Problem 26 - Algebra 1: Concepts and Skills

Question

Solve the percent problem. (Lesson 3.9) How much is \(15 \%\) of 15 dollars?

Step-by-Step Solution

Answer

15% of 15 dollars is $2.25

Step 1: Understand the problem

The question requires finding 15% of 15 dollars. This means you need to calculate the amount of money that constitutes 15% of 15 dollars.

Step 2: Convert the percentage to a decimal

Percentages can be converted to decimals by dividing by 100. So, 15% becomes \(0.15\) when it's divided by 100.

Step 3: Multiply the decimal by the total

Now that we've converted the percentage to a decimal, we'll multiply this decimal by the total amount (in this case, 15 dollars). So, \(0.15 * 15 = 2.25\) dollars.

Key Concepts

Converting Percentages to Decimals

To understand how to work with percentages in various mathematical problems, it's essential to learn how to convert them into decimals. This transformation simplifies many operations since decimals are much easier to work with in calculations. For example, to convert a percentage to a decimal, divide the percentage by 100. This is because the term 'percent' literally means 'per hundred'.
So, if you have 15%, you perform the division 15 ÷ 100, which gives you 0.15. This conversion is the foundational step before any further operations involving percentages, such as finding out what 15% of 15 dollars is. The conversion simplifies the problem, allowing you to multiply the decimal directly by the quantity in question.

Percentages in Algebra

When dealing with algebraic expressions that include percentages, it’s important to recognize that percentages represent a part of a whole. In algebra, percentages are frequently variables themselves or are used to modify other variables. For instance, saying that 'a is 15% of b' translates algebraically to the equation \( a = 0.15 \times b \).
When you have to solve for either variable, converting the percentage to a decimal is crucial, as it allows you to manipulate the equation more easily. This holds true whether you are solving for a specific number, as in the example of 15% of 15 dollars, or working with abstract algebraic expressions.

Basic Arithmetic Operations

At the core of many mathematical problems, including those involving percentages, are the four basic arithmetic operations: addition, subtraction, multiplication, and division. These operations are used in a vast range of scenarios from simple calculations to complex algebraic equations.

• Addition is the process of combining two or more quantities.
• Subtraction is finding the difference between two quantities.
• Multiplication, often used when dealing with percentages as decimals, involves finding the total of one quantity taken multiple times.
• Division is the process of distributing a quantity into equal parts.

It's important to have a firm grasp of these operations as they are not only fundamental in arithmetic but also the building blocks of algebra. In the case of the exercise, multiplication was used to combine the decimal form of the percentage (0.15) with the quantity (15 dollars) in order to find the part of the whole, which is 2.25 dollars.