Final answer:
Proportion in mathematics involves the equivalence of two ratios, and can be direct or inverse. A percentage is a fraction with a denominator of 100, representing parts out of a whole, calculated by dividing the part by the whole and multiplying by 100. Both proportions and percentages are key in comparing sizes, quantities, or concentrations in various contexts.
Step-by-step explanation:
Proportion in mathematics refers to the equivalence of two ratios or fractions. For example, if we have a proportion such as 1/2 = 3/6, it indicates that these two ratios are equivalent. Proportions can represent various relationships, including direct and inverse. A direct proportion would be something like x is directly proportional to y, often expressed as x × y. In contrast, an inverse proportion might be expressed as a inversely proportional to b (a ∞ ¹).
When dealing with scale, such as in maps or models, a unit scale is used to convert between real-life size and the model or map's size, such as 1 inch representing 100 feet. This example, 1 inch/100 ft, is a specific type of ratio.
A percentage, on the other hand, is a fraction with a denominator of 100. It is a universal method to express a portion out of a whole that has been divided into 100 equal parts. Calculating percents involves dividing the part by the whole and then multiplying by 100.
For instance, if someone scores 96 out of 100 on a test, their performance is calculated as (96/100) × 100%, which results in a percentage of 96%.