Problem 49 - Basic College Mathematics

Question

The United States Postal Service estimates that \(\frac{4}{25}\) of the addresses on a mailing list will change in one year. A business has a mailing list of 3000 people. After one year, how many addresses on that list will be incorrect?

Step-by-Step Solution

Answer

480 addresses will be incorrect.

Step 1 - Determine the Fraction of Incorrect Addresses

Identify the fraction of addresses that will change in one year. In this case, it is given as \(\frac{4}{25}\).

Step 2 - Convert the Fraction to a Decimal

Convert \(\frac{4}{25}\) to a decimal by dividing 4 by 25. This results in \(0.16\).

Step 3 - Calculate the Number of Incorrect Addresses

Multiply the total number of addresses (3000) by the decimal \(0.16\) to find the number of addresses that will be incorrect. \(3000 \times 0.16 = 480\).

Key Concepts

Fraction to Decimal Conversion

Converting a fraction to a decimal is a common step in many math problems. It helps to simplify or change the form of the number for easier calculations.
To convert a fraction like \(\frac{4}{25}\), divide the numerator (top number) by the denominator (bottom number).
For \(\frac{4}{25}\):
Numerator: 4
Denominator: 25
Division: 4 ÷ 25 = 0.16
This means \(\frac{4}{25} = 0.16\) as a decimal.

This decimal conversion helps in situations where you need to perform further calculations, like in the exercise.

Percentage of Total Calculation

To find the percentage of a total, you can use either fractions, decimals, or percentages.
In the given exercise, the decimal form of \(\frac{4}{25}\) is used to find the number of incorrect addresses.

Remember, calculations using percentages are quite useful in real-life.
Step-by-step:

• First, convert the fraction to a decimal (0.16 in this case).
• Next, multiply the decimal by the total number to find the part. Here, multiplying the decimal representation (0.16) by the total number of addresses (3000) gives the part that will change.
• Performing the multiplication: 0.16 x 3000 = 480

Hence, 480 addresses will be incorrect after one year.

Basic Arithmetic Operations

Basic arithmetic operations are foundational. They include addition, subtraction, multiplication, and division.
In our problem, we specifically focus on multiplication and division.

• Division: Converting a fraction to decimal involves division. For \(\frac{4}{25}\), you divide 4 by 25.
• Multiplication: After converting to decimal, we multiply. Here, 0.16 is multiplied by the total number of addresses, 3000.

These operations help solve many real-world problems, like in the mailing list exercise.

Understanding and practicing these basic operations solidifies your math foundation, making more complex calculations easier.