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Chapter 10: Problem 91

Solve. What is \(45 \%\) of \(3800 ?\)

Short Answer

Expert verified
1710

Step by step solution

01

- Understand the Problem

The task asks for 45% of 3800. This means you need to find what 45% (or 0.45) of 3800 equals to.
02

- Convert Percentage to Decimal

Convert the percentage to a decimal by dividing by 100. So, 45% becomes 0.45.
03

- Set Up the Equation

Write the equation to find the value: \[ 0.45 \times 3800 \].
04

- Perform the Multiplication

Calculate the result of the equation: \[ 0.45 \times 3800 = 1710 \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Converting Percentages to Decimals
Understanding how to convert percentages to decimals is a key step in many math problems.
This task helps make our calculations simpler and more straightforward.
A percentage represents a part out of 100. So, to convert a percentage to a decimal, you simply divide by 100.

For example, to convert 45% to a decimal:
  • Start with the percentage: 45%
  • Divide 45 by 100: 45 梅 100 = 0.45

Now, 45% is represented as 0.45 in decimal form.
Remember, moving the decimal point two places to the left is essentially a division by 100. This small step makes multiplication easier.
Multiplication
Once you have converted the percentage to a decimal, the next step involves multiplication.
Multiplication is the process of scaling one number by another.

In our problem, we need to find what 45% of 3800 is.
First, we converted 45% to 0.45. Now we multiply this decimal by 3800.

The equation set up is:
\[ 0.45 \times 3800 \]

Next, multiply 0.45 by 3800.
This can be broken down into simpler steps if needed:
  • Multiply 0.45 by 8: 0.45 x 8 = 360
  • Multiply 0.45 by 3000: 0.45 x 3000 = 1350
  • Add the results: 1350 + 360 = 1710

This shows that 0.45 multiplied by 3800 equals 1710.
Hence, 45% of 3800 is 1710.
Problem-Solving Steps
Solving percentage problems can be easy if you follow a step-by-step approach.
Let's summarize the steps used in our example:

  • **Step 1**: Understand the Problem
    Identify that the problem is asking for a percentage of a number.
  • **Step 2**: Convert the Percentage to a Decimal
    Convert the given percentage to a decimal by dividing by 100.
  • **Step 3**: Set Up the Equation
    Multiply the decimal form of the percentage by the number in question.
  • **Step 4**: Perform the Multiplication
    Carry out the multiplication to find the answer.

Following these steps ensures that you approach the problem logically and accurately.
In our example, this method showed that 45% of 3800 is 1710, providing a clear solution.
This systematic approach can be applied to many percentage problems in math.

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