Final answer:
Ratios and rates each compare two numbers using fractions. Although they can also be expressed as percentages or decimals, they typically use fractions, especially when establishing proportional relationships or when expressing rates, such as miles per hour or scale measurements.
Step-by-step explanation:
Ratios and rates each compare two numbers by primarily using fractions. A fraction is a way of expressing one quantity in relation to another, denoting a part of a whole as a simple division of two numbers, where one is the numerator and the other is the denominator. Ratios, like rates, can compare quantities like the number of moles of reactants to the number of moles of products in a chemical equation, and they can be expressed in several ways: as fractions (e.g., 2/3), with a colon (e.g., 2:3), or written out with the word 'to' (e.g., '2 to 3'). Additionally, ratios can be expressed as percentages (a special kind of fraction with a denominator of 100) or as decimals. A proportion occurs when two ratios are equivalent, such as 1/2 = 3/6, and is a concept closely connected to ratios and rates.
On the other hand, rates are a specific kind of ratio that typically involve a time element, such as velocity (distance per unit of time). This is expressed as a unit rate, where one of the measurements has a value of 1, like in the example of 55 miles per hour (55/1 miles/hour). Similarly, in the context of scale models, a unit scale is a ratio that compares the dimensions of an actual object to the dimensions of a representative scale model or drawing, such as a map scale that reads 1 inch = 100 feet.