Problem 49 - Algebra 1: Concepts and Skills

Question

Evaluate. $$ 11 \% \text { of } 50 $$

Step-by-Step Solution

Answer

11% of 50 is 5.5.

Step 1: Understand the problem

The problem is asking to find 11% of 50. In mathematics, the word 'of' usually means multiplication. So, we need to multiply 11% by 50.

Step 2: Convert the percentage to a decimal

Before multiplying, we need to remember to convert the percentage to a decimal. We do this by dividing the percentage by 100. So, 11% becomes \( \frac{11}{100} \) or 0.11.

Step 3: Multiply the decimal by the number

Now, multiply the decimal 0.11 by 50. \(0.11 * 50 = 5.5\).

Key Concepts

Basic Arithmetic Operations

Arithmetic operations are the cornerstone of mathematics and include addition, subtraction, multiplication, and division. Understanding these operations is essential for solving many mathematical problems, including those involving percentages. When the problem states to calculate 11% of 50, the operation actually involved is multiplication. In such expressions, the term 'of' indicates multiplication. In simpler terms, it implies that we need to multiply 50 by a part of it, which is 11%. For percentages, you'll end up multiplying two numbers: the whole (50) and the fraction or decimal that represents the percentage (0.11 in this case). It is important to always perform accurate multiplication, as small mistakes can lead to incorrect answers. Remember:

• "Of" means multiply in percentage problems.
• Convert all percentages to decimals before multiplying.

Decimal Conversion

Decimal conversion is a crucial step when dealing with percentages. Percentages are out of 100, so to convert any percentage into a decimal, you divide the number by 100.For example, to find 11% as a decimal, you calculate:\[\frac{11}{100} = 0.11\]This conversion is necessary for performing operations, like multiplication, that help you find the percentage of a given number. Be sure to practice converting percentages to decimals, as it's a common mathematical task.Simple Steps for Decimal Conversion:

• Identify the percentage you need to convert.
• Divide the percentage by 100.
• Use the decimal form in further calculations.

It's also good practice to check your decimal work, especially in problems involving small or non-round numbers, to ensure calculations are consistently accurate.

Problem Solving

Problem-solving is a skill that involves thinking critically and logically to find solutions. In mathematical contexts, it often follows a series of steps. To solve a problem like finding 11% of 50, follow these straightforward problem-solving steps:

• Understand the Problem: Recognize what the problem is asking. In this example, find 11% of 50.
• Perform Necessary Conversions: Convert 11% to 0.11 to facilitate easier multiplication.
• Execute Calculations: Perform the multiplication, i.e., 0.11 times 50, to get 5.5.
• Reflect on the Result: Does the result make sense? If finding a percentage, the answer should be a proportion of the whole.

Through practice, these problem-solving steps become more intuitive. Always take a moment to check if the steps and final answer logically fit the context of the problem.