Problem 11 - Prealgebra

Question

Solve each of the following problems. What percent of 50 is \(5 ?\)

Step-by-Step Solution

Answer

5 is 10% of 50.

Step 1: Understand the Question

We need to find what percent of 50 is equal to 5. This means we are looking for a percentage that represents 5 as a portion of 50.

Step 2: Set Up the Equation

To find the percentage, we'll use the formula: \[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]Here, the 'Part' is 5 and the 'Whole' is 50.

Step 3: Substitute Values

Substitute the given values into the equation: \[ \text{Percentage} = \left( \frac{5}{50} \right) \times 100 \]

Step 4: Simplify the Fraction

Simplify the fraction \( \frac{5}{50} \). This can be reduced to \( \frac{1}{10} \) because both 5 and 50 are divisible by 5.

Step 5: Calculate the Percentage

Multiply the simplified fraction by 100 to find the percentage: \[ \frac{1}{10} \times 100 = 10 \]So, 5 is 10% of 50.

Key Concepts

Understanding Basic Math and Percentages

In basic math, a percentage is a way to express a number as a part of a whole. It is essentially a fraction with a denominator of 100. When we say "percent," we're referring to "per hundred." This concept allows us to compare parts of different wholes.

When you are determining a percentage of a number, you are simply figuring out how much of that number represents the entire whole when considered in terms of 100 parts.

• It's important to start by setting up the equation properly: \( \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \).
• This helps us find out what portion of the whole a given number is.

Percentages are a fundamental tool in math that helps to simplify and make sense of numbers in terms of their relationships to each other.

Fraction Simplification Fundamentals

Fraction simplification is an important skill in basic math. It involves reducing a fraction to its lowest terms. This means rewriting it in such a way that the numerator and the denominator are as small as possible while still maintaining the same value.

When simplifying a fraction, like \( \frac{5}{50} \), you first look for a common factor of the numerator and the denominator.

• In this case, both 5 and 50 are divisible by 5. Dividing both by 5, we get \( \frac{1}{10} \).
• Finding the greatest common divisor (GCD) is a useful method for simplifying.
• This process makes further calculations like converting to percentages easier.

The importance lies in making numbers more manageable and easier to compare.

Effective Math Problem Solving Techniques

Solving math problems, particularly those involving percentages, requires a clear understanding of the process. Here’s a step-by-step technique to approach such problems:

• **Understand the question:** Break down what is being asked. Determine which number represents the "Part" and what represents the "Whole." This step sets the foundation.
• **Set up your equation:** Use the percentage formula \( \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \). Knowing how to input values correctly into this equation is crucial.
• **Simplify where possible:** As fractions are commonplace in percentage problems, simplification can make the final calculations much simpler and reduce potential mistakes.
• **Perform and confirm calculations:** Execute your equation carefully, ensuring each step is followed, and verify your results.

Through understanding and practicing these steps, one can enhance their math problem-solving skills and handle percentage problems more efficiently.