Problem 13 - Calculate With Confidence

Question

100 is what percentage of 750? ___________________________

Step-by-Step Solution

Answer

100 is 13.33% of 750.

Step 1: Understand the Problem

We need to find the percentage that 100 represents out of 750. This involves determining how much of the whole (750) is made up by the part (100).

Step 2: Set Up the Percentage Formula

Use the percentage formula: \( \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \). Here, the part is 100, and the whole is 750.

Step 3: Substitute Values into the Formula

Substitute 100 for the part and 750 for the whole into the formula: \( \text{Percentage} = \left( \frac{100}{750} \right) \times 100 \).

Step 4: Divide the Part by the Whole

Calculate \( \frac{100}{750} \) which simplifies to \( \frac{2}{15} \) or approximately 0.1333.

Step 5: Convert to a Percentage

Multiply 0.1333 by 100 to convert it to a percentage: \( 0.1333 \times 100 = 13.33\).

Key Concepts

Understanding the Percentage Formula

One of the fundamental concepts in percentage calculation involves using the percentage formula. This formula is a helpful tool in mathematics to determine what fraction or portion a part is of a whole, expressed as a percent. The percentage formula is:\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]This formula allows us to calculate the portion of the whole that the part represents, and then multiply by 100 to convert this fraction into a percentage. It's commonly used in various fields such as finance, statistics, and even in everyday calculations. To apply this formula effectively, ensure you clearly identify the 'part' and 'whole' from the context of the problem.

Exploring the Part-Whole Relationship

To calculate percentages accurately, understanding the part-whole relationship is crucial. This relationship involves identifying how much of a 'whole' a 'part' constitutes. In the exercise given, 100 is considered the 'part', while 750 is the 'whole'. When pondering the part-whole relationship, consider it this way:

• The 'whole' is the total amount or 100%, in this case 750.
• The 'part' is a section or proportion of this whole, namely, 100 in this exercise.

By mastering this concept, you'll be able to apply it in various problems where it’s necessary to ascertain the proportion of a whole that a part represents, expressed as a percentage.

Employing a Step-by-step Solution

Breaking down a problem into manageable steps provides clarity and helps avoid confusion, especially when dealing with percentage calculations. Here’s a quick overview of how the step-by-step solution helps in understanding the exercise:

• Step 1: Know the Problem
  Determine which numbers represent the part and the whole. In our exercise, we've identified 100 as the part and 750 as the whole.
• Step 2: Apply the Formula
  Using the percentage formula, you substitute the values to set up your equation.
• Step 3: Calculate the Fraction
  Divide the part by the whole, \( \frac{100}{750} \), to find the fraction of the total.
• Step 4: Convert into a Percentage
  Multiply the result by 100 to change the decimal to a percentage. Keep computation results clear and precise.

By systematically following these steps, one can solve percentage problems efficiently, simplifying the process with organized calculations.