DIFFERENCE BETWEEN PROPORTION & RATIO -
Proportion and ratio are both mathematical concepts used to compare quantities or parts of a whole, but they are used in slightly different ways and have distinct definitions:
1. Ratio:-
(i) A ratio is a comparison of two or more quantities or numbers in relation to each other.
(ii) It is typically expressed as a fraction, with a colon (":"), or using the word "to."
(iii) Ratios are used to show the relative sizes or quantities of different parts of a whole or different components of a group.
(iv) Ratios do not have to be simplified to their simplest form.
(v) Example: If there are 4 red marbles and 6 blue marbles in a bag, the ratio of red marbles to blue marbles is 4:6 or 4/6, which can be simplified to 2:3 or 2/3.
2. Proportion:-
(i) A proportion is a statement that two ratios are equal to each other.
(ii) It is an equation formed by setting two ratios (fractions) equal to each other.
(iii) Proportions are often used to solve problems involving unknown quantities where you can set up a relationship between known and unknown values using the concept of equality of ratios.
(iv) Proportions must be simplified to their simplest form to determine if they are true or not.
(v) Proportions are written in the form of fractions or equations, such as:
Example: If you have a proportion such as 2/3 = 4/6, you can simplify both sides to 1/1, which means the two ratios are equal and form a true proportion.
In summary, a ratio is a comparison of two quantities, while a proportion is a statement that two ratios are equal. Ratios are used to express relationships between quantities, while proportions are used to solve problems involving equal ratios.