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Chapter 6: Problem 149

Without solving the problem 鈥淲hat is 20% of 300?鈥� think about what the solution might be. Should it be a number that is greater than 300 or less than 300? Explain your reasoning.

Short Answer

Expert verified
It should be less than 300 because 20% is a fraction of 100%.

Step by step solution

01

Understand the Percentage

Recognize that a percentage represents a part of a whole. Here, 20% means 20 per 100.
02

Determine the Calculation

To find 20% of 300, we would normally multiply 300 by 0.2. This calculation helps determine what fraction of 300 is represented by 20%.
03

Estimate the Result

When calculating a percentage of a number, the result is always a fraction of the original number. Since 20% is a part of 100%, the result must be less than 300.
04

Confirm Reasoning

By understanding that 100% of 300 is 300, any percentage less than 100% (such as 20%) must be less than 300. Therefore, the number should be smaller than 300.

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Key Concepts

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

percentages
Percentages are a way of expressing a number as a fraction of 100. This is why percentage calculations often involve multiplying by 100 or converting to a decimal. For example, 20% means 20 out of every 100 parts. In mathematical terms, it is written as 20/100 or 0.2. When you see a percentage, you are looking at how many parts there are per 100. For instance, to find 20% of a number, we multiply the number by 0.2. It's essential to understand that a percentage is always a portion of a whole, so it cannot be larger than the original amount unless specified otherwise.
fractions
A fraction represents a part of a whole, consisting of a numerator and a denominator. In the context of percentages, the numerator is the percentage amount, and the denominator is 100. For example, 20% is equivalent to the fraction 20/100, which can be simplified to 1/5. Recognizing this relationship is crucial for quick mental math and understanding concepts in percentage calculations. Converting percentages to fractions and vice versa is a helpful skill. This conversion helps in understanding that 1/5 of 300 will give the same result as calculating 20% of 300, simplifying the mental process.
estimations
Estimations are useful tools for quickly and efficiently calculating approximations without needing precise solutions. When estimating percentages, one can easily determine an estimated range. For example, we can quickly approximate 20% of 300 by recognizing that 10% of 300 is 30. Since 20% is double 10%, we can double 30 to get 60. Thus, we estimate that 20% of 300 is around 60. Estimating helps confirm that the answer makes sense and should be less than the original number, providing a quick check without needing detailed calculations.

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Most popular questions from this chapter

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