Problem 18 - Algebra 1

Question

Solve the percent problem. How much money is \(35 \%\) of \(\$ 750 ?\)

Step-by-Step Solution

Answer

35% of $750 is $262.50.

Step 1: Understand the Question

The question is asking to find out what 35 percent of $750 is, in dollar terms. This can be solved by multiplication.

Step 2: Convert the Percentage into Decimal

To perform the calculation, the percentage needs to be converted into a decimal. The conversion process includes dividing the percentage by 100. So, 35% in decimal form is \( \frac{35}{100} = 0.35 \).

Step 3: Calculate the Amount

Having converted the percentage to a decimal, next, multiply it with the given amount to find the required quantity. So, \(0.35 \times \$750 = \$262.50\)

Key Concepts

Converting Percentages

Converting a percentage into a decimal is a straightforward process, yet it's crucial for solving many math problems efficiently. When you see a percentage like 35%, think of it as a part of a whole, where the whole is 100%.
To convert a percentage into a decimal, simply divide by 100 because "percent" literally means "per hundred."
For example:

• 35% becomes \( \frac{35}{100} \). When you perform the division, 35 divided by 100 is 0.35.

When you're comfortable with this concept, you can solve percentage problems with ease. It's like converting miles to kilometers, and the understanding will help you make quick mental calculations in everyday life!

Decimal Conversion

Decimal conversion is a fundamental skill in math, especially when dealing with percentages. The conversion helps you to manipulate numbers more easily in equations. Once a percentage is converted to its decimal form, it becomes simple to use in different mathematical operations.

Here's how the process looks:

• Take your percentage number and treat it as an integer (e.g., 35 for 35%).
• Divide that number by 100 to shift it two places to the left on the decimal scale, resulting in 0.35 for 35%.

This decimal form allows you to perform multiplications, divisions, and other operations in algebraic expressions. It's a universal method you can apply regardless of the percentage you're working with.

Multiplication in Algebra

Multiplication in algebra often involves dealing with numbers and variables, but when it comes to percentages, much of the work involves dealing with numbers alone. Once you have a percentage converted into decimal form, the multiplication process begins.

To find out what portion of a number a certain percentage is, multiply the decimal fraction (from your converted percentage) with the total amount you're investigating.

• For instance, with a percentage of 35% converted to a decimal, you multiply 0.35 by the desired amount, such as \(750.
• This equation, \(0.35 \times 750 = 262.50\), gives you the dollar amount that represents 35% of \)750.

Understanding multiplication in this context is about seeing how one value scales relative to another. This skill enhances both your math fluency and problem-solving abilities across various scenarios that involve percentages.