Question

Find the unit rate. 6 ounces for 2.5 servings

Short answer

The unit rate is 2.4 ounces per serving.

Step-by-step solution

Identify the Total Quantity and the Total Number of Servings

The exercise provides that there are 6 ounces and 2.5 servings.

Divide the Total Quantity by the Number of Servings

In this case, it involves dividing 6 ounces by 2.5 servings. Using a calculator preferably, \( \frac{6}{2.5} = 2.4 \)

Interpret the Solution

The solution obtained implies that there are 2.4 ounces per serving.

Key concepts

Ratio and Proportion

Ratios are a way of comparing two or more quantities to give a clear representation of their relationship, typically through using two numbers separated by a colon. For example, if there are 10 apples and 5 oranges in a basket, the ratio of apples to oranges is 2:1. This indicates that for every 2 apples, there is 1 orange. Proportions, on the other hand, are equations that show that two ratios are equivalent. When we say that one quantity is to another as a third is to a fourth, we are expressing a proportion; for instance, if one set of books weighs 3 kg and the other set weighs 6 kg, and a third set of books weighs 2 kg, then the proportionate weight of the hypothetical fourth set would be 4 kg if we want to maintain the same ratio, 3:6 :: 2:4.

Understanding ratios and proportions is crucial when finding unit rates. This term refers to a ratio that compares a quantity to one unit of another quantity, often used in everyday life, such as determining speed (miles per hour) or price rates (cost per item). The unit rate is a type of proportion that tells us the quantity of the first type for exactly one unit of the second type. In our case, determining how many ounces are there for one serving leads us to find the unit rate of this particular ratio.

Solving Ratios

Solving ratios involves finding the value of a missing term in a pair or series of related terms that form a ratio. This is where mathematical operations—mainly division and multiplication—come into play. To simplify or find the unit rate of a ratio, you typically divide one term by the other. As in our textbook example, we divided 6 ounces by 2.5 servings to find out how many ounces there are per serving. This is an essential step in solving ratios as it allows us to understand the relationship between the terms on a per-unit basis.

Additionally, in more complex situations, cross-multiplication is used to solve a proportion, where the product of the means equals the product of the extremes. In essence, solving ratios is about manipulating these relationships until you find a meaningful comparison which often involves creating a unit rate.

Mathematical Operations

Mathematical operations consist of basic processes such as addition, subtraction, multiplication, and division, which are the building blocks for more advanced math concepts. When solving problems involving ratios and unit rates, division is often used to derive the unit rate, and multiplication is applied when finding equivalent ratios. Understanding how to properly perform these operations is fundamental to not only arithmetic, but also to algebra and beyond.

In our exercise, the division of 6 ounces by 2.5 servings is a straightforward operation that yields the unit rate. Nevertheless, sometimes these operations involve more complex numbers or require additional steps, such as converting mixed numbers to improper fractions or dealing with decimals. Grasping mathematical operations not only aids in problem-solving but also enhances logical thinking and accuracy in dealing with quantitative information.