Problem 2 - Intermediate Algebra

Question

Fill in the blanks. In the statement, " 10 is \(20 \%\) of 50 ," 10 is the _____ and 50 is the _____.

Step-by-Step Solution

Answer

10 is the part, and 50 is the whole.

Step 1: Understanding the Statement

The statement "10 is 20% of 50" needs to be broken down. Here, 10 is specified as a part of 50; hence, understanding what 20% of 50 means is crucial.

Step 2: Identify the Percentage Relationship

Recognize that '20%' means 20 parts out of 100. Therefore, if 50 is the entire value, then 20% of 50 results in 10 (because 20% of 50 is 10). This calculation confirms that 10 is the specific part of the total, which is given as 50.

Step 3: Define '10' in Terms of Mathematical Terms

In the context of percentages, '10' is referred to as the **part** of the whole, while 50 is the total or the **whole**.

Step 4: Define '50' in Terms of Mathematical Terms

In percentage terminology, '50' represents the **whole** or the **base**, which is the total from which the percentage is taken to get '10'.

Key Concepts

Percentage Calculation

Percentage calculation is a method of finding a part of a whole in terms of hundreds. It's a way of expressing a number as a fraction of 100. This is an extremely useful mathematical tool used to understand and communicate proportions and comparisons.

To calculate a percentage, follow these simple steps:

• Convert the percentage to a decimal by dividing by 100 (e.g., 20% becomes 0.2).
• Multiply the total amount (the whole) by the decimal (e.g., 0.2 multiplied by 50 equals 10).

This process helps you find what part of the whole you are dealing with. So, in the original exercise, 10 is 20% of 50, because multiplying 50 with 0.2 gives you 10.

Understanding how to perform percentage calculations simplifies many real-world problems, such as calculating discounts, understanding statistics, or analyzing data.

Part-Whole Relationship

The part-whole relationship is a fundamental concept in percentage problems. It describes how a part is related to its whole in percentage terms. Here, the 'part' is a piece or segment of the 'whole,' and understanding this structure is key.

In our exercise example, the number 10 represents the 'part' of the whole (50). The 'whole' or 'total' is the figure from which the percentage is derived. By observing the statement "10 is 20% of 50," we can clearly identify the roles of these numbers:

• Part: The specific value that is a portion of the overall total (10 in this context).
• Whole: The complete value or base from which a percentage is calculated (50 in this context).

Recognizing the part-whole relationship helps clarify the percentage and provides a clearer understanding of the context in which these calculations operate.

Mathematical Terminology in Percentages

Understanding the specific mathematical terminology associated with percentages is crucial for solving percentage problems. Knowing these terms aids in accurately analyzing and interpreting percentage-based questions.

Here are a few key terms in the context of our exercise:

• Percentage: The rate or proportion per hundred. It's what tells us how the part relates to the whole (20% in the exercise).
• Part: Often known as the "amount," it's a segment of the whole, calculated using the percentage (10 in the exercise).
• Whole/Base: The original or entire amount that the percentage is taken from (50 in the exercise). It also can be referred to as the total.

Using these terms properly helps bolster your understanding of the situation. It ensures clarity when dealing with percentages and avoids confusion, making mathematical discussions and calculations much smoother.