Question

Which is greater: \(300 \%\) of \(8,\) or \(250 \%\) of \(10 ?\)

Short answer

250% of 10 is greater than 300% of 8.

Step-by-step solution

Understand the Problem

Identify what needs to be compared: 300% of 8 and 250% of 10.

Convert Percentages to Decimals

Convert 300% to a decimal by dividing by 100: 300% = \(\frac{300}{100} = 3.0\). Similarly, convert 250% to a decimal: 250% = \(\frac{250}{100} = 2.5\).

Calculate 300% of 8

Multiply the decimal form of 300% by 8: \(3.0 \times 8 = 24\).

Calculate 250% of 10

Multiply the decimal form of 250% by 10: \(2.5 \times 10 = 25\).

Compare the Results

Compare the two results: 24 and 25. Since 25 is greater than 24, 250% of 10 is greater than 300% of 8.

Key concepts

Converting Percentages to Decimals

When working with percentages, it's often necessary to convert them into decimals for easier calculations. This is done by dividing the percentage value by 100.
For example:

• To convert 300% into a decimal: \( \frac{300}{100} = 3.0 \).
• To convert 250% into a decimal: \( \frac{250}{100} = 2.5 \).

By doing so, we transform percentages into a form that can be used in various mathematical operations, such as multiplication. This conversion is a vital step in various mathematical problems, including the exercise above.

Multiplying Decimals

Once we have converted the percentages into decimals, the next step is to multiply the decimal by the given number.
For example:

• To find 300% of 8, multiply the decimal 3.0 by 8: \( 3.0 \times 8 = 24 \).
• To find 250% of 10, multiply the decimal 2.5 by 10: \( 2.5 \times 10 = 25 \).

The multiplication of decimals follows the same rules as the multiplication of whole numbers. The only difference is that you need to be careful with the placement of the decimal point in your answer.

Comparing Numerical Values

The final step in problem-solving often involves comparing numerical values. This is straightforward: you just need to determine which number is larger or smaller.
For example, comparing 24 and 25

• 24 is less than 25.

Thus, in the exercise above, 250% of 10 (which is 25) is greater than 300% of 8 (which is 24). Comparisons like this are common in real-world scenarios and math problems alike.