Question

Using the information in the following table, estimate to the nearest hundred the total number of tickets sold at the movie theater last week. (Note: You may not use a calculator.) Movie Tickets Sold The Godmother 721 Moon Wars 391 The Silence of the Goats 813 A Clockwork Lemon 270 Pulp Fake News 602 (A) 2,600 (B) 2,800 (C) 3,000 (D) 3,100

Short answer

The estimated total number of tickets sold at the movie theater last week is approximately 2800 tickets. Hence, the correct choice is (B) 2800.

Step-by-step solution

Understand the Problem

This problem wants an estimate for the total number of tickets sold at a movie theater last week, which means the sum of the tickets sold for each movie. However, it should be done without the use of a calculator and the estimate should be rounded to the nearest hundred.

Round Each Movie's Ticket Count to the Nearest Hundred

Here we round off each movie's ticket count to the nearest hundred: The Godmother: 721 rounds off to 700 Moon Wars: 391 rounds off to 400 The Silence of the Goats: 813 rounds off to 800 A Clockwork Lemon: 270 rounds off to 300 Pulp Fake News: 602 rounds off to 600

Add the Rounded Numbers

Next, the problem is to add up all these values, which is much easier now since all of them are multiples of hundred: 700 + 400 + 800 + 300 + 600 = 2800

Compare the Result to the Given Options

Match the calculated value with the options that were given in the problem: 2600, 2800, 3000, 3100. The value we got from our calculations matches one of these options. So, the estimated total number of tickets sold at the movie theater last week is approximately 2800 tickets. Hence, the correct choice is (B) 2800.

Key concepts

Rounding Numbers

Rounding numbers is a simple yet powerful estimation technique that helps us simplify complex calculations. To 'round' a number means to adjust it to a nearby, simpler number, making mental arithmetic much easier. This is especially useful when exactness isn't necessary or when calculations must be done without a calculator.

The basic rule is to look at the digit to the right of the place you're rounding to. If this digit is 5 or higher, you round up. If it's less than 5, you round down. For example, in the given exercise, "The Godmother" sold 721 tickets. When rounding to the nearest hundred, you look at the tens digit, which is 2. Since 2 is less than 5, you round down to 700.

With practice, rounding becomes second nature, allowing you to group numbers quickly. This exercise demonstrates rounding to the nearest hundred, but the skill applies to any place value, such as the nearest ten, thousand, or even beyond. Developing precision in rounding is crucial for accurate estimation in everyday problem-solving.

Arithmetical Operations

Once you've rounded your numbers, the next step in estimation is to perform arithmetical operations. Basic operations include addition, subtraction, multiplication, and division. In this exercise, we focus on addition.

• Addition is straightforward when numbers are rounded, as it simplifies calculations significantly.
• For example, adding rounded numbers such as 700, 400, 800, 300, and 600 becomes easier since you are mostly working with the hundreds place.

Understanding these operations as building blocks helps develop your mental math skills. In times when a calculator isn't available, having confidence in these operations is vital for solving problems efficiently.

So, let's add the rounded numbers: 700 + 400 + 800 + 300 + 600 = 2800. The simplicity of the zeroes in these numbers makes mental addition swift and reliable. By practicing these methods, you can enhance your ability to compute quickly and accurately.

Problem-Solving Skills

Enhancing problem-solving skills involves more than just getting the right answer. It's about understanding the steps and why they matter. Estimation teaches valuable critical thinking skills and allows you to plan out your steps strategically.

• Identify what's being asked: In this problem, the task was to estimate the total number of tickets sold.
• Break down the steps: Rounding first makes the arithmetic manageable.
• Verify your solution: Compare your calculated estimate with the provided options to ensure your logic aligns.

Practicing problem-solving improves decision-making in academic tasks and real-world situations. A clear, thoughtful approach boosts confidence and precision. This exercise demonstrates the power of estimation and mental arithmetic, highlighting its applicability in various scenarios. Always remember, there's often more than one way to solve a problem, so be open to considering different approaches and solutions. This flexibility will only strengthen your overall problem-solving abilities.