Problem 26 - Elementary Algebra Within Reach

Question

Solve the percent equation. What number is \(60 \%\) of 820 ?

Step-by-Step Solution

Answer

492 is the number that is 60% of 820.

Step 1: Convert Percentage to Decimal

To convert the percentage to a decimal, divide it by 100. Therefore, \(60 \%\) becomes \(0.60\) when expressed as a decimal.

Step 2: Multiply by the Number Provided

Next, multiply the decimal value by the number provided in the problem, which is 820. The calculation is as follows: \(0.60 * 820 = 492\).

Step 3: Interpret the Result

The result obtained from the multiplication represents the number that is 60% of 820, which is 492. In other words, 492 is 60% of 820.

Key Concepts

Percentage to Decimal Conversion

Understanding how to convert percentages to decimals is crucial when solving percent equations. The process is rather straightforward. A percentage is essentially a number out of 100. So to convert a percentage to a decimal, you simply divide the percentage by 100.

For example, to convert 60% to a decimal, you divide 60 by 100, which gives you (0.60). This step is the foundation for solving many problems involving percentages as it prepares the number for further arithmetic operations, like multiplication or division.

Here are some tips to remember when converting percentages to decimals:

• Shift the decimal point two places to the left to divide by 100 (e.g., 75% becomes 0.75).
• If there is no decimal point visible in the percentage, it is assumed to be on the right side of the last digit (e.g., 7% is treated as 7.0%, which converts to 0.07).
• Practicing with different percentages will help solidify your understanding of converting to decimals.

Multiplication with Decimals

Once you've converted the percentage into a decimal, the next step is to multiply it by the number in question to find the desired portion. Multiplication with decimals is just like multiplication with whole numbers but requires an extra step of placing the decimal point in the answer.

For instance, if you have the decimal 0.60 and you want to find what that represents of 820, you multiply 0.60 by 820. Align the numbers without regard to the decimal point and multiply as usual. Afterward, count the number of digits to the right of the decimal in the factors, and place the decimal point in the product so that it has the same number of decimal places.

A helpful tip for multiplying with decimals:

• Use a calculator for multiplying longer decimal numbers to avoid errors in placing the decimal point.

Interpreting Percentages

Interpreting the result of a percentage problem allows us to understand what the calculation actually means in context. After calculating that 60% of 820 equals 492, it's important to grasp what this signifies. In this case, it means that if you have 820 items, and you need to find 60% of these, you would have 492 items.

The skill of interpreting percentages extends to various aspects of daily life, from calculating discounts on products to understanding statistical data presented in percentages. A percentage is a way to express a ratio, a fraction, or a comparison between two numbers.

Remember when interpreting percentages:

• Percentages can be translated into fractions, decimals, and even visual representations like pie charts to better understand the division of a whole.
• Always consider the real-world context of the percentage to give the correct meaning to the number.