Math Proportions

To understand what a proportion means, we should first know what are ratios? A ratio is a comparison of two quantities by division.
Definition of proportion (Proportion definition)
A proportion is when you set two ratios equal to each other. Two ratios when are set equal to each other are called in proportion. So this is how we define proportion. A proportion can be written in two ways: -
• In fractions like a/b = c/d
• Using a colon a:b = c:d
For example: -
5/4 = 25/20
Or 5:4 = 25:20
How to solve proportions? (Solving proportions or proportion solver)
Proportions can be solved by cross – multiplication. When the terms of a proportion are cross multiplied, the cross products are equal. So when the two ratios are equal their cross products are equal.
For example if a/b and c/d are in proportion then ad = bc
To solve the missing value in a proportion, we simply cross multiply and simplify.
For instance if we have been given that x/4 = 1/12
To solve proportion, we cross multiply first, we get
12x = 4
Hence, x = 3
This is how we solve proportions.
Direct proportion
Direct proportion is defined as the increase in one quantity due to the increase in the other quantity. When two quantities are in direct proportion, their ratios are constant. For example: -
If a and b are in direct proportion then if there will be any increase in ‘a’ then it would cause the changes in ‘b’ too by the same factor. We can represent the directly proportional terms by the symbol ‘a’
For example: -
If x is directly proportional to y, then we can write it as: -
x a y
or x = ky
where k is called the constant of proportionality.