Ratio and proportion are fundamental mathematical concepts used to compare quantities and establish relationships between them.

They are commonly used in various real-life scenarios, such as cooking, scaling, and financial calculations.

Ratio:

A ratio is a comparison of two or more quantities of the same kind. It is expressed as a fraction, with a colon (:) or as the word “to” between the numbers.

For example, a ratio of 2:3 or 2 to 3 compares two quantities, indicating that one quantity is two parts and the other is three parts of the whole.

Example 1: If there are 5 red balls and 3 blue balls in a bag, the ratio of red balls to blue balls is 5:3.

Example 2: In a recipe, the ratio of flour to sugar is 2:1, meaning there are two parts of flour for every one part of sugar.

Proportion:

A proportion is an equation that states that two ratios are equal. In other words, when two ratios have the same value, they are said to be in proportion.

Proportions are typically written as fractions or using the symbol “=”. If a proportion is true, you can use it to solve for an unknown value.

Example 1: If the ratio of apples to oranges in a fruit basket is 3:2, and there are 15 apples, how many oranges are there?

Solution: Let x be the number of oranges. The proportion is (3/2) = (15/x). Cross-multiplying, we get 3x = 30, and solving for x, we find x = 10. Therefore, there are 10 oranges in the fruit basket.

Example 2: A map scale indicates that 1 inch on the map represents 5 miles in real life. If the distance between two cities on the map is 3.5 inches, what is the actual distance in miles?

Solution: Let d be the actual distance in miles. The proportion is (1/5) = (3.5/d). Solving for d, we get d = 5 × 3.5 = 17.5 miles.