Problem 70 - Elementary Algebra

Question

About \(8.2\) million Americans own recreational vehicles (RVs). Find the number of RV owners who plan to purchase another RV. Round to the nearest tenth of a million. Two-thirds of current owners plan to purchase another RV. Among all U.S. households, nearly one quarter (23 percent) intend to purchase an RV in the future. (Source: www.rvia -org, Feb. 19, 2009)

Step-by-Step Solution

Answer

5.5 million RV owners plan to purchase another RV.

Step 1: Identify the given values

The problem states that there are currently 8.2 million American RV owners, and two-thirds of them plan to purchase another RV.

Step 2: Calculate the number of RV owners planning to purchase another RV

To find the number of RV owners planning to purchase another RV, multiply the total number of RV owners by two-thirds.\[ \text{Number of RV owners planning to purchase another RV} = 8.2 \text{ million} \times \frac{2}{3} \]

Step 3: Compute the multiplication

Perform the multiplication.\[ 8.2 \times \frac{2}{3} = \frac{16.4}{3} \ \frac{16.4}{3} \rightarrow 5.4666667 \text{ million} \]

Step 4: Round to the nearest tenth of a million

Round the result to the nearest tenth of a million.\[ 5.4666667 \text{ million} \rightarrow 5.5 \text{ million} \]

Key Concepts

Rounding Numbers

Rounding is an essential math skill that simplifies numbers to make them easier to work with. Here's a quick guide to rounding numbers to the nearest tenth:
Identify the digit in the place you are rounding to. For example, in the number 5.4666667, the digit in the tenths place is 4.
Look at the digit immediately to the right of the target digit. This is often called the 'next digit.' In our example, it's 6.
If the next digit is 5 or greater, round up. If it is 4 or less, round down. Given that the next digit is 6, we round 5.4666667 up to 5.5.
Rounding makes calculations easier and results more readable. When dealing with real-life situations, rounding helps in making decisions quickly without complex math.

Multiplication of Fractions

Multiplying fractions is straightforward yet important. Follow these steps to multiply fractions seamlessly:
Multiply the numerators (the top numbers) together. In our example, multiplying 8.2 by 2 gives us 16.4.
Multiply the denominators (the bottom numbers) together. Here, you simply have 1 multiplied by 3, giving you 3.
Your intermediate result will be a fraction. For example, \( \frac{16.4}{3} \).
Finally, divide the numerator by the denominator to get the result as a decimal or a whole number. Performing \( \frac{16.4}{3} = 5.4666667 \).
Multiplying fractions becomes even easier if you first simplify the fractions, but in this case, that's not necessary.

Basic Arithmetic Operations

Understanding basic arithmetic operations is vital. Here is how multiplication works:
Multiplication is a faster way of adding multiple groups of the same size. For example, 2 \times 3 is the same as adding 2 three times (2 + 2 + 2).
It's commutative, meaning that changing the order of the numbers does not change the result; 3 \times 2 is the same as 2 \times 3.
When multiplying a whole number by a fraction, treat the whole number as a fraction with a denominator of 1. For instance, 8.2 can be written as \frac{8.2}{1}\, so the operation is \( \frac{8.2}{1} \times \frac{2}{3} \).
Apply the multiplication rule: Multiply the numerators and multiply the denominators. In our case, 8.2 \times 2 gives 16.4; 1 \times 3 gives 3. Hence, you get \frac{16.4}{3}\.
The final calculation step usually involves some addition, subtraction, or division. Basic arithmetic is the foundation of all math, so mastering these operations is crucial for more complex problem-solving.