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Chapter 7: Problem 19

Identify the amount, base, and \(p\) value. 50 hr is \(125 \%\) of 40 hr.

Short Answer

Expert verified
The amount is 50 hr, the base is 40 hr, and the percent is 125%.

Step by step solution

01

Identify the Base

The base is the original amount from which the percentage is calculated. In the given problem, the base is 40 hr.
02

Identify the Percent

The percent is the value that represents the fraction with respect to the base. Here, the percent is 125%.
03

Identify the Amount

The amount is the value that results from applying the percent to the base. In this case, the amount is 50 hr.
04

Check the Computation (Optional)

To verify, calculate 125% of 40 hr. Convert 125% to a decimal by dividing by 100, which yields 1.25. Then, multiply: - The above is erroneous.

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Key Concepts

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

Base Value
To understand percentage calculations, it is essential to grasp the concept of the 'Base Value'. This is the original amount or quantity on which you are calculating a percentage. For instance, in the problem '50 hr is 125% of 40 hr', the 'Base Value' is 40 hr. All the calculations will be built upon this number.

Whenever you encounter a percentage problem, identify the base value first. It acts as your reference point.
  • Base Value is the part you start with.
  • It is the denominator when converting to decimals or fractions.
Percent Value
Next, let鈥檚 talk about the 'Percent Value'. This number tells you what fraction of the base value you are dealing with. In our example, the percentage is 125%. This means we are working with 125% of 40 hours.

Percentages are essentially fractions. The percent value can be understood as out of every 100 parts of the base value.
  • 125% means 125 parts out of 100.
  • Always remember to convert percent to decimal for calculations.
Resulting Amount
The 'Resulting Amount' is what you get after applying the percent value to the base value. In our problem, when we apply 125% to 40 hours, we received 50 hours. This is our resulting amount.

To find the resulting amount:
  • First, convert the percent to decimal.
  • Then multiply the decimal by the base value.
Example Calculation:

Convert 125% to decimal:
125% 梅 100 = 1.25
Then, multiply the decimal by the base value:
1.25 脳 40 hr = 50 hr
This gives us our resulting amount, 50 hours.
Decimal Conversion
Understanding 'Decimal Conversion' is very important in percentage calculations. Since percentages are out of 100, converting to decimals makes computation easier.

To convert a percentage to a decimal, simply divide by 100:
  • For 125%, divide 125 by 100.
  • This converts 125% to 1.25 as a decimal.
This simple conversion allows you to perform multiplications directly instead of dealing with fractions.

Example:
125% of 40 hours
Convert to decimal:
125 梅 100 = 1.25
Then, multiply:
1.25 脳 40 hr = 50 hr

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Most popular questions from this chapter

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{5}{11}$$

Write the fraction in percent notation to the nearest tenth of a percent. $$\frac{8}{11}$$

Explain the difference between \(10 \%\) and \(0.10 \%\)

Convert the fraction to a percent. $$\frac{5}{8}$$

Solve the problem using a percent equation. What is \(18 \frac{1}{2} \%\) of \(3000 ?\)
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