Trouble understanding the quotient of a ratio

I'll get straight to an example:

If you have 3 glasses of water and 5 glasses of juice, your ratio of water to juice is 3/5. The part I'm not understanding is if you were to divide the amount of water by the amount of juice, you'd get .6. What does this .6 represent? Why and how did dividing the amount of juice into the amount of water result in it? What does it mean?

This is one of the more basic concepts that I never 'got' in my math classes. It's pretty basic, but has always tripped me up. I'd really like to understand why and how it works. What exactly is happening here?

Thank you for any and all help.

Re: Trouble understanding the quotient of a ratio

You need to think of a ratio kind of like "we are going to think of this amount of water being equivalent to this amount of juice". Your ratio of water to juice is 3:5, or 3/5 : 1. This means that for every glass of juice, you would consider yourself as having 3/5 of a cup of water.

Re: Trouble understanding the quotient of a ratio

Quote:

Originally Posted by

**Prove It** You need to think of a ratio kind of like "we are going to think of this amount of water being equivalent to this amount of juice". Your ratio of water to juice is 3:5, or 3/5 : 1. This means that for every glass of juice, you would consider yourself as having 3/5 of a cup of water.

I never thought of it like that!

For every glass of juice you have 3/5 a glass of water.

For every glass of water you have 5/3 a glass of juice.

For every glass of juice you have 60% water.

For every glass of water you have 16% juice.

Let me use another example to make sure I understand! :)

If you have a ratio of boys to girls, and there are 5 boys for every 12 girls, you'd have 5/12!

For each girl you will have 42% boys.

For each boy you will have (12/5) 240% girls.

I just want to make sure I full understand this concept. Thank you for helping me. :)

Re: Trouble understanding the quotient of a ratio

Quote:

Originally Posted by

**MiguelTime**

For every glass of juice you have 3/5 a glass of water.

For every glass of water you have 5/3 a glass of juice.

For every glass of juice you have 60% water.

For every glass of water you have 16% juice.

Shouldn't these percents add up to 100?

If you have more juice(5) than water(3), why do you have more water than juice upon dividing(60%)?

I am a little confused.

Re: Trouble understanding the quotient of a ratio

When we have to mix up two things we need to know as to what concentration we want.

For example to make one glass of apple juice the vendor adds 1/5 glass of apple juice and 4/5 glass of water. Now we can say that the ratio of apple juice to water is 1:4. In percentage it would be for 20% apple juice to 80%water.

You would observe every time the sum of the percentages will come to 100%. In case of glass it will add up to 1 glass. 1/5 + 4/5 = 1

Re: Trouble understanding the quotient of a ratio

Also if one considers your illustration we have 3 glasses of water and 5 glasses of juice. Thus you get in all 8 glasses.

In 8 glasses you have 3 glasses of water i.e., 3/8*100 = 37.5% and juice = 5/8*100 = 62.5% and the percentages add up to 100%

Re: Trouble understanding the quotient of a ratio

I see, thank you both for your help. I understand now! :)