Question

Translate to an equation and solve. What number is \(3.5 \%\) of \(24,500 ?\)

Short answer

Answer: 857.5

Step-by-step solution

Convert percentage to decimal

To convert 3.5% to a decimal, divide the percentage by 100. In this case, it would be: \( \frac{3.5}{100} = 0.035 \)

Multiply the decimal by the given number

Now, to find out the number which is 3.5% of 24,500, we multiply the decimal (0.035) by the given number (24,500). \( 0.035 \times 24,500 = 857.5 \) So, 3.5% of 24,500 is 857.5.

Key concepts

Converting Percentages to Decimals

Understanding how to convert percentages to decimals is a fundamental skill in mathematics that is often used in real-life situations. To convert a percentage to a decimal, one simply divides the percentage value by 100. This is because the term 'percent' means 'per hundred'. So, when we talk about '3.5%', we are actually saying '3.5 per 100' or '3.5 out of 100'.

To illustrate, let's take the number 3.5% as an example. Dividing 3.5 by 100 can be done as follows:
\[\frac{3.5}{100} = 0.035\]
This resulting decimal, 0.035, is equivalent to the original percentage and can now be used in various arithmetic operations, such as finding a certain percentage of a given number as seen in our problem.

Basic Algebra

Basic algebra introduces the concept of using symbols, often letters like 'x' or 'y', to represent unknown numbers. It provides the tools for writing and solving equations, which is a crucial skill in not just mathematics, but also in various fields like economics, engineering, and physics. In the context of solving percentage word problems, basic algebra allows us to set up the equation to find an unknown value.

For example, if we want to find what number corresponds to 3.5% of 24,500, we can let 'x' be the unknown number we are looking for. Then our algebraic equation based on the percentage formula becomes\[x = 0.035 \times 24,500\].
By solving this equation, we find the value of 'x' that satisfies the equation. Here, basic algebra involves the operation of multiplication to find the product.

Arithmetic Operations

Arithmetic operations involve the basic building blocks of mathematics: addition, subtraction, multiplication, and division. These are operations we use in everyday calculations to manage finances, measure ingredients for cooking, and determine durations for travel, among other things.

In percentage word problems, after converting the percentage to decimal, multiplication is the key operation. When we ask 'What number is 3.5% of 24,500?', we perform a multiplication:\[0.035 \times 24,500 = 857.5\].
The number 857.5 is the product of the multiplication, and this represents 3.5% of 24,500. Being confident in arithmetic operations allows one to accurately solve such real-world problems.