Question

Write and solve an equation to answer the question. Each household in the United States receives about 676 pieces of junk mail per year. About how many pieces does a household receive per week?

Short answer

An average household in the United States receives approximately 13 pieces of junk mail per week.

Step-by-step solution

Understand the Conversion Between Years and Weeks

One first needs to understand that there are 52 weeks in a year. This will be helpful in the subsequent step where the number of junk mail pieces for a year will be divided by the number of weeks in a year.

Construct and Execute the Division

Set up a division equation, which is 676 (the total pieces of junk mail per year) divided by 52 (the number of weeks in a year). In mathematical notation, this can be expressed as \(\frac{676}{52}\). Carry out the division to find the number of pieces of junk mail a household receives per week.

Interpret the Result

The result from the division operation in step 2 represents the number of pieces of junk mail an average household in the United States receives per week.

Key concepts

Conversion Between Years and Weeks

When we talk about measuring time, we usually use standard units such as seconds, minutes, hours, days, weeks, months, and years. Understanding how these units relate to each other is crucial in many aspects of everyday life, including mathematics. Converting from one unit of time to another is a fundamental skill that's often used in solving algebraic equations, particularly when dealing with rates or averages over time.

For instance, there are exactly 52 weeks in a year. This piece of information is essential when you're attempting to break down an annual amount into weekly quantities. Let's look at the example presented: a household receives 676 pieces of junk mail per year. To determine how much junk mail they receive on a weekly basis, one must divide the yearly amount by the number of weeks in a year -- that is, 52.

This conversion process is not limited to years and weeks; it's a versatile method that can be applied to various situations. By mastering the relationship between different units of time, you can unlock the ability to swiftly convert and understand rates, proportions, and averages in numerous contexts.

Division in Mathematics

Division is one of the four basic operations in arithmetic, alongside addition, subtraction, and multiplication. It represents an equal distribution of a quantity into a specified number of parts.

In our example with the junk mail, we encounter the division operation when figuring out how many pieces of mail are received on average each week. To perform this, we set up a division equation, written as \(\frac{676}{52}\) in mathematical notation. Division can be understood as the process of dividing the numerator (the number on top, representing the total amount to be divided, in this case, 676) by the denominator (the number at the bottom which represents the number of parts to divide into, which is 52 for weeks in a year).

Understanding division is key to problem-solving, as it helps break down larger quantities into more manageable, smaller parts. It's a crucial skill not just in mathematics, but in making informed decisions in daily life.

Interpretation of Mathematical Results

Interpreting results in mathematics is just as important as solving the equations that lead to those results. This final step in the problem-solving process involves understanding what the number, ratio, or solution you've calculated actually means in the context of the problem at hand.

Returning to our example, once we've completed the division of 676 by 52, we get a result that tells us the average amount of junk mail a household receives each week. Understanding that this number is an 'average' is vital—it represents a typical value rather than an exact count for every single household. Recognizing the implications of an average helps in making sense of the data and applying the information properly.

Whenever you reach a solution in a mathematical problem, it's essential to step back and consider its real-world implications. Whether you're budgeting your finances or analyzing data, the ability to interpret mathematical results correctly leads to better decision-making and a deeper comprehension of the numbers in our lives.