note I also, add salt and cooking oil for taste but, this does not come into play in this discussion. I do not use any particular ratio. I just eye ball it). The question is what is should the new ratio should be so it comes out the same.

Ok, lets say that instead of the normal 2 cups of rice, you want to do 3 cups of rice. So, you set up your ratio. I will put the rice on top and the water on the bottom but, you can reverse them. The trick here is that you have to be consistent on both sides of the equaltion. If you do the water on top on the left then you must also do the water on top on the other side of the equation. Anyways, here is how we find out the new ratio.

known rice/ known water = new known rice/ unknown water.

or

2 cups of rice 3 cups of rice
--------------------- = -------------------
3 cups of water X cups of water

we cross mutiplie. we get

2x = 3*3
2x = 9
x = 9/2
x= 4.5 cups of water.

So, if you want to make 3 cups of rice according to my recipe and ratio then you will have to add 4.5 cups of water so that the rice has the same consistency as the 2/3 ratio.

Hope this helps.