Problem 24 - Algebra 1: Concepts and Skills

Question

Find the unit rate. 3 dollars for 5 containers of yogurt

Step-by-Step Solution

Answer

The unit rate is 0.6 dollars per container or 60 cents per container.

Step 1: Identify the Quantities

The quantities given in the problem are 3 dollars and 5 containers of yogurt. The task is to find how much one container of yogurt costs.

Step 2: Perform the Division

This can be identified by dividing the total cost (3 dollars) by the total number of containers (5). Carry out the division \(\frac{3}{5}\) which equals 0.6.

Step 3: State the Unit Rate

With 0.6 obtained from the division, it can be stated that the unit rate - the cost per one container of yogurt - is 0.6 dollars or 60 cents.

Key Concepts

Unit Rate Calculation

Understanding the concept of a unit rate is essential for solving problems that involve comparing different quantities. It's a specific kind of ratio where the second term is always 1 unit. For instance, if you're told '3 dollars for 5 containers of yogurt', the unit rate tells you the cost for one single container.

A unit rate can be found by dividing the first quantity by the second quantity. In essence, you are scaling down the given quantities to find out what one unit of the second quantity would equate to in terms of the first. Mathematically, you would express this computation as a division problem: if the cost of 5 containers is 3 dollars, the cost of 1 container, which is the unit rate, would be calculated using the division \(\frac{3}{5}\). This equals 0.6, so the unit rate is $0.6 per container. Remember, unit rates are incredibly useful for making comparisons and informed decisions in everyday situations, like shopping or budgeting.

Real-world Application

Take for instance, shopping for groceries. Comparing unit rates of different brands helps you to find the most cost-effective option, ensuring you get the best deal for your money.

Performing Division

Performing division is a fundamental mathematical operation that is vital for calculating unit rates. When faced with finding the cost per container, like in our exercise, division is the tool we use to break down the total cost into smaller, individual parts.

Division requires two numbers; the numerator (dividend) and the denominator (divisor). The result of division is known as the quotient. In our scenario, the numerator is the total amount of money (3 dollars), and the denominator is the total number of containers (5). The quotient, then, tells us how much one container costs: \(\frac{3 dollars}{5 containers} = 0.6 dollars/container\).

To perform division, especially when the numbers don't divide evenly, you can either do it manually or use a calculator. In both cases, the process involves breaking down the total quantity (3 dollars) into smaller parts that can be equally distributed among another quantity (5 containers), resulting in the unit rate.

Quick Tip

Always check to ensure that your quotient makes sense in the real-world context. If the result seems off, double-check your calculations or the units involved.

Identifying Quantities

Before performing any operations like division, it is crucial to correctly identify the quantities involved in the problem. Quantities represent how much or how many of something we have and can include things such as time, cost, distance, volume, and more.

In the exercise, the quantities to identify are the total cost and the total number of containers. Identifying the correct quantities allows you to set up your division problem accurately. To find the unit rate, we distinguish between the quantity that represents a collective whole (3 dollars) and the quantity that we are measuring per unit (5 containers). Keep in mind that the quantity representing the collective whole is usually the numerator, and the one representing the individual unit is the denominator.

Importance in Real Life

Being able to identify quantities is not just a math skill; it's a life skill. Whether you're cooking and need to measure ingredients, or you're budgeting your monthly expenses, the ability to pinpoint and articulate quantities is indispensable.