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Chapter 7: Problem 47

Solve the problem using a percent equation. What is \(45 \%\) of \(62 ?\)

Short Answer

Expert verified
27.9

Step by step solution

01

- Understand the Percent Equation

The percent equation is given by: \[ \text{Part} = \text{Percent} \times \text{Whole} \]. Here, the percent is 45%, and the whole is 62. We need to find the part.
02

- Convert Percent to Decimal

Convert the percent (45%) into a decimal by dividing by 100. So, \[ 45\text{\text%} = \frac{45}{100} = 0.45 \].
03

- Substitute the Values

Substitute the decimal value and the whole number into the percent equation: \[ \text{Part} = 0.45 \times 62 \].
04

- Calculate the Part

Perform the multiplication: \[ 0.45 \times 62 = 27.9 \]. So, 45% of 62 is 27.9.

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Key Concepts

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

percentage calculations
Percentage calculations are essential for determining portions of a whole. They involve converting percentages to decimals and then using these values in calculations. To find a specific percentage of any number, we use the percent equation:
  • First, identify the percentage and the whole number.
  • Convert the percentage to a decimal.
  • Multiply the decimal by the whole number.
For example, if you want to find what 45% of 62 is, you start by understanding that the percent equation is \[ \text{Part} = \text{Percent} \times \text{Whole} \]. Here, the 'part' is the portion you鈥檙e trying to find, which is 45% of 62.
Converting percentages to decimals makes these calculations straightforward. Once the conversion is done, multiplying the decimal by the whole number gives you the answer.
decimal conversion
Decimal conversion is a crucial step in percentage calculations. Percentages represent parts per hundred, but working with decimals is easier. To convert a percentage to a decimal:
  • Divide the percentage by 100.
This shifts the decimal point two places to the left. For example, converting 45% to a decimal involves dividing 45 by 100, which gives us 0.45.
Here are a few more examples:
  • 50% becomes 0.50 after dividing by 100.
  • 25% turns into 0.25.
  • 10% converts to 0.10.
Once the conversion is done, you can easily multiply this decimal with the whole number to find the desired value.
multiplication operations
After converting the percentage to a decimal, the next step in solving percentage problems is the multiplication operation. Multiplying decimals by whole numbers can be done by:
  • Aligning the decimal point properly.
  • Multiplying as if they are whole numbers.
  • Placing the decimal point in the final answer.
For example, to determine what 45% of 62 is, you'll first convert 45% to 0.45. Then, multiply 0.45 by 62:
\[0.45 \times 62 = 27.9\].
Breaking it down:
  • Multiply 45 by 62 (ignoring the decimal for now).
  • Get the result, which is 2790.
  • Since 0.45 has two decimal places, place the decimal point two places from the right, resulting in 27.9.
This shows step-by-step how multiplication helps in calculating percentages effectively.

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