Problem 58 - Prealgebra

Question

Express each ratio as a unit rate. 9 monthly issues for \(\$ 11.25\)

Step-by-Step Solution

Answer

Each issue costs $1.25.

Step 1: Identify the Ratio

The given ratio is 9 monthly issues for $11.25. This represents the number of monthly issues you receive per cost.

Step 2: Set Up the Division

To find the unit rate, you need to determine the cost for one issue. This is done by dividing the total cost by the number of issues. Set up the division as \( \frac{11.25}{9} \).

Step 3: Perform the Division

Divide 11.25 by 9 to find the cost for one issue. It helps to perform this calculation either by using a calculator or by setting up the division manually. When you divide, you get approximately \( 1.25 \).

Step 4: State the Unit Rate

The unit rate, or the cost per one issue, is \( \\(1.25 \). This means each monthly issue costs \)1.25.

Key Concepts

Understanding Ratios

A ratio is a way to compare two quantities by indicating how many times one value contains or is contained within the other. In simple terms, it describes a relationship between numbers or amounts. In our exercise, the ratio is given as 9 monthly issues to $11.25. This shows how many magazines can be obtained at a particular cost.

Ratios can be represented in several ways:

• Using a colon, such as 9:11.25.
• As a fraction, which is often more convenient for calculations (9/11.25).
• In words, like "9 issues for every $11.25".

Understanding how to manipulate and convert these ratios is crucial in solving real-world problems, as they often involve comparing different quantities to find a meaningful figure, like a unit rate.
Using ratios helps us assess and analyze relationships, such as the price per product or resource per hour. This is why they are widely used in various fields, from finance to cooking and even scientific experiments.

division in mathematics

Division in mathematics is the operation of splitting into equal parts or groups. It is one of the four basic operations and is the inverse of multiplication. When you divide, you are essentially determining how many times one number is contained within another.

For our unit rate example, the total cost of \(11.25 is divided by the number of monthly issues, 9, to find the cost per issue. If you set up the division as \( \frac{11.25}{9} \), you are asking "how much does each of the 9 magazines cost if they together add up to \)11.25?"

The process of division involves:

• Identifying the dividend (the number being divided, in our case $11.25).
• Identifying the divisor (how many groups, here it’s 9).
• Calculating the quotient, which tells us how much each individual group is worth (in this problem, the result is 1.25).

In mathematical contexts, division helps break down complex amounts into simpler units, making it easier to analyze costs, portions, or any other measure evenly.

Cost Calculation

Calculating costs is a crucial skill in everyday life, allowing individuals and businesses to understand the true price of goods or services. Cost calculation often involves determining a unit rate, which simplifies how we think about pricing.

For our example of 9 monthly issues for \(11.25, calculating the unit rate involves finding how much one issue costs. This is crucial for understanding affordability or comparing different subscription options. By dividing the total cost by the number of issues (\( \frac{11.25}{9} \)), we find a rate of \)1.25 per issue.

• This means, for every individual issue, the customer pays $1.25.
• Knowing this unit cost can help users make informed decisions, such as increasing their subscription if the unit rate is satisfactory or looking for cheaper alternatives.

Unit cost calculation is therefore not just about solving a mathematical problem; it's about applying that solution in practical, real-world ways. It can assist with budgeting, evaluating expenses, and making cost-effective choices, ensuring that consumers can maximize value and minimize waste.