Question

Perform the indicated operations. \(40 \%\) of 140 ______

Short answer

40% of 140 is 56.

Step-by-step solution

Understand the Problem

We need to find 40% of 140. This involves calculating the percentage of a given number.

Convert Percentage to a Decimal

To find a percentage of a number, convert the percentage to a decimal by dividing by 100. So, 40% becomes 0.4.

Multiply the Decimal by the Number

Now multiply the decimal by the number you are finding the percentage of. So, multiply 0.4 by 140: \(0.4 \times 140\) = 56.

State the Result

After performing the multiplication, we find that 40% of 140 is 56.

Key concepts

Mathematical Operations

Let's dive into the world of mathematical operations to tackle percentage problems effectively. Calculating a percentage of a number is a multi-step process that involves a clear understanding of basic math operations such as division and multiplication.
When you're asked to perform operations like finding a percentage, you're essentially executing a series of integer arithmetic steps. We'll break it down:

• First, identify the percentage you are dealing with, like 40% in our given problem.
• Then, determine the whole number from which you're calculating the percentage, which is 140 in this case.

By understanding these components, you can see how each operation combines to solve the problem at hand.
These are the fundamental elements that set the stage for further calculations.

Decimal Conversion

Before you can multiply a percentage, it's important to convert it from a percentage into a decimal form. This transformation is quite straightforward. You do this by simply dividing the percentage by 100.
For example, with 40%, you calculate \[40\% = \frac{40}{100} = 0.4\]This conversion turns a percentage into a number form that is easy to use in mathematical calculations. This step is crucial because working with decimals allows for seamless multiplication with any whole number.
Ultimately, decimal conversion helps in representing the percentage as an actual part of a whole, which leads into the multiplication phase.

Multiplication Process

The multiplication process is the heart of solving percentage problems, where the converted decimal is used to find the desired percentage of a number. After converting 40% to 0.4, as in our example, you undertake the straightforward multiplication:
\[0.4 \times 140 = 56\]Here, you're essentially finding what 40 hundredths of 140 amounts to. Performing this step requires a clear understanding of how multiplication operates at a fundamental level.

• Line up your numbers carefully, ensuring decimal places are addressed correctly.
• Multiply as you would with whole numbers.
• Count the total decimal places in the numbers being multiplied to correctly position the decimal in your answer.

Practicing this step allows you to quickly and accurately find percentages of various numbers.

Educational Mathematics

Educational mathematics is designed to help students connect theory with practice. Topics like percentage calculation are foundational because they appear frequently in everyday scenarios and advanced math alike.
The importance of understanding how to calculate percentages prepares students for practical tasks, such as budgeting or data analysis, where these calculations are essential.
Therefore, educational mathematics emphasizes not just performing these calculations but understanding their application and significance.

• Incorporates real-world problems to solidify the conceptual comprehension.
• Focuses on promoting numerical literacy that applies beyond academic settings.

By engaging with these mathematical concepts, students gain confidence and competence that extends to future academic pursuits and everyday use.