Proportion

We know that ratio is comparison of two numbers and if two ratios are equal then it is called Proportion. So, Proportion says that two ratios are equal.
Though ratio and proportion are different terms for the same mathematical concept but they are often used together as a phrase, "ratio and proportion". 8/10 = 12/15
Here, the common ratio is 4/5.
Do the ratios 18/9 and 2/1 form a proportion? (Answer it by yourself)

#Take another example of word problem so that you can understand it more.
Rob can eat 10 cakes in 60 minutes. In this way, how much time will it take to eat 35 cakes?
Let's think, it will take M minutes. Then
10/60=35/M
10M= 60 × 35
10M=2100
M= 2100/10

M=210

So, it will take 210 minutes to eat all the 35 cakes.

#You are making lemonade. The amount of sugar you need depends on the amount of lemonade mix you use. Is the amount of sugar you need proportional to the amount of lemonade mix you use?

Cups of sugar	1/3	1	3
Packets of lemonade mix	1	3	9

For each column in the table, let's write the ratio (in simplest form) of cups of sugar to packets of lemonade mix.
1/(1/3) =3 3/1=3 9/3=3
So, the answer is yes.

Ratios

We often compare two things and this comparison is called 'Ratio' in mathematics. A ratio compares two different quantities. So, it also a relation between two quantities. 

For example, there are 10 instructors and 30 girls in a hall room. So the ration between instructor and girl is 10 to 30 and in simplification it is 1 to 3 which means for every 3 girls there is one instructor.

Here are a few different ways we can describe the ratio of instructors to girls:

• There is 1 instructor for every 3 girls.
• The ratio of instructor to girls 1 to 3.
• The ratio of instructor to girls 1/3
• The ratio of instructor to girls 1:3

Ways to write ratios:

Here are several ways to describe the same ratio:

-  6 to 11

-  6:11

-  6/11