Problem 27 - Algebra 1: Concepts and Skills

Question

Find the unit rate. 20 ounces in 2.5 servings

Step-by-Step Solution

Answer

The unit rate is 8 ounces per serving. It can be calculated by dividing 20 ounces by 2.5 servings, which equals 8.

Step 1: Understanding the problem

The problem states that there are 20 ounces in 2.5 servings. This gives a ratio of ounces to servings.

Step 2: Formulate the applicable ratio

The applicable ratio here is defined as 20 ounces per 2.5 servings.

Step 3: Convert the given ratio to a unit rate

To find the unit rate, divide 20 ounces by 2.5 servings. Using a calculator will likely be helpful at this stage.

Key Concepts

Ratio and Proportion

Understanding the fundamental concepts of ratio and proportion is crucial in mathematics, especially when dealing with various quantities and their relationships. A ratio is a way of comparing two or more quantities, telling us how much of one thing there is compared to another. For example, the problem presented involves comparing the amount of ounces to servings, which can be written as a ratio.

In proportions, we discuss the equality of two ratios. Considering the exercise, if we had another scenario where we had 40 ounces in 5 servings, we could set up a proportion because the ratios of ounces to servings would equate. This concept is vital when we are looking to find out if two ratios are equivalent or to solve for unknown quantities when one part of the proportion is not immediately apparent.

Understanding ratios and proportions allows one to solve real-world problems, such as converting recipes or determining the speed of a vehicle over a certain distance.

Solving Ratios

The process of solving ratios involves finding the value of a missing term that will balance the ratio or converting a given ratio to a simpler form that can be easily understood or applied. In the context of our exercise, to solve the ratio and find the unit rate, we need to perform division. A unit rate defines the quantity of one thing per one unit of another thing.

To solve for the unit rate, we take the 20 ounces and divide it by 2.5 servings, giving us the amount of ounces per one serving. It's akin to simplifying the ratio to its lowest terms possible, where the denominator (the second value in the ratio) is 1. When dealing with fractions or decimal numbers, as in the given problem, using a calculator can simplify the process to quickly reach the solution.

Mathematical Conversion

Mathematical conversion is a pivotal skill, involving the transformation of one quantity or unit to another, maintaining its value across different units or measures. This is regularly applied in various fields, such as cooking, construction, and science.

In our exercise, the conversion involves finding how many ounces are in one serving. This is key when applying unit rates—converting raw data to a more usable form. Outside the academic context, we often use conversions without realizing their mathematical background. For instance, changing miles to kilometers, kilograms to pounds, or in this case, total ounces to ounces per serving.

Mastering mathematical conversions allows one to adapt information to the required unit of measure, which is not only useful in solving textbook problems but also extremely applicable in day-to-day problem-solving situations.